{"topic":"quantum-error-correction","sort":"top","limit":25,"offset":0,"count":25,"papers":[{"id":"arxiv:2312.03982","kind":"article","title":"Logical quantum processor based on reconfigurable atom arrays","authors":["Dolev Bluvstein","Simon J. Evered","Alexandra A. Geim","Sophie H. Li","Hengyun Zhou","Tom Manovitz","Sepehr Ebadi","Madelyn Cain","Marcin Kalinowski","Dominik Hangleiter","J. Pablo Bonilla Ataides","Nishad Maskara","Iris Cong","Xun Gao","Pedro Sales Rodriguez","Thomas Karolyshyn","Giulia Semeghini","Michael J. Gullans","Markus Greiner","Vladan Vuletić","Mikhail D. Lukin"],"author_count":21,"year":2023,"published":"2023-12-06","venue":"Nature","cited_by":1118,"doi":"10.1038/s41586-023-06927-3","arxiv_id":"2312.03982","nct_id":null,"source_url":"https://doi.org/10.1038/s41586-023-06927-3","archive_url":"https://space-kitty.com/papers/arxiv:2312.03982","updated":"2023-12-07","pmid":"38056497","pmcid":null,"openalex_id":"W4389373471","pdf_url":"https://arxiv.org/pdf/2312.03982","abstract":"Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Utilizing logical-level control and a zoned architecture in reconfigurable neutral atom arrays, our system combines high two-qubit gate fidelities, arbitrary connectivity, as well as fully programmable single-qubit rotations and mid-circuit readout. Operating this logical processor with various types of encodings, we demonstrate improvement of a two-qubit logic gate by scaling surface code distance from d=3 to d=7, preparation of color code qubits with break-even fidelities, fault-tolerant creation of logical GHZ states and feedforward entanglement teleportation, as well as operation of 40 color code qubits. Finally, using three-dimensional [[8,3,2]] code blocks, we realize computationally complex sampling circuits with up to 48 logical qubits entangled with hypercube connectivity with 228 logical two-qubit gates and 48 logical CCZ gates. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling. These results herald the advent of early error-corrected quantum computation and chart a path toward large-scale logical processors.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2207.06431","kind":"article","title":"Suppressing quantum errors by scaling a surface code logical qubit","authors":["Google Quantum AI","Rajeev Acharya","I. L. Aleǐner","R. M. Allen","Trond I. Andersen","M. Ansmann","Frank Arute","Kunal Arya","Abraham T. Asfaw","Juan Atalaya","Ryan Babbush","Dave Bacon","Joseph C. Bardin","Joao Basso","Andreas Bengtsson","Sergio Boixo","Gina Bortoli","Alexandre Bourassa","Jenna Bovaird","Leon Brill","Michael Broughton","Bob B. Buckley","David A. Buell","Tim Burger","Brian Burkett"],"author_count":100,"year":2023,"published":"2023-02-22","venue":"Nature","cited_by":1102,"doi":"10.1038/s41586-022-05434-1","arxiv_id":"2207.06431","nct_id":null,"source_url":"https://doi.org/10.1038/s41586-022-05434-1","archive_url":"https://space-kitty.com/papers/arxiv:2207.06431","updated":"2022-07-20","pmid":"36813892","pmcid":null,"openalex_id":"W4321610982","pdf_url":"https://www.nature.com/articles/s41586-022-05434-1.pdf","abstract":"Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle ($2.914\\%\\pm 0.016\\%$ compared to $3.028\\%\\pm 0.023\\%$). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a $1.7\\times10^{-6}$ logical error per round floor set by a single high-energy event ($1.6\\times10^{-7}$ when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1402.4848","kind":"article","title":"Superconducting quantum circuits at the surface code threshold for fault tolerance","authors":["R. Barends","J. Kelly","A. Megrant","Andrzej Veitia","D. Sank","Evan R. Jeffrey","T. White","J. Mutus","Austin G. Fowler","B. Campbell","Yanbin Chen","Z. Chen","B. Chiaro","A. Dunsworth","C. Neill","P. J. J. O’Malley","P. Roushan","A. Vainsencher","J. Wenner","Alexander N. Korotkov","Andrew N. Cleland","John M. Martinis"],"author_count":22,"year":2014,"published":"2014-04-01","venue":"Nature","cited_by":1741,"doi":"10.1038/nature13171","arxiv_id":"1402.4848","nct_id":null,"source_url":"https://doi.org/10.1038/nature13171","archive_url":"https://space-kitty.com/papers/arxiv:1402.4848","updated":"2014-02-19","pmid":"24759412","pmcid":null,"openalex_id":"W1968850365","pdf_url":"https://arxiv.org/pdf/1402.4848","abstract":"A quantum computer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%. Here, we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantum computing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger (GHZ) state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["Quantum Information and Cryptography"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2408.13687","kind":"article","title":"Quantum