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Exact simulations of quantum circuits (QCs) are currently limited to $\sim$50qubits because the memory and computational cost required to store the QC wavefunction scale exponentially with qubit number. Therefore, developing efficientschemes for approximate QC simulations is a current research focus. Here weshow simulations of QCs with a method inspired by density functional theory(DFT), a widely used approach to study many-electron systems. Our calculationscan predict marginal single-qubit probabilities (SQPs) with over 90% accuracyin several classes of QCs with universal gate sets, using memory andcomputational resources linear in qubit number despite the formal exponentialcost of the SQPs. This is achieved by developing a mean-field description ofQCs and formulating optimal single- and two-qubit gate functionals $-$ analogsof exchange-correlation functionals in DFT $-$ to evolve the SQPs withoutcomputing the QC wave function. Current limitations and future extensions ofthis formalism are discussed.

Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density Functional Theory