Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density
Functional Theory
- URL: http://arxiv.org/abs/2210.16465v3
- Date: Thu, 19 Oct 2023 22:12:23 GMT
- Title: Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density
Functional Theory
- Authors: Marco Bernardi
- Abstract summary: Exact simulations of quantum circuits (QCs) are currently limited to $sim$50 qubits.
Here we show simulations of QCs with a method inspired by density functional theory (DFT)
Our calculations can predict marginal single-qubit probabilities with over 90% accuracy in several classes of QCs with universal gate sets.
- Score: 1.3561290928375374
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Exact simulations of quantum circuits (QCs) are currently limited to $\sim$50
qubits because the memory and computational cost required to store the QC wave
function scale exponentially with qubit number. Therefore, developing efficient
schemes for approximate QC simulations is a current research focus. Here we
show simulations of QCs with a method inspired by density functional theory
(DFT), a widely used approach to study many-electron systems. Our calculations
can predict marginal single-qubit probabilities (SQPs) with over 90% accuracy
in several classes of QCs with universal gate sets, using memory and
computational resources linear in qubit number despite the formal exponential
cost of the SQPs. This is achieved by developing a mean-field description of
QCs and formulating optimal single- and two-qubit gate functionals $-$ analogs
of exchange-correlation functionals in DFT $-$ to evolve the SQPs without
computing the QC wave function. Current limitations and future extensions of
this formalism are discussed.
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