error correction below the surface code threshold","authors":["Rajeev Acharya","Laleh Aghababaie-Beni","Igor Aleiner","Trond I. Andersen","Markus Ansmann","Frank Arute","Kunal Arya","Abraham Asfaw","Nikita Astrakhantsev","Juan Atalaya","Ryan Babbush","Dave Bacon","Brian Ballard","Joseph C. Bardin","Johannes Bausch","Andreas Bengtsson","Alexander Bilmes","Sam Blackwell","Sergio Boixo","Gina Bortoli","Alexandre Bourassa","Jenna Bovaird","Leon Brill","Michael Broughton","David A. Browne"],"author_count":249,"year":2024,"published":"2024-08-24","venue":"Nature 638 (2025) 920-926","cited_by":774,"doi":"10.1038/s41586-024-08449-y","arxiv_id":"2408.13687","nct_id":null,"source_url":"https://arxiv.org/abs/2408.13687","archive_url":"https://space-kitty.com/papers/arxiv:2408.13687","updated":"2024-08-24","pmid":"39653125","pmcid":null,"openalex_id":"W4405183524","pdf_url":"https://arxiv.org/pdf/2408.13687","abstract":"Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $Λ$ = 2.14 $\\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $μ$s at distance-5 up to a million cycles, with a cycle time of 1.1 $μ$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by-nc-nd","is_open_access":true,"peer_reviewed":null,"categories":["quant-ph"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1905.09749","kind":"article","title":"How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits","authors":["Craig Gidney","Martin Ekerå"],"author_count":2,"year":2021,"published":"2021-04-15","venue":"Quantum","cited_by":829,"doi":"10.22331/q-2021-04-15-433","arxiv_id":"1905.09749","nct_id":null,"source_url":"https://doi.org/10.22331/q-2021-04-15-433","archive_url":"https://space-kitty.com/papers/arxiv:1905.09749","updated":"2021-04-13","pmid":null,"pmcid":null,"openalex_id":"W2946582523","pdf_url":"https://quantum-journal.org/papers/q-2021-04-15-433/pdf/","abstract":"We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Ekerå-Håstad 2017, Ekerå 2017, Ekerå 2018, Gidney-Fowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible physical assumptions for large-scale superconducting qubit platforms: a planar grid of qubits with nearest-neighbor connectivity, a characteristic physical gate error rate of $10^{-3}$, a surface code cycle time of 1 microsecond, and a reaction time of 10 microseconds. We account for factors that are normally ignored such as noise, the need to make repeated attempts, and the spacetime layout of the computation. When factoring 2048 bit RSA integers, our construction's spacetime volume is a hundredfold less than comparable estimates from earlier works (Van Meter et al. 2009, Jones et al. 2010, Fowler et al. 2012, Gheorghiu et al. 2019). In the abstract circuit model (which ignores overheads from distillation, routing, and error correction) our construction uses $3 n + 0.002 n \\lg n$ logical qubits, $0.3 n^3 + 0.0005 n^3 \\lg n$ Toffolis, and $500 n^2 + n^2 \\lg n$ measurement depth to factor $n$-bit RSA integers. We quantify the cryptographic implications of our work, both for RSA and for schemes based on the DLP in finite fields.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2112.03708","kind":"article","title":"Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code","authors":["Sebastian Krinner","Nathan Lacroix","Ants Remm","Agustin Di Paolo","Elie Genois","Catherine Leroux","Christoph Hellings","Stefania Lazar","Francois Swiadek","Johannes Herrmann","Graham J. Norris","Christian Kraglund Andersen","Markus Müller","Alexandre Blais","Christopher Eichler","Andreas Wallraff"],"author_count":16,"year":2021,"published":"2021-12-07","venue":"Nature 605, 669 (2022)","cited_by":686,"doi":"10.1038/s41586-022-04566-8","arxiv_id":"2112.03708","nct_id":null,"source_url":"https://arxiv.org/abs/2112.03708","archive_url":"https://space-kitty.com/papers/arxiv:2112.03708","updated":"2021-12-07","pmid":"35614249","pmcid":null,"openalex_id":"W4200634137","pdf_url":"https://arxiv.org/pdf/2112.03708","abstract":"Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors. Using 17 physical qubits in a superconducting circuit we encode quantum information in a distance-three logical qubit building up on recent distance-two error detection experiments. In an error correction cycle taking only $1.1\\,μ$s, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit- and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in postprocessing. We find a low error probability of $3\\,\\%$ per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error correction cycles, together with recent advances in ion traps, support our understanding that fault-tolerant quantum computation will be practically realizable.