Modeling error correction with Lindblad dynamics and approximate channels

• URL: http://arxiv.org/abs/2402.16727v3
• Date: Sun, 18 May 2025 07:59:00 GMT
• Title: Modeling error correction with Lindblad dynamics and approximate channels
• Authors: Zohar Schwartzman-Nowik, Liran Shirizly, Haggai Landa,
• Abstract summary: We study how different approximations of the noise capture the success rate of a code.<n>A Pauli approximation going beyond a single-qubit channel is sensitive to the details of the noise, state, and decoder.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We analyze the performance of a quantum error correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how different approximations of the noise capture the success rate of a code. Focusing on the five-qubit code and adapting it to partially correct two-qubit errors in relevant parameter regimes according to the noise model, we find that a composite-channel approximation where every noise term is considered separately captures the behavior in many physical cases up to long timescales, eventually failing due to the effect of noncommuting terms. In contrast, we find that single-qubit approximations do not properly capture the error correction dynamics with two-qubit noise, even for short times. A Pauli approximation going beyond a single-qubit channel is sensitive to the details of the noise, state, and decoder, and succeeds at short timescales relative to the noise strength, beyond which it fails. Furthermore, we point out a mechanism for a Pauli model failure where it underestimates the failure rate of a code even with frequent syndrome projection and correction cycles. These results shed light on the performance of error correction in the presence of realistic noise and can advance the ongoing efforts towards useful quantum error correction.

Related papers

• Impact of Temporally Correlated Dephasing Noise on the Fidelity of the 2-Qubit Deutsch-Jozsa Algorithm [0.76146285961466]
  Noise in quantum systems often exhibits temporal correlations, leading to non-Markovian dynamics.<n>This paper investigates the impact of temporally correlated noise on the fidelity of the 2-qubit Deutsch-Jozsa algorithm.
  arXiv  Detail & Related papers  (2025-06-05T18:48:50Z)
• Measurement-free quantum error correction optimized for biased noise [1.2161145818221]
  We derive measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased.<n>The noise bias is adapted for neutral atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions.
  arXiv  Detail & Related papers  (2025-05-21T15:46:13Z)
• Improving error suppression with noise-aware decoding [0.0]
  We show that noise-aware decoding increases the error suppression factor of the surface code, yielding reductions in the logical error rate that increase exponentially with the code distance. Our results indicate that these noise characterisation experiments could be performed and processed in seconds for superconducting quantum computers.
  arXiv  Detail & Related papers  (2025-02-28T13:39:41Z)
• Bayesian Quantum Amplitude Estimation [49.1574468325115]
  We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation.<n>In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically characterize it and self-adapt.<n>We propose a benchmark for amplitude estimation algorithms and use it to test BAE against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Detrimental non-Markovian errors for surface code memory [0.5490714603843316]
  We study the structure of non-Markovian correlated errors and their impact on surface code memory performance. Our analysis shows that while not all temporally correlated structures are detrimental, certain structures, particularly multi-time "streaky" correlations, can severely degrade logical error rate scaling.
  arXiv  Detail & Related papers  (2024-10-31T09:52:21Z)
• Limitations to Dynamical Error Suppression and Gate-Error Virtualization from Temporally Correlated Nonclassical Noise [0.0]
  We study a minimal exactly solvable single-qubit model under Gaussian quantum dephasing noise.<n>For digital periodic control, we prove that the gate fidelity saturates at a value that is strictly smaller than the one attainable in the absence of control history.<n>We find that only if decoupling can keep the qubit highly pure over a timescale larger than the correlation time of the noise, the bath approximately converges to its original statistics.
  arXiv  Detail & Related papers  (2024-07-05T18:00:00Z)
• Quantum error correction with an Ising machine under circuit-level noise [0.4977217779934656]
  We develop a decoder for circuit-level noise that solves the error estimation problems as Ising-type optimization problems. We confirm that the threshold theorem in the surface code under the circuitlevel noise is reproduced with an error threshold of approximately 0.4%.
  arXiv  Detail & Related papers  (2023-08-01T08:21:22Z)
• A framework of partial error correction for intermediate-scale quantum computers [0.7046417074932257]
  We show that brick-layered circuits display on average slower concentration to the "useless" uniform distribution. We find that this advantage only comes when the number of error-corrected qubits passes a specified threshold.
  arXiv  Detail & Related papers  (2023-06-27T15:00:57Z)
• Quantum error correction with dissipatively stabilized squeezed cat qubits [68.8204255655161]
  We propose and analyze the error correction performance of a dissipatively stabilized squeezed cat qubit. We find that for moderate squeezing the bit-flip error rate gets significantly reduced in comparison with the ordinary cat qubit while leaving the phase flip rate unchanged.
  arXiv  Detail & Related papers  (2022-10-24T16:02:20Z)
• 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)
• Measuring NISQ Gate-Based Qubit Stability Using a 1+1 Field Theory and Cycle Benchmarking [50.8020641352841]
  We study coherent errors on a quantum hardware platform using a transverse field Ising model Hamiltonian as a sample user application. We identify inter-day and intra-day qubit calibration drift and the impacts of quantum circuit placement on groups of qubits in different physical locations on the processor. This paper also discusses how these measurements can provide a better understanding of these types of errors and how they may improve efforts to validate the accuracy of quantum computations.
  arXiv  Detail & Related papers  (2022-01-08T23:12:55Z)
• 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)
• Pauli channels can be estimated from syndrome measurements in quantum error correction [0.7264378254137809]
  We show that a stabilizer code can be used to estimate Pauli channels with correlations across a number of qubits given by the pure distance. It also allows for measurement errors within the framework of quantum data-syndrome codes. It is our hope that this work opens up interesting applications, such as the online adaptation of a decoder to time-varying noise.
  arXiv  Detail & Related papers  (2021-07-29T18:01:10Z)
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions [62.997667081978825]
  We present a study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level.
  arXiv  Detail & Related papers  (2020-12-21T14:20:40Z)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)
• Optimal noise estimation from syndrome statistics of quantum codes [0.7264378254137809]
  Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. Traditionally, this information is obtained by benchmarking the device before operation. We address the question of what can be learned from only the measurements done during decoding.
  arXiv  Detail & Related papers  (2020-10-05T18:00:26Z)

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.