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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
© 2019 1QB Information Technologies. All rights reserved.�6
Quantum algorithms with quantum advantages
• Quantum Fourier transformation
• Quantum search algorithms
• Quantum simulation
© 2019 1QB Information Technologies. All rights reserved.�7
P
NP
QMA
BQP
P : Easy on classical computerNP : Difficult on classical computer
BQP : Easy on quantum computerQMA : Difficult on quantum computer
© 2019 1QB Information Technologies. All rights reserved.�8
Challenges in near-term quantum computing
• Number of qubits
• Noise and errors, short coherence
• Connectivity
• Error mitigation, quantum error correction
© 2019 1QB Information Technologies. All rights reserved. �9
Matrices for useful quantum computing
Circuit Depth
Num
ber o
f Qub
its Error Rate
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© 2019 1QB Information Technologies. All rights reserved.�10
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=">AAADKHicbVJdb9MwFHXD1ygfa+GRF4sKaUhQkoG0PU7wwuOQ1m1SEyrHuc2s2U5k37BkUX4KryDxa3hDe+WPgJtW2pruSLaOzjnX17ZunEth0fevet6du/fuP9h62H/0+MnT7cHw2bHNCsNhwjOZmdOYWZBCwwQFSjjNDTAVSziJzz8t/JNvYKzI9BFWOUSKpVrMBWfopNlgGFqhaAhlvvMW3x3Ngtezwcgf+y3oJglWZERWOJwNe//CJOOFAo1cMmungZ9jVDODgkto+mFhIWf8nKUwdVQzBTaq27s39JVTEjrPjFsaaaverKiZsrZSsUsqhme26y3E27xpgfP9qBY6LxA0XzaaF5JiRhcfQRNhgKOsHGHcCHdXys+YYRzdd/UdbjaK1Rsax6qhLdYsa7jE0r1SwwXPlGI6qUMDSTMNojpEKLF9U72Q6lHQdJKpAdDd7FK8JR3LArrhVltm++tp5jqyr3WYsDQF0z3Llo3bRKpcpNwwq2uz2jAvr81LZ7qRCboDskmOd8fB+/Hulw+jg4+r4dkiL8hLskMCskcOyGdySCaEkwvynfwgP71f3m/vj3e1jHq9Vc1zsgbv7397YAmn</latexit>
: Energy relaxationT1<latexit sha1_base64="bGDa/8zOq72V/YxcwWGdXwVEpGc=">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</latexit>
© 2019 1QB Information Technologies. All rights reserved.�11
|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=">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</latexit>
© 2019 1QB Information Technologies. All rights reserved.�12
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
© 2019 1QB Information Technologies. All rights reserved.�13
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
© 2019 1QB Information Technologies. All rights reserved. �14
• Superconducting qubits • Trapped ions • Ultracold atoms and molecules • Electron spin based • Topological qubits • etc.
Quantum hardware platforms
© 2019 1QB Information Technologies. All rights reserved. �15
© 2019 1QB Information Technologies. All rights reserved. �16
© 2019 1QB Information Technologies. All rights reserved. �17
© 2019 1QB Information Technologies. All rights reserved. �18
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
© 2019 1QB Information Technologies. All rights reserved. �19
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
© 2019 1QB Information Technologies. All rights reserved. �20
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
© 2019 1QB Information Technologies. All rights reserved. �21
© 2019 1QB Information Technologies. All rights reserved. �22
Variational Quantum Eigensolver
© 2019 1QB Information Technologies. All rights reserved. �23
[1512.06860]Experimental result : Google
Hydrogen molecule
© 2019 1QB Information Technologies. All rights reserved. �24
U = e�i✓X0Y1<latexit sha1_base64="0IF/33NT5chuzjRcEz9IJaF7WbY=">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</latexit>
Unitary Coupled Cluster:
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Experimental results: IBM [1704.05018]
Hardware-efficient ansatz
d=1
© 2019 1QB Information Technologies. All rights reserved. �26
H = J
X
ij
(XiXj + YiYj + ZiZj) +B
X
i
Zi
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Heisenberg model
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[1803.11173]Concentration of measure
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Schroedinger Equation
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[1611.09301]
Hybrid method for solving Schroedinger Eq
Error
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Imaginary time evolution
[1804.03023]
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VQE
VQE
LiH
42 parameters: Hardware efficient circuit: Random initial values
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Error Mitigation
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Experimental results: IBM
Error mitigation[1805.04492]
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