Quantum Algorithms for Estimating Physical Quantities using Block-Encodings

Abstract

We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique for the manipulation of arbitrary non-unitary matrices on a quantum computer. We describe how to 'sketch' these quantities via the kernel polynomial method which is a standard strategy in numerical condensed matter physics. These algorithms use amplitude estimation to obtain a quadratic speedup in the accuracy over previous results, can capture any observables and Hamiltonians presented as linear combinations of Pauli matrices, and are modular enough to leverage future advances in Hamiltonian simulation and state preparation.

11 pages, 1 figure

References in corpus (21)

• The Kernel Polynomial Method
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Hamiltonian simulation with nearly optimal dependence on all parameters
• Fixed-point quantum search with an optimal number of queries
• Chebyshev matrix product state approach for spectral functions
• Quantum Approximate Counting, Simplified
• Time-dependent Hamiltonian simulation with $L^1$-norm scaling
• Linear Response on a Quantum Computer
• Efficient Quantum Algorithm for Computing n-time Correlation Functions
• Simulating the dynamics of time-dependent Hamiltonians with a truncated Dyson series
• Hamiltonian Simulation in the Interaction Picture
• Local density of optical states in the band gap of a finite photonic crystal
• Spectral density estimation with the Gaussian Integral Transform
• Hamiltonian Simulation by Uniform Spectral Amplification
• Finding Angles for Quantum Signal Processing with Machine Precision
• Computational Difficulty of Computing the Density of States
• Spectral densities and partition functions of modular quantum systems as derived from a central limit theorem
• Approximate symmetries of Hamiltonians
• Bounded Independence Fools Halfspaces

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