Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry

Abstract

Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conduct density-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level of tolerable depolarizing gate-errors. We find that: (i) The best-performing VQEs require gate-error probabilities between $10^{-6}$ and $10^{-4}$ ( $10^{-4}$ and $10^{-2}$ with error mitigation) to predict, within chemical accuracy, ground-state energies of small molecules with $4-14$ orbitals. (ii) ADAPT-VQEs that construct ansatz circuits iteratively outperform fixed-circuit VQEs. (iii) ADAPT-VQEs perform better with circuits constructed from gate-efficient rather than physically-motivated elements. (iv) The maximally-allowed gate-error probability, $p_c$, for any VQE to achieve chemical accuracy decreases with the number $\ncx$ of noisy two-qubit gates as $p_c\approxprop\ncx^{-1}$. Additionally, $p_c$ decreases with system size, even with error mitigation, implying that larger molecules require even lower gate-errors. Thus, quantum advantage via gate-based VQEs is unlikely unless gate-error probabilities are decreased by orders of magnitude.

arXiv comment25 pages, 8 figures

References in corpus (55)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Surface codes: Towards practical large-scale quantum computation
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Dynamical Decoupling of Open Quantum Systems
• Quantum computational chemistry
• Dynamical suppression of decoherence in two-state quantum systems
• Superconducting Qubits: Current State of Play
• Error mitigation for short-depth quantum circuits
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Semiconductor Spin Qubits
• Hartree-Fock on a superconducting qubit quantum computer
• Towards Practical Quantum Variational Algorithms
• Quantum Error Mitigation
• Roads towards fault-tolerant universal quantum computation
• Computing with spin qubits at the surface code error threshold
• Noise tailoring for scalable quantum computation via randomized compiling
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Decoherence in Josephson Qubits from Junction Resonances
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Mitigating measurement errors in multi-qubit experiments
• The Future of Quantum Computing with Superconducting Qubits
• Scalable mitigation of measurement errors on quantum computers
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Learning-based quantum error mitigation
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Gate Set Tomography
• A perspective on the current state-of-the-art of quantum computing for drug discovery applications
• Fundamental limits of quantum error mitigation
• Mitigating depolarizing noise on quantum computers with noise-estimation circuits
• Qubit-excitation-based adaptive variational quantum eigensolver
• Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Efficient quantum circuits for quantum computational chemistry
• Surface code with decoherence: An analysis of three superconducting architectures
• ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus
• High-fidelity Two-qubit Gates Using a MEMS-based Beam Steering System for Individual Qubit Addressing
• Accuracy and Resource Estimations for Quantum Chemistry on a Near-term Quantum Computer
• Quantum Filter Diagonalization with Double-Factorized Hamiltonians
• Measurement Error Mitigation in Quantum Computers Through Classical Bit-Flip Correction
• Variational Quantum Eigensolver with Reduced Circuit Complexity
• Universal cost bound of quantum error mitigation based on quantum estimation theory
• Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ansätze
• Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space
• Batch Optimization of Frequency-Modulated Pulses for Robust Two-qubit Gates in Ion Chains
• Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor
• Simulating noisy variational quantum eigensolver with local noise models
• Efficient Quantum Analytic Nuclear Gradients with Double Factorization

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