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["quant-ph","cond-mat.mes-hall"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1411.7403","kind":"article","title":"State preservation by repetitive error detection in a superconducting quantum circuit","authors":["J. Kelly","R. Barends","Austin G. Fowler","A. Megrant","Evan R. Jeffrey","T. White","D. Sank","J. Mutus","B. Campbell","Yu Chen","Z. Chen","B. Chiaro","A. Dunsworth","I.-C. Hoi","C. Neill","P. J. J. O’Malley","Chris Quintana","P. Roushan","A. Vainsencher","J. Wenner","Andrew N. Cleland","John M. Martinis"],"author_count":22,"year":2015,"published":"2015-03-03","venue":"Nature","cited_by":918,"doi":"10.1038/nature14270","arxiv_id":"1411.7403","nct_id":null,"source_url":"https://doi.org/10.1038/nature14270","archive_url":"https://space-kitty.com/papers/arxiv:1411.7403","updated":"2014-11-26","pmid":"25739628","pmcid":null,"openalex_id":"W2089540019","pdf_url":"https://arxiv.org/pdf/1411.7403","abstract":"Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation by guaranteeing increasingly larger clusters of errors will not cause logical failure - a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here, we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural precursor of the two-dimensional surface code QEC scheme, and track errors as they occur by repeatedly performing projective quantum non-demolition (QND) parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 for five qubits and a factor of 8.5 for nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger (GHZ) state. The successful suppression of environmentally-induced errors strongly motivates further research into the many exciting challenges associated with building a large-scale superconducting quantum computer.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["Quantum Information and Cryptography"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2304.05420","kind":"article","title":"High-fidelity parallel entangling gates on a neutral-atom quantum computer","authors":["Simon J. Evered","Dolev Bluvstein","Marcin Kalinowski","Sepehr Ebadi","Tom Manovitz","Hengyun Zhou","Sophie H. Li","Alexandra A. Geim","Tout T. Wang","Nishad Maskara","Harry Levine","Giulia Semeghini","Markus Greiner","Vladan Vuletić","Mikhail D. Lukin"],"author_count":15,"year":2023,"published":"2023-10-11","venue":"Nature","cited_by":521,"doi":"10.1038/s41586-023-06481-y","arxiv_id":"2304.05420","nct_id":null,"source_url":"https://doi.org/10.1038/s41586-023-06481-y","archive_url":"https://space-kitty.com/papers/arxiv:2304.05420","updated":"2023-04-11","pmid":"37821591","pmcid":null,"openalex_id":"W4387542025","pdf_url":"https://www.nature.com/articles/s41586-023-06481-y.pdf","abstract":"The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing. Neutral atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture. The major outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface code threshold for error correction. Our method employs fast single-pulse gates based on optimal control, atomic dark states to reduce scattering, and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications, characterize the physical error sources, and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms, error-corrected circuits, and digital simulations.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Cold Atom Physics and Bose-Einstein Condensates"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1411.7041","kind":"article","title":"Bulk locality and quantum error correction in AdS/CFT","authors":["Ahmed Almheiri","Xi Dong","Daniel Harlow"],"author_count":3,"year":2015,"published":"2015-04-01","venue":"Journal of High Energy Physics","cited_by":803,"doi":"10.1007/jhep04(2015)163","arxiv_id":"1411.7041","nct_id":null,"source_url":"https://doi.org/10.1007/jhep04(2015)163","archive_url":"https://space-kitty.com/papers/arxiv:1411.7041","updated":"2015-07-28","pmid":null,"pmcid":null,"openalex_id":"W2098838878","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP04(2015)163.pdf","abstract":"We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a \"quantum secret sharing scheme\", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard \"operator algebra quantum error correction\" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of \"subregion-subregion\" duality in AdS/CFT, and clarifies the limits of its validity.