Algorithmic Fault Tolerance for Fast Quantum Computing

• URL: http://arxiv.org/abs/2406.17653v1
• Date: Tue, 25 Jun 2024 15:43:25 GMT
• Title: Algorithmic Fault Tolerance for Fast Quantum Computing
• Authors: Hengyun Zhou, Chen Zhao, Madelyn Cain, Dolev Bluvstein, Casey Duckering, Hong-Ye Hu, Sheng-Tao Wang, Aleksander Kubica, Mikhail D. Lukin,
• Abstract summary: We show that fault-tolerant logical operations can be performed with constant time overhead for a broad class of quantum codes. We prove that the deviation from the ideal measurement result distribution can be made exponentially small in the code distance. Our work sheds new light on the theory of fault tolerance, potentially reducing the space-time cost of practical fault-tolerant quantum computation by orders of magnitude.
• Score: 37.448838730002905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fast, reliable logical operations are essential for the realization of useful quantum computers, as they are required to implement practical quantum algorithms at large scale. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and subsequently correct errors, one can achieve very low logical error rates. However, for most practical quantum error correcting (QEC) codes such as the surface code, it is generally believed that due to syndrome extraction errors, multiple extraction rounds -- on the order of the code distance d -- are required for fault-tolerant computation. Here, we show that contrary to this common belief, fault-tolerant logical operations can be performed with constant time overhead for a broad class of QEC codes, including the surface code with magic state inputs and feed-forward operations, to achieve "algorithmic fault tolerance". Through the combination of transversal operations and novel strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal measurement result distribution can be made exponentially small in the code distance. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Our work sheds new light on the theory of fault tolerance, potentially reducing the space-time cost of practical fault-tolerant quantum computation by orders of magnitude.

Related papers

• Measurement-free, scalable and fault-tolerant universal quantum computing [1.2600261666440378]
  We present a complete toolbox for fault-tolerant universal quantum computing without the need for measurements during algorithm execution. We develop new fault-tolerant, measurement-free protocols to transfer encoded information between 2D and 3D color codes. Our measurement-free approach provides a practical and scalable pathway for universal quantum computing on state-of-the-art quantum processors.
  arXiv  Detail & Related papers  (2024-10-17T14:04:14Z)
• Accelerating Error Correction Code Transformers [56.75773430667148]
  We introduce a novel acceleration method for transformer-based decoders. We achieve a 90% compression ratio and reduce arithmetic operation energy consumption by at least 224 times on modern hardware.
  arXiv  Detail & Related papers  (2024-10-08T11:07:55Z)
• Low-overhead fault-tolerant quantum computation by gauging logical operators [0.7673339435080445]
  Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes for fault-tolerant logical measurement do not always achieve low qubit overhead. We present a low-overhead method to implement fault-tolerant logical measurement in a quantum error-correcting code by treating the logical operator as a symmetry and gauging it.
  arXiv  Detail & Related papers  (2024-10-03T05:04:12Z)
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code [0.0]
  Many current quantum error correcting codes that achieve full fault-tolerance suffer from having low ratios of logical to physical qubits and significant overhead. We propose a middle ground: constructions in the [[n,n-2,2]] quantum error detecting code that can detect any error from a single faulty gate.
  arXiv  Detail & Related papers  (2024-08-27T07:25:36Z)
• Time-efficient logical operations on quantum LDPC codes [5.881311286656519]
  We propose schemes capable of measuring an arbitrary set of commutative logical Pauli operators in time independent of the number of operators. The only condition is commutativity, a fundamental requirement for simultaneous measurements in quantum mechanics.
  arXiv  Detail & Related papers  (2024-08-02T15:35:05Z)
• Testing the Accuracy of Surface Code Decoders [55.616364225463066]
  Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC) This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes.
  arXiv  Detail & Related papers  (2023-11-21T10:22:08Z)
• Modular decoding: parallelizable real-time decoding for quantum computers [55.41644538483948]
  Real-time quantum computation will require decoding algorithms capable of extracting logical outcomes from a stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks.
  arXiv  Detail & Related papers  (2023-03-08T19:26:10Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes [61.411482146110984]
  We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
  arXiv  Detail & Related papers  (2022-03-09T18:48:54Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.