Quantum-state preparation with universal gate decompositions

TL;DR

This paper presents a simplified quantum circuit scheme for preparing arbitrary quantum states, reducing the circuit depth and CNOT gate count, which enhances the efficiency of quantum state preparation.

Contribution

It introduces a universal circuit scheme that leverages any full quantum gate decomposition, significantly reducing circuit depth and CNOT gate count for state preparation.

Findings

Reduces circuit depth by a factor of 2.

Decreases CNOT gates from 2^n to approximately 23/24 2^n.

Specifically lowers CNOT count from 11 to 9 and depth from 11 to 5 for four qubits.

Abstract

In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when judging the complexity of the circuit: the total number of CNOT gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of 2. It also reduces the total number of CNOT gates from 2^n to 23/24 2^n in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from 11 CNOT gates to 9 and the depth from 11 to 5 steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.