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Black Holes and Theoretical Physics"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2308.07915","kind":"article","title":"High-threshold and low-overhead fault-tolerant quantum memory","authors":["Sergey Bravyi","Andrew W. Cross","Jay M. Gambetta","Dmitri Maslov","Patrick Rall","Theodore J. Yoder"],"author_count":6,"year":2023,"published":"2023-08-15","venue":"Nature 627, 778-782 (2024)","cited_by":454,"doi":"10.1038/s41586-024-07107-7","arxiv_id":"2308.07915","nct_id":null,"source_url":"https://arxiv.org/abs/2308.07915","archive_url":"https://space-kitty.com/papers/arxiv:2308.07915","updated":"2024-02-21","pmid":"38538939","pmcid":null,"openalex_id":"W4393234688","pdf_url":"https://arxiv.org/pdf/2308.07915","abstract":"Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high encoding rate that achieves an error threshold of $0.8\\%$ for the standard circuit-based noise model. This is on par with the surface code which has remained an uncontested leader in terms of its high error threshold for nearly 20 years. The full syndrome measurement cycle for a length-$n$ code in our family requires $n$ ancillary qubits and a depth-7 circuit composed of nearest-neighbor CNOT gates. The required qubit connectivity is a degree-6 graph that consists of two edge-disjoint planar subgraphs. As a concrete example, we show that 12 logical qubits can be preserved for nearly one million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of $0.1\\%$. We argue that achieving the same level of error suppression on 12 logical qubits with the surface code would require nearly 3000 physical qubits. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["quant-ph","cs.ET"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2108.02626","kind":"article","title":"Fast universal quantum gate above the fault-tolerance threshold in silicon","authors":["Akito Noiri","Kenta Takeda","Takashi Nakajima","Takashi Kobayashi","Amir Sammak","Giordano Scappucci","Seigo Tarucha"],"author_count":7,"year":2022,"published":"2022-01-19","venue":"Nature","cited_by":472,"doi":"10.1038/s41586-021-04182-y","arxiv_id":"2108.02626","nct_id":null,"source_url":"https://doi.org/10.1038/s41586-021-04182-y","archive_url":"https://space-kitty.com/papers/arxiv:2108.02626","updated":"2021-08-10","pmid":"35046603","pmcid":null,"openalex_id":"W4206801895","pdf_url":"https://www.nature.com/articles/s41586-021-04182-y.pdf","abstract":"Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are particularly promising for a large-scale quantum computer due to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent due to the slow operation.Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the condition of qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate the universal gate fidelity beyond the fault-tolerance threshold and pave the way for scalable silicon quantum computers.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["Quantum and electron transport phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1111.4022","kind":"article","title":"Surface code quantum computing by lattice surgery","authors":["Dominic C. Horsman","Austin G. Fowler","Simon J. Devitt","Rodney Van Meter"],"author_count":4,"year":2012,"published":"2012-12-01","venue":"New Journal of Physics","cited_by":597,"doi":"10.1088/1367-2630/14/12/123011","arxiv_id":"1111.4022","nct_id":null,"source_url":"https://doi.org/10.1088/1367-2630/14/12/123011","archive_url":"https://space-kitty.com/papers/arxiv:1111.4022","updated":"2013-02-21","pmid":null,"pmcid":null,"openalex_id":"W1985315536","pdf_url":"https://iopscience.iop.org/article/10.1088/1367-2630/14/12/123011/pdf","abstract":"In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by-nc-sa","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"doi:10.1126/science.abi8378","kind":"article","title":"Realizing topologically ordered states on a quantum processor","authors":["Kevin J. Satzinger","Yu-Jie Liu","Adam Smith","Christina Knapp","Newman, M.","C. Jones","Zidan Chen","Chris Quintana","Xiao Mi","A. Dunsworth","Craig Gidney","I. L. Aleǐner","Frank Arute","Kunal Arya","Juan Atalaya","Ryan Babbush","Joseph C. Bardin","R. Barends","Joao Basso","Andreas Bengtsson","Alexander Bilmes","Broughton, M.","Bob B. Buckley","David A. Buell","Brian Burkett"],"author_count":98,"year":2021,"published":"2021-12-02","venue":"Repository@Nottingham (University of Nottingham)","cited_by":426,"doi":"10.1126/science.abi8378","arxiv_id":null,"nct_id":null,"source_url":"https://nottingham-repository.worktribe.com/output/7340738","archive_url":"https://space-kitty.com/papers/doi:10.1126/science.abi8378","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W3216031933","pdf_url":"https://nottingham-repository.worktribe.com/preview/7341334/2104.01180-2.pdf","abstract":"The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error-correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of -ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex","attribution":"Abstract of \"Realizing topologically ordered states on a quantum processor\" by Kevin J. Satzinger, Yu-Jie Liu, Adam Smith et al., https://doi.org/10.1126/science.abi8378, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified."