Decomposition of Unitary Matrices for Finding Quantum Circuits: Application to Molecular Hamiltonians

TL;DR

This paper introduces a group leaders optimization algorithm to decompose unitary matrices into minimal quantum gate sequences, facilitating efficient quantum circuit design for molecular Hamiltonians and other quantum algorithms.

Contribution

It presents a novel optimization-based method for decomposing unitaries into cost-effective quantum circuits, applicable to molecular Hamiltonians and scalable to larger systems.

Findings

Successfully decomposed known quantum gates like Toffoli and Fourier transform.

Designed quantum circuits for hydrogen and water molecule Hamiltonians.

Method reduces circuit complexity and cost for quantum simulations.

Abstract

Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.