Non-Markovian Noise Mitigation: Practical Implementation, Error Analysis, and the Role of Environment Spectral Properties

• URL: http://arxiv.org/abs/2501.05019v3
• Date: Mon, 27 Jan 2025 05:33:10 GMT
• Title: Non-Markovian Noise Mitigation: Practical Implementation, Error Analysis, and the Role of Environment Spectral Properties
• Authors: Ke Wang, Xiantao Li,
• Abstract summary: We propose a non-Markovian Noise Mitigation(NMNM) method by extending the probabilistic error cancellation (PEC) method in the QEM framework to treat non-Markovian noise.<n>We establish a direct connection between the overall approximation error and sampling overhead of QEM and the spectral property of the environment.
• Score: 3.1003326924534482
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error mitigation(QEM), an error suppression strategy without the need for additional ancilla qubits for noisy intermediate-scale quantum~(NISQ) devices, presents a promising avenue for realizing quantum speedups of quantum computing algorithms on current quantum devices. However, prior investigations have predominantly been focused on Markovian noise. In this paper, we propose a non-Markovian Noise Mitigation(NMNM) method by extending the probabilistic error cancellation (PEC) method in the QEM framework to treat non-Markovian noise. We present the derivation of a time-local quantum master equation where the decoherence coefficients are directly obtained from bath correlation functions(BCFs), key properties of a non-Markovian environment that will make the error mitigation algorithms environment-aware. We further establish a direct connection between the overall approximation error and sampling overhead of QEM and the spectral property of the environment. Numerical simulations performed on a spin-boson model further validate the efficacy of our approach.

Related papers

• Quantum Error Corrected Non-Markovian Metrology [0.0]
  Heisenberg limit (HL) is the fundamental precision bound set by quantum mechanics. HL is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit. We analyze a hidden Markov model in which a quantum probe coupled to an inaccessible environment undergoes joint evolution.
  arXiv  Detail & Related papers  (2025-03-10T18:01:34Z)
• Noise-Robust Estimation of Quantum Observables in Noisy Hardware [0.0]
  Noise-Robust Estimation is a noise-agnostic framework that systematically reduces estimation bias. NRE exploits a bias-dispersion correlation uncovered in this work. We experimentally validate NRE on an IQM superconducting quantum processor.
  arXiv  Detail & Related papers  (2025-03-09T17:18:16Z)
• Bayesian Quantum Amplitude Estimation [49.1574468325115]
  We introduce BAE, a noise-aware Bayesian algorithm for quantum amplitude estimation.<n>We show that BAE achieves Heisenberg-limited estimation and benchmark it against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Robust quantum gap estimation with a noise-resilient hybrid algorithm [0.0]
  We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra.<n>Our analysis extends to a broader class of Markovian noise using numerical methods.<n>The algorithm's robustness is demonstrated through noisy simulations on the Qiskit Aer simulator and demonstrations on IBM Quantum processors.
  arXiv  Detail & Related papers  (2024-05-16T17:57:15Z)
• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps [46.350147604946095]
  We introduce Lindblad-like quantum tomography (L$ell$QT) as a quantum characterization technique of time-correlated noise in quantum information processors. We discuss L$ell$QT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function.
  arXiv  Detail & Related papers  (2024-03-28T19:29:12Z)
• Leveraging hardware-control imperfections for error mitigation via generalized quantum subspace [0.8399688944263843]
  In the era of quantum computing without full fault-tolerance, it is essential to suppress noise effects via the quantum error mitigation techniques to enhance the computational power of the quantum devices. One of the most effective noise-agnostic error mitigation schemes is the generalized quantum subspace expansion (GSE) method. We propose the fault-subspace method, which constructs an error-mitigated quantum state with copies of quantum states with different noise levels.
  arXiv  Detail & Related papers  (2023-03-14T07:01:30Z)
• Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis [42.275148861039895]
  Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy processors. gate noise due to imperfections and decoherence affects the gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits. QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently small.
  arXiv  Detail & Related papers  (2022-09-23T10:48:04Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm [0.0]
  Noise mitigation can be performed up to some error for which we derive upper bounds. Experiments on 15 (23) qubits using IBM's devices to test both the noise model and the error-mitigation scheme. We show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.
  arXiv  Detail & Related papers  (2021-01-07T02:19:58Z)
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems [69.33243249411113]
  We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels. We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
  arXiv  Detail & Related papers  (2020-12-15T15:51:27Z)
• 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.