},{"id":"arxiv:1410.6419","kind":"article","title":"Demonstration of a quantum error detection code using a square lattice of four superconducting qubits","authors":["Antonio D. Corcoles","Easwar Magesan","Srikanth J. Srinivasan","Andrew W. Cross","Matthias Steffen","Jay Gambetta","Jerry M. Chow"],"author_count":7,"year":2015,"published":"2015-04-29","venue":"Nature Communications","cited_by":489,"doi":"10.1038/ncomms7979","arxiv_id":"1410.6419","nct_id":null,"source_url":"https://doi.org/10.1038/ncomms7979","archive_url":"https://space-kitty.com/papers/arxiv:1410.6419","updated":"2014-10-23","pmid":"25923200","pmcid":null,"openalex_id":"W2092458348","pdf_url":"https://www.nature.com/articles/ncomms7979.pdf","abstract":"To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information encoded in the system. Stabilizer codes are attractive solutions to this problem, as they are analogous to classical linear codes, have simple and easily computed encoding networks, and allow efficient syndrome extraction. In these codes, syndrome extraction is performed via multi-qubit stabilizer measurements, which are bit and phase parity checks up to local operations. Previously, stabilizer codes have been realized in nuclei, trapped-ions, and superconducting qubits. However these implementations lack the ability to perform fault-tolerant syndrome extraction which continues to be a challenge for all physical quantum computing systems. Here we experimentally demonstrate a key step towards this problem by using a two-by-two lattice of superconducting qubits to perform syndrome extraction and arbitrary error detection via simultaneous quantum non-demolition stabilizer measurements. This lattice represents a primitive tile for the surface code, which is a promising stabilizer code for scalable quantum computing. Furthermore, we successfully show the preservation of an entangled state in the presence of an arbitrary applied error through high-fidelity syndrome measurement. Our results bolster the promise of employing lattices of superconducting qubits for larger-scale fault-tolerant quantum computing.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Information and Cryptography"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2102.06132","kind":"article","title":"Exponential suppression of bit or phase errors with cyclic error correction","authors":["Google Quantum AI","Zijun Chen","Kevin J. Satzinger","Juan Atalaya","Alexander N. Korotkov","A. Dunsworth","D. Sank","Chris Quintana","Matt McEwen","R. Barends","Paul V. Klimov","Sabrina Hong","Cody Jones","A. G. Petukhov","Dvir Kafri","Sean Demura","Brian Burkett","Craig Gidney","Austin G. Fowler","Alexandru Paler","Harald Putterman","I. L. Aleǐner","Frank Arute","Kunal Arya","Ryan Babbush"],"author_count":97,"year":2021,"published":"2021-07-14","venue":"Nature","cited_by":385,"doi":"10.1038/s41586-021-03588-y","arxiv_id":"2102.06132","nct_id":null,"source_url":"https://doi.org/10.1038/s41586-021-03588-y","archive_url":"https://space-kitty.com/papers/arxiv:2102.06132","updated":"2021-02-11","pmid":"34262210","pmcid":null,"openalex_id":"W3178633198","pdf_url":"https://www.nature.com/articles/s41586-021-03588-y.pdf","abstract":"Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\\times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2108.01646","kind":"article","title":"Fault-tolerant operation of a logical qubit in a diamond quantum processor","authors":["M. H. Abobeih","Y. Wang","J. Randall","S. J. H. Loenen","C. E. Bradley","M. Markham","D. J. Twitchen","B. M. Terhal","T. H. Taminiau"],"author_count":9,"year":2021,"published":"2021-08-03","venue":"Nature (2022)","cited_by":231,"doi":"10.1038/s41586-022-04819-6","arxiv_id":"2108.01646","nct_id":null,"source_url":"https://arxiv.org/abs/2108.01646","archive_url":"https://space-kitty.com/papers/arxiv:2108.01646","updated":"2021-08-03","pmid":null,"pmcid":null,"openalex_id":"W3189526869","pdf_url":"https://arxiv.org/pdf/2108.01646","abstract":"Solid-state spin qubits are a promising platform for quantum computation and quantum networks. Recent experiments have demonstrated high-quality control over multi-qubit systems, elementary quantum algorithms and non-fault-tolerant error correction. Large-scale systems will require using error-corrected logical qubits that are operated fault-tolerantly, so that reliable computation is possible despite noisy operations. Overcoming imperfections in this way remains a major outstanding challenge for quantum science. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the 5-qubit code with a recently discovered flag protocol that enables fault-tolerance using a total of seven qubits. We encode the logical qubit using a novel protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. While future improvements in fidelity and the number of qubits will be required, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards large-scale quantum information processing based on solid-state spins.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":false,"peer_reviewed":null,"categories":["quant-ph","cond-mat.mes-hall"],"details":null,"provenance":"arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1808.02892","kind":"article","title":"A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery","authors":["Daniel Litinski"],"author_count":1,"year":2019,"published":"2019-03-05","venue":"Quantum","cited_by":408,"doi":"10.22331/q-2019-03-05-128","arxiv_id":"1808.02892","nct_id":null,"source_url":"https://doi.org/10.22331/q-2019-03-05-128","archive_url":"https://space-kitty.com/papers/arxiv:1808.02892","updated":"2019-02-03","pmid":null,"pmcid":null,"openalex_id":"W2886696706","pdf_url":"https://quantum-journal.org/papers/q-2019-03-05-128/pdf/","abstract":"Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales. They are strategies for space-time trade-offs, going from slow computations using few qubits to fast computations using many qubits. Our schemes are based on surface-code patches, which not only feature a low space cost compared to other surface-code schemes, but are also conceptually simple, simple enough that they can be described as a tile-based game with a small set of rules. Therefore, no knowledge of quantum error correction is necessary to understand the schemes in this paper, but only the concepts of qubits and measurements. As an example, assuming a physical error rate of $10^{-4}$ and a code cycle time of 1 $μ$s, a classically intractable 100-qubit quantum computation with a $T$ count of $10^8$ and a $T$ depth of $10^6$ can be executed in 4 hours using 55,000 qubits, in 22 minutes using 120,000 qubits, or in 1 second using 330,000,000 qubits.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1309.5452","kind":"article","title":"Universal control and error correction in multi-qubit spin registers in diamond","authors":["T. H. Taminiau","Julia Cramer","Toeno van der Sar","V. V. Dobrovitski","Ronald Hanson"],"author_count":5,"year":2014,"published":"2014-02-01","venue":"Nature Nanotechnology","cited_by":429,"doi":"10.1038/nnano.2014.2","arxiv_id":"1309.5452","nct_id":null,"source_url":"https://doi.org/10.1038/nnano.2014.2","archive_url":"https://space-kitty.com/papers/arxiv:1309.5452","updated":"2013-09-26","pmid":"24487650","pmcid":null,"openalex_id":"W2099345738","pdf_url":"https://arxiv.org/pdf/1309.5452","abstract":"Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing. Pioneering experiments selected defects with favourably located nuclear spins having particularly strong hyperfine couplings. For progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single- and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["Diamond and Carbon-based Materials Research"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1609.09700","kind":"article","title":"Silicon CMOS architecture for a spin-based quantum computer","authors":["Menno Veldhorst","H. G. J. Eenink","C. H. Yang","Andrew S. Dzurak"],"author_count":4,"year":2017,"published":"2017-11-20","venue":"Nature Communications","cited_by":400,"doi":"10.1038/s41467-017-01905-6","arxiv_id":"1609.09700","nct_id":null,"source_url":"https://doi.org/10.1038/s41467-017-01905-6","archive_url":"https://space-kitty.com/papers/arxiv:1609.09700","updated":"2016-09-30","pmid":"29242497","pmcid":null,"openalex_id":"W2527981872","pdf_url":"https://www.nature.com/articles/s41467-017-01905-6.pdf","abstract":"Recent advances in quantum error correction (QEC) codes for fault-tolerant quantum computing \\cite{Terhal2015} and physical realizations of high-fidelity qubits in a broad range of platforms \\cite{Kok2007, Brown2011, Barends2014, Waldherr2014, Dolde2014, Muhonen2014, Veldhorst2014} give promise for the construction of a quantum computer based on millions of interacting qubits. However, the classical-quantum interface remains a nascent field of exploration. Here, we propose an architecture for a silicon-based quantum computer processor based entirely on complementary metal-oxide-semiconductor (CMOS) technology, which is the basis for all modern processor chips. We show how a transistor-based control circuit together with charge-storage electrodes can be used to operate a dense and scalable two-dimensional qubit system. The qubits are defined by the spin states of a single electron confined in a quantum dot, coupled via exchange interactions, controlled using a microwave cavity, and measured via gate-based dispersive readout \\cite{Colless2013}. This system, based entirely on available technology and existing components, is compatible with general surface code quantum error correction \\cite{Terhal2015}, enabling large-scale universal quantum computation.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum and electron transport phenomena"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1907.11157","kind":"article","title":"Quantum error correction: an introductory guide","authors":["Joschka Roffe"],"author_count":1,"year":2019,"published":"2019-07-03","venue":"Contemporary Physics","cited_by":365,"doi":"10.1080/00107514.2019.1667078","arxiv_id":"1907.11157","nct_id":null,"source_url":"https://doi.org/10.1080/00107514.2019.1667078","archive_url":"https://space-kitty.com/papers/arxiv:1907.11157","updated":"2019-07-25","pmid":null,"pmcid":null,"openalex_id":"W2963127785","pdf_url":"https://arxiv.org/pdf/1907.11157","abstract":"Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. As such, familiarity with quantum coding is an essential prerequisite for the understanding of current and future quantum computing architectures. In this review, we provide an introductory guide to the theory and implementation of quantum error correction codes. Where possible, fundamental concepts are described using the simplest examples of detection and correction codes, the working of which can be verified by hand. We outline the construction and operation of the surface code, the most widely pursued error correction protocol for experiment. Finally, we discuss issues that arise in the practical implementation of the surface code and other quantum error correction codes.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2112.13505","kind":"article","title":"Realization of an Error-Correcting Surface Code with Superconducting Qubits","authors":["Youwei Zhao","Yangsen Ye","He-Liang Huang","Yiming Zhang","Dachao Wu","Huijie Guan","Qingling Zhu","Zuolin Wei","Tan He","Sirui Cao","Fusheng Chen","Tung-Hsun Chung","Huiqiu Deng","Daojin Fan","Ming Gong","Cheng Guo","Shaojun Guo","Lianchen Han","Na Li","Shaowei Li","Yuan Li","Futian Liang","Jin Lin","Haoran Qian","Hao Rong"],"author_count":39,"year":2022,"published":"2022-07-11","venue":"Physical Review Letters","cited_by":321,"doi":"10.1103/physrevlett.129.030501","arxiv_id":"2112.13505","nct_id":null,"source_url":"https://doi.org/10.1103/physrevlett.129.030501","archive_url":"https://space-kitty.com/papers/arxiv:2112.13505","updated":"2022-01-29","pmid":"35905349","pmcid":null,"openalex_id":"W4285029287","pdf_url":"https://arxiv.org/pdf/2112.13505","abstract":"Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum error correction code for two-dimensional grid architecture. So far, the repeated error correction capability of the surface code has not been realized experimentally. Here, we experimentally implement an error-correcting surface code, the distance-3 surface code which consists of 17 qubits, on the \\textit{Zuchongzhi} 2.1 superconducting quantum processor. By executing several consecutive error correction cycles, the logical error can be significantly reduced after applying corrections, achieving the repeated error correction of surface code for the first time. This experiment represents a fully functional instance of an error-correcting surface code, providing a key step on the path towards scalable fault-tolerant quantum computing.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1805.09072","kind":"article","title":"Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit","authors":["Ling Hu","Yuwei Ma","Weizhou Cai","Xianghao Mu","Yuan Xu","Weiting Wang","Yukai Wu","Haiyan Wang","Yipu Song","Changling Zou","S. M. Girvin","L-M. Duan","Luyan Sun"],"author_count":13,"year":2018,"published":"2018-05-23","venue":"Nature Physics 15, 503-508 (2019)","cited_by":313,"doi":"10.1038/s41567-018-0414-3","arxiv_id":"1805.09072","nct_id":null,"source_url":"https://arxiv.org/abs/1805.09072","archive_url":"https://space-kitty.com/papers/arxiv:1805.09072","updated":"2018-05-23","pmid":null,"pmcid":null,"openalex_id":"W2803186226","pdf_url":"https://arxiv.org/pdf/1805.09072","abstract":"Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and high-fidelity (97.0% process fidelity on average) universal quantum gate set on the logical qubit. The protected logical qubit has shown 2.8 times longer lifetime than the uncorrected one. A Ramsey experiment on a protected logical qubit is demonstrated for the first time with two times longer coherence than the unprotected one. Our experiment represents an important step towards fault-tolerant quantum computation based on bosonic encoding.