Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate...

Shunji Matsuura

Introduction to Quantum Computing

Riken, 2019/ May 13-15

© 2019 1QB Information Technologies. All rights reserved. �2

Initial problem with known solution

Target problem with unknown solution

Annealing path

Quantum Annealing

© 2019 1QB Information Technologies. All rights reserved.

Gate Model Quantum ComputingQuantum circuits, analogue to digital circuits

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SolutionMeasurementIntermediate StateInitial State

Gate Operations

© 2019 1QB Information Technologies. All rights reserved.

Challenges in simulating quantum systems on classical computers

Head-Gordon, Artacho Physics Today (2008)

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Hilbert space dimension

Various classical methods:

Density functional theory Coupled Cluster (with truncation) Tensor network Monte Carlo

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© 2019 1QB Information Technologies. All rights reserved.�5

Garnet Chan at IBM conference (2017)Classical frontiers


Quantum algorithms with quantum advantages

• Quantum Fourier transformation

• Quantum search algorithms

• Quantum simulation


P

NP

QMA

BQP

P : Easy on classical computerNP : Difficult on classical computer

BQP : Easy on quantum computerQMA : Difficult on quantum computer


Challenges in near-term quantum computing

• Number of qubits

• Noise and errors, short coherence

• Connectivity

• Error mitigation, quantum error correction


Matrices for useful quantum computing

Circuit Depth

Num

ber o

f Qub

its Error Rate

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A qubit is a 2 energy level quantum system.

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Probability of being in |1i<latexit sha1_base64="iJffb1QG5R6plE8lC2zBaNMWJSs=">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</latexit>

⇠ exp(�t/T1)<latexit sha1_base64="rn0HbC3NhQ3b6kvJOmQjOxrsB5g=">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</latexit>

: Energy relaxationT1<latexit sha1_base64="bGDa/8zOq72V/YxcwWGdXwVEpGc=">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</latexit>


|1i<latexit sha1_base64="iJffb1QG5R6plE8lC2zBaNMWJSs=">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</latexit>

|0i<latexit sha1_base64="yYj4HmDWx2VLt7LCBRh8Km+v7xU=">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</latexit>

Probability of being in |0i<latexit sha1_base64="yYj4HmDWx2VLt7LCBRh8Km+v7xU=">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</latexit>

t<latexit sha1_base64="QOXibzq8kKnWftyynaCMmG92/eU=">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</latexit>

: DephasingT'<latexit sha1_base64="CTv4h+CSXjVOmMa6Q6ackpVFfQE=">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</latexit>

T2<latexit sha1_base64="BHe6FMfSGfh0KiUCrpFvpxTVzCg=">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</latexit>

: Overall decoherence time1

T2=

1

2T1+

1

T'<latexit sha1_base64="+vaTz00TJ1B1gvPsN9J8A4FkPAY=">AAADT3icbVJdb9MwFHVbPrbysQ4eebGokJBAVZJVbHtAmuCFxyG126SmVI5zm1qznch2RjvLf4VfwytIPPJLeAPctLB+7EiOTs45zvV1blJwpk0Q/KzVG3fu3ru/s9t88PDR473W/pMznZeKQp/mPFcXCdHAmYS+YYbDRaGAiITDeXL5fu6fX4HSLJc9MytgKEgm2ZhRYrw0ah3FCS/B2jDOfQz3RjZy7u2/16g3Ct2rFTO+IqqYMOfcqNUOOkEFvE3CJWmjJU5H+7U/cZrTUoA0lBOtB2FQmKElyjDKwTXjUkNB6CXJYOCpJAL00FYtOvzCKyke58ovaXClru6wRGg9E4lPCmImetObi7d5g9KMj4aWyaI0IOmi0Ljk2OR4fl84ZQqo4TNPCFXMnxXTCVGEGn+rTY/VQol4jZNEOFxhzdKKcjP1XUr4THMhiExtrCB1g3BoYwNTU/Vk55Jth24jmSkAuZldiLek5/90M1xpi2xzPU18RfLJxinJMlCb39JT5x8sEz4y3TJnN+Zsy7y+Ma+9WY3McRhEB29wRbrB4YKEx93/I3MWdcKDTvSx2z55txyeHfQMPUcvUYgO0Qn6gE5RH1H0BX1F39D3+o/6r/rvxjJary3JU7SGxu5fZbsZBg==</latexit>


Gate fidelity

Probability of being in |0i<latexit sha1_base64="X+1HHh4qZpv7/X39rwUE4SLRgyQ=">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</latexit>

A0↵m +B0

<latexit sha1_base64="JhDmP3HtWpk1QY9xNW/7zjWSNWs=">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</latexit>

↵<latexit sha1_base64="A7UBF+hIbCV2wpovscvwDv4mtCs=">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</latexit>

Error per gate

Fidelity

m


Readout fidelity

1

2[P (1|0) + P (0|1)]

<latexit sha1_base64="dOgcOjfv2ZWXXIjEfVI1Rbs9h4I=">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</latexit>

Readout error:

Fidelity = 1- Readout error


• Superconducting qubits • Trapped ions • Ultracold atoms and molecules • Electron spin based • Topological qubits • etc.

Quantum hardware platforms


6

3

11

Hardware Platforms

Max

imum

Deg

ree

of C

onne

ctiv

ity

0

2

4

6

8

10

12

IBM Q20 Tokyo Rigetti 19Q IonQ

Maximum Degree of Connectivity Realized Between Qubits in Current Hardware Platforms


99.991.72 93.3

99.8

Hardware Platforms

Read

-Out

Fid

eliti

es (%

)

0

25

50

75

100

Google Bristlecone IBM Q20 Tokyo Rigetti 19Q IonQ

Read-Out Gate Fidelities for Current Hardware Platforms


Year

Num

ber o

f Qub

its

0

50

100

150

1995 2000 2005 2010 2015 2020

Realized Number of Qubits

Trendline for Number of Qubits

Chronological Increase in Number of Qubits as a Function of Time

Oxford University, UK

IBM, UC Berkley, Stanford, MIT

NEC

Los Alamos National Laboratory,US

Technical University of Munich, Germany

Institute for Quantum Computing, Perimeter Institute for Theorietical Physics, MIT

IBM IonQ

Rigetti: 16Q Aspen Intel

Rigetti: 19Q Acorn IBM: Tokyo

IBM Intel: Tangle Lake

Google: Bristlecone

IonQ

Rigetti

IonQ

Prototype Number of Qubits


Variational Quantum Eigensolver


[1512.06860]Experimental result : Google

Hydrogen molecule


U = e�i✓X0Y1<latexit sha1_base64="0IF/33NT5chuzjRcEz9IJaF7WbY=">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</latexit>

Unitary Coupled Cluster:


Experimental results: IBM [1704.05018]

Hardware-efficient ansatz

d=1


H = J

X

ij

(XiXj + YiYj + ZiZj) +B

X

i

Zi

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Heisenberg model


[1803.11173]Concentration of measure


Schroedinger Equation


[1611.09301]

Hybrid method for solving Schroedinger Eq

Error


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Imaginary time evolution

[1804.03023]


VQE

VQE

LiH

42 parameters: Hardware efficient circuit: Random initial values


Error Mitigation


Experimental results: IBM

Error mitigation[1805.04492]

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