Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors

Abstract

Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing Greenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

arXiv comment16 pages, 9 figures

References in corpus (33)

• Quantum Computing in the NISQ era and beyond
• Error mitigation for short-depth quantum circuits
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Extending the computational reach of a noisy superconducting quantum processor
• Probing entanglement entropy via randomized measurements
• Practical Quantum Error Mitigation for Near-Future Applications
• Experimental Comparison of Two Quantum Computing Architectures
• Direct Fidelity Estimation from Few Pauli Measurements
• Verified Quantum Information Scrambling
• Mixed-state entanglement from local randomized measurements
• Practical characterization of quantum devices without tomography
• Learning-based quantum error mitigation
• Virtual Distillation for Quantum Error Mitigation
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• Cross-Platform Verification of Intermediate Scale Quantum Devices
• Robust shadow estimation
• Exponential Error Suppression for Near-Term Quantum Devices
• Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
• Many-body topological invariants from randomized measurements
• Unified approach to data-driven quantum error mitigation
• Many-body Chern number from statistical correlations of randomized measurements
• The Dominant Eigenvector of a Noisy Quantum State
• Error-Mitigated Quantum Metrology via Virtual Purification
• Dual-state purification for practical quantum error mitigation
• Correcting detection error in quantum computation and state engineering through data processing
• Quantum Virtual Cooling
• Cross-Platform Comparison of Arbitrary Quantum Computations
• Importance sampling of randomized measurements for probing entanglement
• Relationship between costs for quantum error mitigation and non-Markovian measures
• Estimating expectation values using approximate quantum states
• Quantum Error Mitigation Relying on Permutation Filtering
• Validating and Certifying Stabilizer States

Cited by in corpus (40)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum Error Mitigation
• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
• Quantum Error Mitigated Classical Shadows
• Performance analysis of multi-shot shadow estimation
• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Testing platform-independent quantum error mitigation on noisy quantum computers
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Dual frame optimization for informationally complete quantum measurements
• Mitigating algorithmic errors in quantum optimization through energy extrapolation
• Enhanced estimation of quantum properties with common randomized measurements
• Classical shadows based on locally-entangled measurements
• Characterizing Error Mitigation by Symmetry Verification in QAOA
• Dissipative variational quantum algorithms for Gibbs state preparation
• Optimising quantum tomography via shadow inversion
• Localized Virtual Purification
• Virtual distillation with noise dilution
• Virtual quantum error detection
• Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
• Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models
• Measuring energy by measuring any other observable
• Robust ultra-shallow shadows
• Improving the efficiency of learning-based error mitigation
• Resource-efficient Generalized Quantum Subspace Expansion
• Quantum Circuit Cutting for Classical Shadows
• More buck-per-shot: Why learning trumps mitigation in noisy quantum sensing
• Estimating many properties of a quantum state via quantum reservoir processing
• Holographic Classical Shadow Tomography
• Agnostic Process Tomography
• Low Depth Virtual Distillation of Quantum Circuits by Deterministic Circuit Decomposition
• Dual-unitary shadow tomography
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Circuit-Noise-Resilient Virtual Distillation
• An Error Mitigated Non-Orthogonal Quantum Eigensolver via Shadow Tomography
• Hardware-efficient quantum annealing with error mitigation via classical shadow
• Learning mixed quantum states in large-scale experiments
• Classical Shadows with Improved Median-of-Means Estimation
• Optimal randomized measurements for a family of non-linear quantum properties
• Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates
• Error-mitigated inference of quantum network topology