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["quant-ph"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2103.06309","kind":"article","title":"Quantum Low-Density Parity-Check Codes","authors":["Nikolas P. Breuckmann","Jens Niklas Eberhardt"],"author_count":2,"year":2021,"published":"2021-10-11","venue":"PRX Quantum","cited_by":328,"doi":"10.1103/prxquantum.2.040101","arxiv_id":"2103.06309","nct_id":null,"source_url":"https://doi.org/10.1103/prxquantum.2.040101","archive_url":"https://space-kitty.com/papers/arxiv:2103.06309","updated":"2021-10-25","pmid":null,"pmcid":null,"openalex_id":"W3207755657","pdf_url":"http://link.aps.org/pdf/10.1103/PRXQuantum.2.040101","abstract":"Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are alternatives to the surface code, which is the currently leading candidate to implement quantum fault-tolerance. We introduce the zoo of LDPC quantum codes and discuss their potential for making quantum computers robust against noise. In particular, we explain recent advances in the theory of LDPC quantum codes related to certain product constructions and discuss open problems in the field.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex+arxiv","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:2102.13071","kind":"article","title":"Logical-qubit operations in an error-detecting surface code","authors":["J. F. Marques","B. M. Varbanov","M. S. Moreira","H. Ali","N. Muthusubramanian","C. Zachariadis","F. Battistel","M. Beekman","N. Haider","W. Vlothuizen","A. Bruno","B. M. Terhal","L. DiCarlo"],"author_count":13,"year":2021,"published":"2021-02-25","venue":"Nature Physics 18, 80 (2022)","cited_by":141,"doi":"10.1038/s41567-021-01423-9","arxiv_id":"2102.13071","nct_id":null,"source_url":"https://arxiv.org/abs/2102.13071","archive_url":"https://space-kitty.com/papers/arxiv:2102.13071","updated":"2021-02-25","pmid":null,"pmcid":null,"openalex_id":"W4225797040","pdf_url":"https://arxiv.org/pdf/2102.13071","abstract":"We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":"cc-by","is_open_access":true,"peer_reviewed":null,"categories":["quant-ph","cond-mat.supr-con"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."},{"id":"arxiv:1912.09410","kind":"article","title":"Repeated Quantum Error Detection in a Surface Code","authors":["Christian Kraglund Andersen","Ants Remm","Stefania Lazar","Sebastian Krinner","Nathan Lacroix","Graham J. Norris","Mihai Gabureac","Christopher Eichler","Andreas Wallraff"],"author_count":9,"year":2019,"published":"2019-12-19","venue":"Nature Physics (2020)","cited_by":342,"doi":"10.1038/s41567-020-0920-y","arxiv_id":"1912.09410","nct_id":null,"source_url":"https://arxiv.org/abs/1912.09410","archive_url":"https://space-kitty.com/papers/arxiv:1912.09410","updated":"2019-12-19","pmid":null,"pmcid":null,"openalex_id":"W3033912009","pdf_url":"https://arxiv.org/pdf/1912.09410","abstract":"The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set of physical qubits. One such scalable approach is based on the surface code. Here we experimentally implement its smallest viable instance, capable of repeatedly detecting any single error using seven superconducting qubits, four data qubits and three ancilla qubits. Using high-fidelity ancilla-based stabilizer measurements we initialize the cardinal states of the encoded logical qubit with an average logical fidelity of 96.1%. We then repeatedly check for errors using the stabilizer readout and observe that the logical quantum state is preserved with a lifetime and coherence time longer than those of any of the constituent qubits when no errors are detected. Our demonstration of error detection with its resulting enhancement of the conditioned logical qubit coherence times in a 7-qubit surface code is an important step indicating a promising route towards the realization of quantum error correction in the surface code.","abstract_license":"CC0-1.0 (arXiv descriptive metadata)","license":null,"is_open_access":true,"peer_reviewed":null,"categories":["quant-ph"],"details":null,"provenance":"arxiv+openalex","attribution":"Abstract: arXiv descriptive metadata (CC0). Thank you to arXiv for use of its open access interoperability. This service was not reviewed or approved by, nor does it necessarily express or reflect the policies or opinions of, arXiv."}],"next":"https://space-kitty.com/api/v1/topics/quantum-error-correction/papers?sort=top&limit=25&offset=25"}