Iterative Quantum Assisted Eigensolver

Abstract

The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for approximating the ground state of a Hamiltonian that builds on the powerful Krylov subspace method in a way that is suitable for current quantum computers. Our algorithm systematically constructs the Ansatz using any given choice of the initial state and the unitaries describing the Hamiltonian. The only task of the quantum computer is to measure overlaps and no feedback loops are required. The measurements can be performed efficiently on current quantum hardware without requiring any complicated measurements such as the Hadamard test. Finally, a classical computer solves a well characterized quadratically constrained optimization program. Our algorithm can reuse previous measurements to calculate the ground state of a wide range of Hamiltonians without requiring additional quantum resources. Further, we demonstrate our algorithm for solving problems consisting of thousands of qubits. The algorithm works for almost every random choice of the initial state and circumvents the barren plateau problem.

arXiv comment11 pages, 7 figures

References in corpus (28)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Quantum Computational Supremacy
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Training variational quantum algorithms is NP-hard
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Tapering off qubits to simulate fermionic Hamiltonians
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• A Non-Orthogonal Variational Quantum Eigensolver
• Methodology for replacing indirect measurements with direct measurements
• Decoding quantum errors with subspace expansions
• Quantum Power Method by a Superposition of Time-Evolved States
• Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation
• Near-term quantum algorithms for linear systems of equations
• Quantum inverse iteration algorithm for programmable quantum simulators
• On the natural gradient for variational quantum eigensolver
• Hamiltonian operator approximation for energy measurement and ground state preparation
• Quantum Assisted Eigensolver

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• Quantum Dynamics in Krylov Space: Methods and Applications
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