量子机器学习入门：工程师指南

版权申诉

5星 · 超过95%的资源 48 浏览量更新于2024-07-03 收藏 1.74MB PDF 举报

"《工程师的量子机器学习导论》是一本深入浅出的教程，适合程序员和工程师了解量子计算和量子机器学习。该资源由Osvaldo Simeone撰写，发表在《信号处理基础与趋势》期刊上，涵盖量子位（qubits）、量子门、量子系统的基本概念以及量子纠缠等内容，旨在将读者引入这个前沿领域。" 量子机器学习是计算机科学与量子物理的交叉学科，它利用量子力学的原理来改进和加速机器学习算法。在本资源中，作者首先介绍了经典位（cbits）与量子位（qubits），这是理解量子计算的基础。经典位表示二进制信息，而量子位则能同时处于0和1的叠加态，这一特性使得量子计算具有并行处理的潜力。 1.1 引言部分概述了量子机器学习的基本概念，为后续章节铺垫。 1.2 随机经典位解释了信息在经典计算机中的存储方式。 1.3 量子位部分详细讨论了量子位的性质，包括叠加态和测量的概念。 1.4 单量子位量子门是量子计算的基本操作单元，如Hadamard门和Pauli门等在此被介绍。 1.5 幅度图和干涉理论展示了量子系统如何通过干涉现象实现超越经典计算的能力。 1.6 量子干涉是量子计算中重要的物理现象，允许量子系统表现出非经典的特性。 1.7 结论部分总结了前文，并为读者提供了深入研究的方向。 1.8 推荐资源列表提供了一些进一步学习量子机器学习的书籍和论文。 1.9 问题部分可能包含了一些练习题，帮助读者巩固理解。接下来，2.2节探讨了多个随机经典位，即多比特系统在经典计算中的作用。2.3节转向多量子位系统，介绍量子位如何以量子纠缠的形式相互关联，这是量子计算中的一大特点。2.4节阐述封闭量子系统的概念，以及单位变换和并行单量子位门的应用，这些是实现量子并行性的重要工具。最后，2.5节的"Entanglement"预示着将深入讨论量子纠缠，这是量子计算中一种至关重要的非局域性现象，对量子通信和量子信息处理有深远影响。这篇资源为工程师和程序员提供了一个全面的入门框架，涵盖了量子机器学习的基础知识，包括量子位的性质、量子门的操作和量子纠缠的概念，这些都是理解和实践量子计算与量子机器学习的关键。通过学习这些内容，读者将能够更好地把握这一新兴领域的核心思想和技术。

12 Classical Bit (Cbit) and Quantum Bit (Qubit)

qubit is described by a two-dimensional amplitude vector

|ψi =

= α

|0i + α

|1i. (1.14)

There are two key diﬀerences between the state

|ψi

in (1.14) of a

quantum qubit and the state p of a random cbit:

•

Unlike a probability vector

, the amplitude vector has complex

entries

and

. (Note that complex entries include real-valued

entries as a special case.)

•

The qubit state vector (1.14) has the deﬁning property of having

unitary norm, i.e.,

|||ψi||

= hψ|ψi = |α

+ |α

= 1. (1.15)

This condition is diﬀerent from the property (1.11) satisﬁed by

probability vectors, which stipulates that the sum of the entries

– and not the norm of the vector – equals 1. We observe that

property (1.15) is consistent with the convention introduced in

the previous section of considering all kets (and bras) to have

unitary norm.

While being distinct from the state of a random cbit, the qubit

state (1.14) recovers as special cases the two possible states, expressed

as one-hot amplitude vectors, of a deterministic cbit. In fact, setting

the amplitudes as

= 1 (and hence

= 0), or

= 1 (and hence

= 0), recovers the deterministic cbit states

and

, respectively.

Therefore, a qubit that can only assume states

and

is equivalent

to a deterministic cbit.

By (1.14), we say that the qubit is in a

superposition

of states

and

, with respective complex amplitudes

and

. Mathemat-

ically, this implies that the state of a qubit is a vector that lies in a

two-dimensional complex linear vector space, referred to as the

Hilbert

space

of dimension two. The states

and

form the so-called

com-

putational basis

of the Hilbert space. A geometric interpretation of a

quantum state, simpliﬁed by representing real amplitudes, is provided

by the left part of Fig. 1.1.

16 Classical Bit (Cbit) and Quantum Bit (Qubit)

of a qubit state as the square root of a probability vector. Even more

treacherously, this perspective may lead one to treat a qubit as merely

being a random cbit deﬁned by a probability vector

= [

|α

, |α

]

†

Accordingly, one would model a qubit in the superposition state (1.14)

as having a true, but unknown, classical state

|xi,

with

x ∈ {

}

, which

is only revealed upon measurement. This temptation should be resisted!

By Born’s rule (1.19), the viewpoint described in the previous

paragraph provides the correct description of the output of the standard

measurement of a qubit. However, a qubit in state (1.23) behaves very

diﬀerently from a random cbit state deﬁned by the probability vector

= [

|α

, |α

]

†

in terms of how it evolves over time and of how it

interacts with other qubits. Speciﬁcally, as we will detail in Sec. 1.6,

the two amplitudes

and

deﬁning the superposition state

|ψi

can

combine over time in ways that produce subsequent measurements that

cannot be described by the evolution of a random cbit. (So, Schrodinger’s

cat is actually neither dead nor alive, but it behaves according to a

superposition of the two states.)

1.4 Single-Qubit Quantum Gates

In this section, we describe how the state of a qubit evolves in a closed

quantum system, introducing the key concept of a quantum gate.

1.4.1 Closed Quantum Systems and Unitary Transformations

Consider a

closed quantum system

consisting of a single qubit that

is not subject to measurement. Note that implementing a measurement

would require the presence of an instrument connecting the qubit to

the outside world of an “observer”. In a closed system, by the laws of

quantum physics, the state of a qubit evolves according to

linear and

reversible transformations

. Linearity may come as a surprise, as

one may expect that nature could produce more complex behavior, but

it is a model that has stood the test of time through a large number of

experimental validations. Reversibility is a consequence of the principle

that a closed system should conserve information.

To elaborate on this last point, irreversible operations imply a loss of

剩余205页未读，继续阅读

chenxin0215

粉丝: 26
资源: 16

量子机器学习入门：工程师指南

量子神经网络：解决上下文多臂强盗问题的新突破

量子力学新解释推动量子AI与机器人融合：实证量子神经网络与优化应用

"量子信息掩蔽：研究进展与应用

Quantum machine learning for data scientists

Quantum Machine Learning_ What Quantum Computing Means to Data Mining

A Introduction to Quantum Computing for

Introduction to Quantum Mechanics

An Introduction to Quantum Computing

AN INTRODUCTION TO QUANTUM OPTICS

Introduction to Quantum Theory.pdf

最新资源