Linear programming bounds for quantum amplitude damping codes

• URL: http://arxiv.org/abs/2001.03976v1
• Date: Sun, 12 Jan 2020 18:46:59 GMT
• Title: Linear programming bounds for quantum amplitude damping codes
• Authors: Yingkai Ouyang and Ching-Yi Lai
• Abstract summary: We introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist.
• Score: 9.975163460952047
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds do not directly apply to AQEC codes. Herein, we introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. In particular, we introduce an auxiliary exact weight enumerator that is intrinsic to a code space and moreover, we establish a linear relationship between the quantum weight enumerators for AD errors and this auxiliary exact weight enumerator. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist. To illustrate our linear program, we numerically rule out the existence of three-qubit AD codes that are capable of correcting an arbitrary AD error.

Related papers

• Quantum Error Transmutation [1.8719295298860394]
  We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly. We call these quantum error transmuting codes. They are of particular interest for the simulation of noisy quantum systems, and for use in algorithms inherently robust to errors of a particular character.
  arXiv  Detail & Related papers  (2023-10-16T11:09:59Z)
• Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits [84.60542868688235]
  leakage out of the computational subspace arising from the multi-level structure of qubit implementations. We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
  arXiv  Detail & Related papers  (2023-09-13T16:21:32Z)
• Fault-Tolerant Computing with Single Qudit Encoding [49.89725935672549]
  We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth.
  arXiv  Detail & Related papers  (2023-07-20T10:51:23Z)
• Achieving metrological limits using ancilla-free quantum error-correcting codes [1.9265037496741413]
  Existing quantum error-correcting codes generally exploit entanglement between one probe and one noiseless ancilla of the same dimension. Here we construct two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free.
  arXiv  Detail & Related papers  (2023-03-02T00:51:02Z)
• 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)
• Finite-round quantum error correction on symmetric quantum sensors [8.339831319589134]
  Heisenberg limit provides a quadratic improvement over the standard quantum limit. It remains elusive because of the inevitable presence of noise decohering quantum sensors. We side-step this no-go result by using an optimal finite number of rounds of quantum error correction.
  arXiv  Detail & Related papers  (2022-12-12T23:41:51Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• 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)
• Effectiveness of Variable Distance Quantum Error Correcting Codes [1.0203602318836442]
  We show that quantum programs can tolerate non-trivial errors and still produce usable output. In addition, we propose using variable strength (distance) error correction, where overhead can be reduced by only protecting more sensitive parts of the quantum program with high distance codes.
  arXiv  Detail & Related papers  (2021-12-19T02:45:18Z)
• Linear programming bounds for quantum channels acting on quantum error-correcting codes [9.975163460952047]
  We introduce corresponding quantum weight enumerators that naturally generalize the Shor-Laflamme quantum weight enumerators. An exact weight enumerator completely quantifies the quantum code's projector, and is independent of the underlying noise process. Our framework allows us to establish the non-existence of certain quantum codes that approximately correct amplitude damping errors.
  arXiv  Detail & Related papers  (2021-08-10T03:56:25Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)

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.