Statistical Signal Processing for Quantum Error Mitigation

• URL: http://arxiv.org/abs/2506.00683v1
• Date: Sat, 31 May 2025 19:34:19 GMT
• Title: Statistical Signal Processing for Quantum Error Mitigation
• Authors: Kausthubh Chandramouli, Kelly Mae Allen, Christopher Mori, Dror Baron, Mário A. T. Figueiredo,
• Abstract summary: We present a statistical signal processing approach to quantum error mitigation (QEM)<n>Our model assumes that circuit depth is sufficient for depolarizing noise, producing corrupted observations.<n>We show that our method scales to larger qubit counts using synthetically generated data consistent with our noise model.
• Score: 12.804941908319792
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely noiseless outputs from noisy quantum measurements. Our model assumes that circuit depth is sufficient for depolarizing noise, producing corrupted observations that resemble a uniform distribution alongside classical bit-flip errors from readout. Our method consists of two steps: a filtering stage that discards uninformative depolarizing noise and an expectation-maximization (EM) algorithm that computes a maximum likelihood (ML) estimate over the remaining data. We demonstrate the effectiveness of this approach on small-qubit systems using IBM circuit simulations in Qiskit and compare its performance to contemporary statistical QEM techniques. We also show that our method scales to larger qubit counts using synthetically generated data consistent with our noise model. These results suggest that principled statistical methods can offer scalable and interpretable solutions for quantum error mitigation in realistic NISQ settings.

Related papers

• Calibration of Quantum Devices via Robust Statistical Methods [45.464983015777314]
  We numerically analyze advanced statistical methods for Bayesian inference against the state-of-the-art in quantum parameter learning.<n>We show advantages of these approaches over existing ones, namely under multi-modality and high dimensionality.<n>Our findings have applications in challenging quantumcharacterization tasks namely learning the dynamics of open quantum systems.
  arXiv  Detail & Related papers  (2025-07-09T15:22:17Z)
• Prospects of Quantum Error Mitigation for Quantum Signal Processing [0.0]
  This work explores the performance of zero-noise-extrapolation (ZNE) on a Hamiltonian simulation algorithm designed within quantum signal processing (QSP)<n>We quantify for which noise and depth regimes our ZNE protocol can recover an approximation of the noiseless expectation value.<n>We briefly discuss and present a numerical study on the region where ZNE is unusable, even given an unlimited sample budget.
  arXiv  Detail & Related papers  (2025-05-08T19:49:54Z)
• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations [44.99833362998488]
  This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM)<n>We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall.<n>Our results confirm the validity of the approach, achieving median error fidelities on the order of $10-3$ and success probabilities sufficient for practical quantum state sampling.
  arXiv  Detail & Related papers  (2025-04-17T15:41:48Z)
• Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation [0.0]
  We introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines Symmetry Verification (SV) and low bias of Probabilistic Error Cancellation (PEC) QEM techniques.<n>We study the performance of our method by simulating the Trotterized time evolution of the spin-1/2 Fermi-Hubbard model (FHM) using a variety of local fermion-to-qubit encodings.
  arXiv  Detail & Related papers  (2025-03-14T18:20:54Z)
• Non-Markovian Noise Mitigation: Practical Implementation, Error Analysis, and the Role of Environment Spectral Properties [3.1003326924534482]
  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.
  arXiv  Detail & Related papers  (2025-01-09T07:22:06Z)
• 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)
• Noise-resilient and resource-efficient hybrid algorithm for robust quantum gap estimation [0.0]
  We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra.<n>We employ error mitigation strategies that optimize the utilization of quantum resources.<n>Results underscore the potential to enable accurate quantum simulations on near-term noisy quantum devices.
  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.<n>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)
• Mitigating Errors on Superconducting Quantum Processors through Fuzzy Clustering [38.02852247910155]
  A new Quantum Error Mitigation (QEM) technique uses Fuzzy C-Means clustering to specifically identify measurement error patterns. We report a proof-of-principle validation of the technique on a 2-qubit register, obtained as a subset of a real NISQ 5-qubit superconducting quantum processor. We demonstrate that the FCM-based QEM technique allows for reasonable improvement of the expectation values of single- and two-qubit gates based quantum circuits.
  arXiv  Detail & Related papers  (2024-02-02T14:02:45Z)
• Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing [93.83016310295804]
  AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for computer vision tasks. In this work, we explore the potential of using this information for probabilistic balanced k-means clustering. Instead of discarding non-optimal solutions, we propose to use them to compute calibrated posterior probabilities with little additional compute cost. This allows us to identify ambiguous solutions and data points, which we demonstrate on a D-Wave AQC on synthetic tasks and real visual data.
  arXiv  Detail & Related papers  (2023-10-18T17:59:45Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• 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)
• 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)
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices [0.5872014229110214]
  Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. Most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate. We show it can be effectively suppressed by a novel QEM method.
  arXiv  Detail & Related papers  (2020-01-14T16:51:35Z)

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.