A stochastic quantum Krylov protocol with double factorized Hamiltonians

Abstract

We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator, $e^{-i\hat{H}\tau }$, as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorized electronic-structure Hamiltonian. To demonstrate the potential of the proposed rQKD algorithm, we provide numerical benchmarks for a variety of molecular systems with circuit-based statevector simulators, achieving ground state energy errors of less than 1~kcal~mol${}^{-1}$ with circuit depths orders of magnitude shallower than those required for low-rank deterministic Trotter-Suzuki decompositions.

References in corpus (43)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Quantum Simulation
• The theory of variational hybrid quantum-classical algorithms
• Error mitigation for short-depth quantum circuits
• Recent developments in the PySCF program package
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Extending the computational reach of a noisy superconducting quantum processor
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• A Theory of Trotter Error
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• A random compiler for fast Hamiltonian simulation
• Solving strongly correlated electron models on a quantum computer
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Automated construction of molecular active spaces from atomic valence orbitals
• From transistor to trapped-ion computers for quantum chemistry
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Faster quantum simulation by randomization
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Low rank representations for quantum simulation of electronic structure
• A Non-Orthogonal Variational Quantum Eigensolver
• Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
• Gate-efficient simulation of molecular eigenstates on a quantum computer
• Exploiting locality in quantum computation for quantum chemistry
• Decoding quantum errors with subspace expansions
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Quantum Power Method by a Superposition of Time-Evolved States
• A randomized quantum algorithm for statistical phase estimation
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Faster Digital Quantum Simulation by Symmetry Protection
• Generalized quantum subspace expansion
• Quantum Filter Diagonalization with Double-Factorized Hamiltonians
• Concentration for random product formulas
• A theory of quantum subspace diagonalization
• Compilation by stochastic Hamiltonian sparsification
• Hybridized Methods for Quantum Simulation in the Interaction Picture
• Orbital transformations to reduce the 1-norm of the electronic structure Hamiltonian for quantum computing applications
• Quantum simulations of molecular systems with intrinsic atomic orbitals
• Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

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• Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach
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