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

Area of Science:

• Quantum Computing
• Computational Physics
• Quantum Information Science

Background:

• Exact simulations of quantum circuits (QCs) are computationally expensive, scaling exponentially with qubit number.
• Current limitations restrict exact simulations to approximately 50 qubits.
• Efficient approximate simulation methods are crucial for advancing QC research.

Purpose of the Study:

• To develop an efficient approximate simulation method for quantum circuits.
• To enable accurate prediction of marginal single-qubit probabilities (SQPs) for larger QCs.
• To reduce the memory and computational cost associated with QC simulations.

Main Methods:

• A novel method inspired by density functional theory (DFT) was employed.
• A mean-field description of quantum circuits was developed.
• Optimal single- and two-qubit gate functionals were formulated, analogous to DFT's exchange-correlation functionals.

Main Results:

• The method accurately predicts marginal single-qubit probabilities (SQPs) with over 90% accuracy for several classes of QCs.
• Simulations utilize memory and computational resources that scale linearly with qubit number.
• The approach avoids the need to compute the full QC wave function.

Conclusions:

• The DFT-inspired method offers a computationally efficient alternative for simulating quantum circuits.
• This formalism significantly expands the scale of quantum circuits that can be simulated.
• Future extensions of this method hold promise for further advancements in quantum computing research.