Error-mitigated fermionic classical shadows on noisy quantum devices

Abstract

Efficiently estimating fermionic Hamiltonian expectation values is vital for simulating various physical systems. Classical shadow (CS) algorithms offer a solution by reducing the number of quantum state copies needed, but noise in quantum devices poses challenges. We propose an error-mitigated CS algorithm assuming gate-independent, time-stationary, and Markovian (GTM) noise. For $n$-qubit systems, our algorithm, which employs the easily prepared initial state $|0^n⟩⟨0^n|$ assumed to be noiseless, efficiently estimates $k$-RDMs with $\tilde{\mathcal{O}}(k{n}^k)$ state copies and $\tilde{\mathcal{O}}(\sqrt{n})$ calibration measurements for GTM noise with constant fidelities. We show that our algorithm is robust against noise types like depolarizing, damping, and $X$-rotation noise with constant strengths, showing scalings akin to prior CS algorithms for fermions but with better noise resilience. Numerical simulations confirm our algorithm's efficacy in noisy settings, suggesting its viability for near-term quantum devices.

31 pages, 5 figures

References in corpus (34)

• Variational Quantum Algorithms
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Fermionic quantum computation
• Robust randomized benchmarking of quantum processes
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Classical simulation of noninteracting-fermion quantum circuits
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Soundness and completeness of quantum root-mean-square errors
• Efficient estimation of Pauli observables by derandomization
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Quantum algorithms to simulate many-body physics of correlated fermions
• Fermionic partial tomography via classical shadows
• Robust shadow estimation
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• Efficient estimation of Pauli channels
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Classical Shadows With Noise
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Matchgate Shadows for Fermionic Quantum Simulation
• Quantum scrambling with classical shadows
• Overlapped grouping measurement: A unified framework for measuring quantum states
• Tight bounds on the convergence of noisy random circuits to the uniform distribution
• Matchgate benchmarking: Scalable benchmarking of a continuous family of many-qubit gates
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices
• Fermionic Linear Optics Revisited
• Classical shadows with Pauli-invariant unitary ensembles
• Quantum Error Mitigated Classical Shadows
• Performance analysis of multi-shot shadow estimation
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Classical shadows based on locally-entangled measurements
• A classification of Markovian fermionic Gaussian master equations

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• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Machine learning on quantum experimental data toward solving quantum many-body problems
• Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
• Stability of classical shadows under gate-dependent noise
• Holographic Classical Shadow Tomography
• Decoded Quantum Interferometry Under Noise
• Quantum Advantage via Efficient Post-processing on Qudit Classical Shadow tomography
• Classical Shadows with Improved Median-of-Means Estimation