Linear-time general decoding algorithm for the surface code

Darmawan, Andrew S.; Poulin, David

doi:10.1103/physreve.97.051302

Cited by 42 publications

(27 citation statements)

References 39 publications

(53 reference statements)

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“…We observe a similar improvement in performance using the tensor-network decoder described in Ref. [29] when defined on the rotated layout and with an analogous tensor-network layout. Exact decoding is achieved with χ = 4 for pure Y noise, which is not as efficient as the improved MPS decoder described above but substantially more efficient than the MPS decoder on the standard layout.…”

Section: Improved Tensor-network Decoding Of Rotated Codes With Bsupporting

confidence: 66%

Tailoring Surface Codes for Highly Biased Noise

et al. 2019

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The surface code, with a simple modification, exhibits ultrahigh error-correction thresholds when the noise is biased toward dephasing. Here, we identify features of the surface code responsible for these ultrahigh thresholds. We provide strong evidence that the threshold error rate of the surface code tracks the hashing bound exactly for all biases and show how to exploit these features to achieve significant improvement in logical failure rate. First, we consider the infinite bias limit, meaning pure dephasing. We prove that the error threshold of the modified surface code for pure dephasing noise is 50%, i.e., that all qubits are fully dephased, and this threshold can be achieved by a polynomial-time decoding algorithm. We demonstrate that the subthreshold behavior of the code depends critically on the precise shape and boundary conditions of the code. That is, for rectangular surface codes with standard rough and smooth open boundaries, it is controlled by the parameter g = gcd(j, k), where j and k are dimensions of the surface code lattice. We demonstrate a significant improvement in logical failure rate with pure dephasing for coprime codes that have g = 1, and closely-related rotated codes, which have a modified boundary. The effect is dramatic: The same logical failure rate achievable with a square surface code and n physical qubits can be obtained with a coprime or rotated surface code using only O( √ n) physical qubits. Finally, we use approximate maximum-likelihood decoding to demonstrate that this improvement persists for a general Pauli noise biased toward dephasing. In particular, comparing with a square surface code, we observe a significant improvement in logical failure rate against biased noise using a rotated surface code with approximately half the number of physical qubits.

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Section: Improved Tensor-network Decoding Of Rotated Codes With Bsupporting

confidence: 66%

Tailoring Surface Codes for Highly Biased Noise

et al. 2019

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“…In contrast, CNOT 12 showed the worst fidelity and the worst unitarity but a reasonably good performance, without suffering from the systematic error present in CR2 and CR4. Hence the gate metrics under investigation do not provide reliable information of how well and how often a certain gate may be used in an algorithm (see also the conclusion in [50]). As this information is essential for potential users of gate-based quantum computers, it should be included in the specification sheet of the physical device.…”

Section: Discussionmentioning

confidence: 99%

Gate-error analysis in simulations of quantum computers with transmon qubits

et al. 2017

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In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schrödinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm.

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“…In [21], a hard decoding algorithm was proposed for optimizing thresholds of concatenated codes afflicted by general Markovian noise channels. In [22,23], tensor network algorithms were used for simulating the surface code and obtaining efficient decoders for general noise features. However, the above schemes are not adapted to fault-tolerant protocols where gate and measurement errors plays a significant role.…”

Section: Introductionmentioning

confidence: 99%

Deep neural decoders for near term fault-tolerant experiments

Chamberland

Ronagh

2018

Quantum Sci. Technol.

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Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep neural decoders and apply them to analyze several fault-tolerant error correction protocols such as the surface code as well as Steane and Knill error correction. Our methods require no knowledge of the underlying noise model afflicting the quantum device making them appealing for real-world experiments. Our analysis is based on a full circuitlevel noise model. It considers both distance-three and five codes, and is performed near the codes pseudo-threshold regime. Training deep neural decoders in low noise rate regimes appears to be a challenging machine learning endeavour. We provide a detailed description of our neural network architectures and training methodology. We then discuss both the advantages and limitations of deep neural decoders. Lastly, we provide a rigorous analysis of the decoding runtime of trained deep neural decoders and compare our methods with anticipated gate times in future quantum devices. Given the broad applications of our decoding schemes, we believe that the methods presented in this paper could have practical applications for near term fault-tolerant experiments.

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Linear-time general decoding algorithm for the surface code

Cited by 42 publications

References 39 publications

Tailoring Surface Codes for Highly Biased Noise

Tailoring Surface Codes for Highly Biased Noise

Gate-error analysis in simulations of quantum computers with transmon qubits

Deep neural decoders for near term fault-tolerant experiments

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