Universal Programmable Quantum Circuit Schemes to Emulate an Operator

TL;DR

This paper introduces two general programmable quantum circuit schemes capable of simulating any operator by adjusting rotation gate angles, enabling flexible and efficient quantum simulations including molecular Hamiltonians.

Contribution

The authors present novel circuit schemes that are independent of matrix decomposition, allowing high-accuracy simulations of non-unitary and unitary operators with minimal classical computation.

Findings

Circuits can simulate any operator by setting rotation angles.

Complexity analysis shows similar quantum costs to non-general circuits.

High-accuracy molecular Hamiltonian simulations demonstrated.

Abstract

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. They have almost the same quantum complexities as non-general circuits. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.