AutoQC Automated Synthesis of Quantum Circuits Using Neural Network Kentaro Murakami

2025-04-27 0 0 647.13KB 9 页 10玖币

侵权投诉

AutoQC: Automated Synthesis of Quantum Circuits

Using Neural Network

Kentaro Murakami

Kyushu University

Fukuoka, Japan

murakami.kentaro.514@gmail.com

Jianjun Zhao

Kyushu University

Fukuoka, Japan

zhao@ait.kyushu-u.ac.jp

Abstract—While the ability to build quantum computers is

improving dramatically, developing quantum algorithms is very

limited and relies on human insight and ingenuity. Although

a number of quantum programming languages have been

developed, it is challenging for software developers who are

not familiar with quantum computing to learn and use these

languages. It is, therefore, necessary to develop tools to support

developing new quantum algorithms and programs automatically.

This paper proposes AutoQC, an approach to automatically

synthesizing quantum circuits using the neural network from

input and output pairs. We consider a quantum circuit a

sequence of quantum gates and synthesize a quantum circuit

probabilistically by prioritizing with a neural network at each

step. The experimental results highlight the ability of AutoQC

to synthesize some essential quantum circuits at a lower cost.

Keyword – Quantum computing; program synthesis; neu-

ral network; software development

I. INTRODUCTION

In recent years, the practical use of quantum computers

has been advancing. While the ability to build quantum

computers is improving dramatically [1], the ability to develop

quantum algorithms is very limited and relies on human insight

and ingenuity. Although a number of quantum programming

languages such as Q# [2], Scaffold [3], OpenQASM [4],

ProjectQ [5], and Qiskit [6] have been developed, it is still

challenging for software developers who are not familiar with

quantum computing to learn and use these languages. There-

fore, it is necessary to develop tools to support the automated

development of new quantum algorithms and circuits.

Program synthesis [7] is the task of automatically construct-

ing executable code fragments, given a user’s intent, using

various forms of constraints, such as input-output examples,

demonstrations, and natural languages. Program synthesis has

direct applications [8], [9] for various users such as students

and teachers, software developers, and algorithm designers in

classical computing. Recently, the idea of program synthesis

has also been applied to quantum computing to support the

synthesis of quantum circuits during the quantum compiling

process [10], [11]. In this thread of research, quantum circuit

synthesis is regarded as a process in which an arbitrary unitary

operation is decomposed into a sequence of gates from a

universal set, typically one which a quantum computer can

implement both efﬁciently and fault-tolerantly. That is, given

an arbitrary quantum circuit Cand a universal gate set G, one

seeks to ﬁnd a decomposition UkUk−1. . . U2U1=C, where

Ui∈G. However, there is little research on program synthesis

in the quantum computing domain that aims to help software

developers synthesize quantum circuits and code pieces.

This paper proposes AutoQC, an approach to automatically

synthesizing quantum circuits using the neural network from

input and output pairs. In contrast, to support the quantum

compilation process, our goal is to help software developers

automatically synthesize a quantum circuit or algorithm using

machine learning from a problem speciﬁcation provided as

an example of assumed input/output pairs. As the ﬁrst step,

this paper focuses on quantum circuits with classical inputs

and outputs, i.e., the problem to be solved by the quantum

algorithm is classical bits.

Our paper makes the following contributions:

•Synthesis Approach. It presents a novel automated syn-

thesis approach that uses a neural network to explore the

space of possible quantum circuit designs by using the

input-output pairs.

•Tool Support: It implements a synthesis tool called

AutoQC to support the automated synthesis of quantum

circuits.

•Experimental Results: It presents experimental results

using AutoQC to synthesize seven quantum circuits

from their input-output pairs automatically. The results

highlight the ability of AutoQC to synthesize some

important quantum circuits.

The rest of the paper is organized as follows. Section II

brieﬂy introduces quantum computers and their computations

as a prerequisite for explaining our approach. Section III

describes our approach for automatically synthesizing quan-

tum circuits, and Section IV describes some experiments on

synthesizing quantum circuits using our approach. Section V

discusses related work, and concluding remarks are given in

Section VI.

II. BACKGROUND

First, we introduce some basic information on quantum

computation. More detailed reading material can be found in

the book by Nielsen and Chuang [12].

arXiv:2210.02766v1 [cs.SE] 6 Oct 2022

A. Quantum State and Quantum Bit

In a classical computer, information is represented by two

states, 0 and 1. For example, the two states are represented

by the on/off state of a switch, the state in which a charge is

accumulated and the state in which it is not, and the high/low

voltage. On the other hand, quantum mechanics allows the

superposition of two different states, so the ”quantum” bit,

the smallest unit of information in the quantum world, can

be described using two complex numbers αand β.αand β

are called complex probability amplitudes and represent the

weight with which the 0 and 1 states are superimposed. The

reason why αand βare complex numbers is that in quantum

theory, discrete quantities such as 0 and 1 have the properties

of waves and can interfere.

The states corresponding to the 0 and 1 of the classical bits

can be represented using Dirac’s bracket notation, which is a

simpliﬁed representation of the column vector, as follows:

|0i=1

0,|1i=0

1

Since |0iand |1iform an orthonormal basis, the qubit state

|ψican be represented by a linear combination of |0iand |1i.

|ψi=α|0i+β|1i=α

β

1) Probability Amplitude: In quantum mechanics, the ob-

server cannot directly interfere with the complex probability

amplitude, and the probability of 0 or 1 is determined only

when a measurement operation is performed. The complex

probability amplitude inﬂuences the probability distribution of

the measurement result. The probability that the measurement

result will be 0 or 1 is denoted as p0and p1, respectively. Then

these probabilities are expressed as the square of the absolute

value of the complex probability amplitude:

p0=|α|2, p1=|β|2

A normalization condition |α|2+|β|2= 1 is imposed to

make the sum of the probabilities be equal to 1.

When a measurement is performed, the quantum state

transitions to the state corresponding to the measurement

result. Speciﬁcally, when the measurement result is 0, the state

transitions to |0i; when it is 1, the state transitions to |1i.

This measurement is called a projective measurement in the

orthonormal basis |0iand |1i.

2) Multiple Qubits: When there are n qubits, their states

are represented using tensor products.

The states of the n classical bits are represented by n 0

or 1 number, with a total of 2npatterns. Since quantum

mechanics allows the superposition of all these patterns, the

state of n qubits can be described by 2ncomplex probability

amplitudes. Each complex probability amplitude represents

which bit sequence is superimposed with which weight.

|ψi=c00...0|00 . . . 0i+c00...1|00 . . . 0i+· · ·+c11...1|11 . . . 1i=







c00...0

c00...1

c11...1







The complex probability amplitudes are assumed to be

normalized: X

ii,...,in

|cii,...,in|2= 1

Then, when we measure the quantum state of these n

qubits, the bit sequence ii, . . . , inis obtained randomly with

probability pii,...,in=|cii,...,in|2, and the state after the

measurement is |ii, . . . , ini.

Thus, the state of n-qubits must be described by a complex

vector of 2ndimensions, which is exponentially large with

respect to n. This is where the difference between a classical

bit and a qubit becomes apparent. The operations on an n-

qubits system are then represented as a 2n×2ndimensional

unitary matrix.

B. Quantum Gates

We ﬁrst describe how operations on qubits are represented,

which is closely related to the following properties of quantum

mechanics:

•Liniarity: The time evolution of a quantum state is

always linear with respect to the superposition of the

states. Since the quantum state of a qubit is represented as

a normalized two-dimensional complex vector, operations

on a qubit, linear operations, are represented by a 2×2

complex matrix.

•Unitarity: Furthermore, using the normalization condi-

tion that the sum of the probabilities is always 1, we can

derive the following constraint on quantum operations U:

U†U=UU†=I

In other words, quantum operations are represented by

unitary matrices.

Here, let us review the terminology. In quantum mechanics,

a linear transformation of a state vector is called an operator,

and the term operator refers to any linear transformation that

is not necessarily unitary. On the other hand, linear transfor-

mations that satisfy the unitarity are called quantum gates.

A quantum operation can be thought of as an operator on a

quantum state that is physically feasible, at least theoretically.

1) Single Qubit Gates: The ﬁrst single-qubit gate is the X

gate, corresponding to NOT in classical computers. The X gate

is one of the Pauli operators of basic quantum arithmetic and

is a matrix such that

X=0 1

1 0 

X gate acts as follows:

X|0i=|1i, X |1i=|0i

Next is the V and V†gates, both of which are a square root

of the X gate as described below:

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

AutoQC:AutomatedSynthesisofQuantumCircuitsUsingNeuralNetworkKentaroMurakamiKyushuUniversityFukuoka,Japanmurakami.kentaro.514@gmail.comJianjunZhaoKyushuUniversityFukuoka,Japanzhao@ait.kyushu-u.ac.jpAbstractWhiletheabilitytobuildquantumcomputersisimprovingdramatically,developingquantumalgorithmsisver...

展开>> 收起<<

AutoQC Automated Synthesis of Quantum Circuits Using Neural Network Kentaro Murakami.pdf

共9页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

AutoQC Automated Synthesis of Quantum Circuits Using Neural Network Kentaro Murakami

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: