Quantum Algorithms for Estimating Physical Quantities using Block-Encodings

• URL: http://arxiv.org/abs/2004.06832v3
• Date: Fri, 24 Jul 2020 14:31:07 GMT
• Title: Quantum Algorithms for Estimating Physical Quantities using Block-Encodings
• Authors: Patrick Rall
• Abstract summary: 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. All algorithms are based on block-encodings - a technique for the manipulation of arbitrary non-unitary combinations on a quantum computer.
• Score: 0.30458514384586405
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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