Quantum subspace expansion in the presence of hardware noise

Abstract

Finding ground state energies on current quantum processing units (QPUs) using algorithms like the variational quantum eigensolver (VQE) continues to pose challenges. Hardware noise severely affects both the expressivity and trainability of parametrized quantum circuits, limiting them to shallow depths in practice. Here, we demonstrate that both issues can be addressed by synergistically integrating VQE with a quantum subspace expansion, allowing for an optimal balance between quantum and classical computing capabilities and costs. We perform a systematic benchmark analysis of the iterative quantum-assisted eigensolver of [K. Bharti and T. Haug, Phys. Rev. A {\bf 104}, L050401 (2021)] in the presence of hardware noise. We determine ground state energies of 1D and 2D mixed-field Ising spin models on noisy simulators and on the IBM QPUs ibmq_quito (5 qubits) and ibmq_guadalupe (16 qubits). To maximize accuracy, we propose a suitable criterion to select the subspace basis vectors according to the trace of the noisy overlap matrix. Finally, we show how to systematically approach the exact solution by performing controlled quantum error mitigation based on probabilistic error reduction on the noisy backend fake_guadalupe.

arXiv comment12 pages, 6 figures

References in corpus (37)

• Variational Quantum Algorithms
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• 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
• Scalable Quantum Simulation of Molecular Energies
• Quantum algorithms for quantum chemistry and quantum materials science
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• Robust determination of molecular spectra on a quantum processor
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Simulating quantum many-body dynamics on a current digital quantum computer
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Model-free readout-error mitigation for quantum expectation values
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Simulation of Nonequilibrium Dynamics on a Quantum Computer
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Efficient estimation of Pauli channels
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Quantum Power Method by a Superposition of Time-Evolved States
• Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Simulating Quantum Materials with Digital Quantum Computers
• Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers
• Exact and efficient Lanczos method on a quantum computer
• Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation
• A theory of quantum subspace diagonalization
• Iterative Quantum Assisted Eigensolver
• Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms
• Automated quantum error mitigation based on probabilistic error reduction

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• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
• Partitioned Quantum Subspace Expansion
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions