Given an arbitrary ${2}^{w}\ifmmode\times\else\texttimes\fi{}{2}^{w}$ unitary matrix $U$ , a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$ -qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. F\"uhr and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates ( $w=1$ ) to gates with arbitrary value of $w$ . The synthesized circuit consists of controlled one-qubit gates, such as negator gates and phasor gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled not gates in the case that $U$ is a permutation matrix.Given an arbitrary ${2}^{w}\ifmmode\times\else\texttimes\fi{}{2}^{w}$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. F\"uhr and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates ($w=1$) to gates with arbitrary value of $w$. The synthesized circuit consists of controlled one-qubit gates, such as negator gates and phasor gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled not gates in the case that $U$ is a permutation matrix.

arXiv:1512.07240Physical Review ANov 14, 201628 citations

Quantum Circuits for the Unitary Permutation Problem

Stefano Facchini, Simon Perdrix

arXiv:1405.5205Lecture notes in computer scienceJan 1, 201516 citations

OptQC: An optimised parallel quantum compiler

T. Loke, J. B. Wang

The software package \emph{Qcompiler} (CPC, 184 (2013) 853) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software \emph{OptQC}, which finds permutation matrices $P$ and $Q$ for a given unitary matrix $U$ such that the number of gates in the quantum circuit of $U = Q^TP^TU'PQ$ is significantly reduced, where $U'$ is equivalent to $U$ up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators.The software package \emph{Qcompiler} (CPC, 184 (2013) 853) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software \emph{OptQC}, which finds permutation matrices $P$ and $Q$ for a given unitary matrix $U$ such that the number of gates in the quantum circuit of $U = Q^TP^TU'PQ$ is significantly reduced, where $U'$ is equivalent to $U$ up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators.

arXiv:1408.1612Aug 7, 20140 citations

Quantum Matrices Using Quantum Gates

Manu Mitra

Jan 1, 20180 citations

Quantum Gates

Andreas Wichert

This chapter introduces Boolean quantum gates that allow us to map any Boolean circuit in such a way that the circuit becomes reversible. It describes quantum gates for one qubit, like for example Clifford gates that are the elements of the Clifford group and can be efficiently simulated with a classical computer. The chapter introduces the controlled-U gates and the unitary decomposition and formulate the process of transpilation. A Boolean quantum circuit represents a permutation in Hilbert space and can be represented by a unitary permutation matrix composed of the unitary matrices representing the quantum gates. Such a mapping does not alter the distribution of the amplitudes; the distribution remains unchanged during the execution of the quantum Boolean gates.This chapter introduces Boolean quantum gates that allow us to map any Boolean circuit in such a way that the circuit becomes reversible. It describes quantum gates for one qubit, like for example Clifford gates that are the elements of the Clifford group and can be efficiently simulated with a classical computer. The chapter introduces the controlled-U gates and the unitary decomposition and formulate the process of transpilation. A Boolean quantum circuit represents a permutation in Hilbert space and can be represented by a unitary permutation matrix composed of the unitary matrices representing the quantum gates. Such a mapping does not alter the distribution of the amplitudes; the distribution remains unchanged during the execution of the quantum Boolean gates.

Chapman & Hall/CRC eBooksNov 28, 20230 citations

Given an arbitrary ${2}^{w}\ifmmode\times\else\texttimes\fi{}{2}^{w}$ unitary matrix

U

, a powerful matrix decomposition can be applied, leading to four different syntheses of a

w

-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. F\"uhr and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates (

w=1

) to gates with arbitrary value of

w

. The synthesized circuit consists of controlled one-qubit gates, such as negator gates and phasor gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled not gates in the case that

U

is a permutation matrix.

P

and

Q

for a given unitary matrix

U

such that the number of gates in the quantum circuit of

U = Q^TP^TU'PQ

is significantly reduced, where

U'

is equivalent to

U

up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators.