introduction to quantum computing...© 2019 1qb information technologies. all rights reserved. gate...
TRANSCRIPT
![Page 1: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/1.jpg)
Shunji Matsuura
Introduction to Quantum Computing
Riken, 2019/ May 13-15
![Page 2: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/2.jpg)
© 2019 1QB Information Technologies. All rights reserved. �2
Initial problem with known solution
Target problem with unknown solution
Annealing path
Quantum Annealing
![Page 3: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/3.jpg)
© 2019 1QB Information Technologies. All rights reserved.
Gate Model Quantum ComputingQuantum circuits, analogue to digital circuits
�3
0
0
0 1
0 1
0 1
0
1
0 1
0 10 0
SolutionMeasurementIntermediate StateInitial State
Gate Operations
![Page 4: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/4.jpg)
© 2019 1QB Information Technologies. All rights reserved.
Challenges in simulating quantum systems on classical computers
Head-Gordon, Artacho Physics Today (2008)
2N<latexit sha1_base64="uT0jYvpOOUbqH+9n/9xBtnRTLFc=">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</latexit><latexit sha1_base64="uT0jYvpOOUbqH+9n/9xBtnRTLFc=">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</latexit><latexit sha1_base64="uT0jYvpOOUbqH+9n/9xBtnRTLFc=">AAADGHicbVLLbtQwFPWEVxleLSzZWIyQWKBRUlWCZQUbVqgIpq00Satr505q1XYi24FJrXwCW5D4GnaILTu+BjyZkdrJ9Ei2js459vW1LquksC6O/w6iGzdv3b6zdXd47/6Dh4+2dx4f2rI2HCe8lKU5ZmBRCo0TJ5zE48ogKCbxiJ2/XfhHn9FYUepPrqkwU1BoMRMcXJA+7p68P90exeO4A90kyYqMyAoHpzuDf2le8lqhdlyCtdMkrlzmwTjBJbbDtLZYAT+HAqeBalBoM9+9taXPg5LTWWnC0o526tUTHpS1jWIhqcCd2b63EK/zprWbvc680FXtUPNloVktqSvponGaC4PcySYQ4EaEt1J+Bga4C98zDLhaiKmXlDHV0g5rljVcunnoUuMXXioFOvepwbydJplPHc5d15NfSH6UtL1kYRB1P7sUr0kzWWM/3GnL7HA9DaEinPg0h6JA07/LztuwiUKFyHzDbC7NZsO8uDQvghlGJukPyCY53B0n8Tj5sDfaf7Mani3ylDwjL0hCXpF98o4ckAnhpCBfyTfyPfoR/Yx+Rb+X0WiwOvOErCH68x899wRR</latexit><latexit sha1_base64="uT0jYvpOOUbqH+9n/9xBtnRTLFc=">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</latexit>
|s1, s2 · · · sN i, si = {0, 1}<latexit sha1_base64="TdoGTuoVbmirhWBpZUuvWKbvpx0=">AAADQXicbVLdahQxGM2OP63r31YvvQkugsiyTIqgN0LRG6+kgtsWdsYhk/l2GppkhiRTdxqnz+DTeKvgU/gI3om3Xmh2dqHd2R5IOJxzki9f+NJScGPD8GcvuHb9xs2t7Vv923fu3rs/2HlwYIpKM5iwQhT6KKUGBFcwsdwKOCo1UJkKOExP3iz8w1PQhhfqg61LiCXNFZ9xRq2XksGzzyYhI5Ps4ohlhTXYJO8iTVUuYITPz03CX0UuHJGo6SeDYTgOW+BNQlZkiFbYT3Z6/6KsYJUEZZmgxkxJWNrYUW05E9D0o8pASdkJzWHqqaISTOzaphr8xCsZnhXaL2Vxq14+4ag0ppapT0pqj03XW4hXedPKzl7GjquysqDYstCsEtgWePFDOOMamBW1J5Rp7t+K2THVlFn/j32Py4VSOcJpKhvcYs0ymgk7910q+MQKKanKXKQha6YkdpGFuW17cgvJDUnTSeYaQHWzS/GKdCoq6IZbbZntr6epr0g/uiijeQ66e5eZN37jufSR+YZZX5j1hnl2YZ417ciQ7oBskoPdMQnH5P3z4d7r1fBso0foMXqKCHqB9tBbtI8miKEv6Cv6hr4HP4Jfwe/gzzIa9FZnHqI1BH//A1PpE44=</latexit><latexit sha1_base64="TdoGTuoVbmirhWBpZUuvWKbvpx0=">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</latexit><latexit sha1_base64="TdoGTuoVbmirhWBpZUuvWKbvpx0=">AAADQXicbVLdahQxGM2OP63r31YvvQkugsiyTIqgN0LRG6+kgtsWdsYhk/l2GppkhiRTdxqnz+DTeKvgU/gI3om3Xmh2dqHd2R5IOJxzki9f+NJScGPD8GcvuHb9xs2t7Vv923fu3rs/2HlwYIpKM5iwQhT6KKUGBFcwsdwKOCo1UJkKOExP3iz8w1PQhhfqg61LiCXNFZ9xRq2XksGzzyYhI5Ps4ohlhTXYJO8iTVUuYITPz03CX0UuHJGo6SeDYTgOW+BNQlZkiFbYT3Z6/6KsYJUEZZmgxkxJWNrYUW05E9D0o8pASdkJzWHqqaISTOzaphr8xCsZnhXaL2Vxq14+4ag0ppapT0pqj03XW4hXedPKzl7GjquysqDYstCsEtgWePFDOOMamBW1J5Rp7t+K2THVlFn/j32Py4VSOcJpKhvcYs0ymgk7910q+MQKKanKXKQha6YkdpGFuW17cgvJDUnTSeYaQHWzS/GKdCoq6IZbbZntr6epr0g/uiijeQ66e5eZN37jufSR+YZZX5j1hnl2YZ417ciQ7oBskoPdMQnH5P3z4d7r1fBso0foMXqKCHqB9tBbtI8miKEv6Cv6hr4HP4Jfwe/gzzIa9FZnHqI1BH//A1PpE44=</latexit><latexit sha1_base64="TdoGTuoVbmirhWBpZUuvWKbvpx0=">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</latexit>
Hilbert space dimension
Various classical methods:
Density functional theory Coupled Cluster (with truncation) Tensor network Monte Carlo
�4
![Page 5: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/5.jpg)
© 2019 1QB Information Technologies. All rights reserved.�5
Garnet Chan at IBM conference (2017)Classical frontiers
![Page 6: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/6.jpg)
© 2019 1QB Information Technologies. All rights reserved.�6
Quantum algorithms with quantum advantages
• Quantum Fourier transformation
• Quantum search algorithms
• Quantum simulation
![Page 7: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/7.jpg)
© 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
![Page 8: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/8.jpg)
© 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
![Page 9: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/9.jpg)
© 2019 1QB Information Technologies. All rights reserved. �9
Matrices for useful quantum computing
Circuit Depth
Num
ber o
f Qub
its Error Rate
n<latexit sha1_base64="3uD505hTeCdWQxuy/aEbnaDLkCw=">AAADFnicbVLLbtQwFPWkPMrwasuSjcUIiQUaJQgJlhVsWLYS01aahOrauZNatZ3IdmBSK1/Alkr9GnaILVu+BjyZkdrJ9Ei2js459vW1LquksC6O/w6irTt3793ffjB8+Ojxk6c7u3tHtqwNxwkvZWlOGFiUQuPECSfxpDIIikk8ZucfF/7xVzRWlPqzayrMFBRazAQHF6RDfbozisdxB7pJkhUZkRUOTncH/9K85LVC7bgEa6dJXLnMg3GCS2yHaW2xAn4OBU4D1aDQZr57aUtfBiWns9KEpR3t1JsnPChrG8VCUoE7s31vId7mTWs3e595oavaoebLQrNaUlfSRds0Fwa5k00gwI0Ib6X8DAxwFz5nGHCzEFOvKWOqpR3WLGu4dPPQpcZvvFQKdO5Tg3k7TTKfOpy7rie/kPwoaXvJwiDqfnYp3pJmssZ+uNOW2eF6GkJF+OLTHIoCTf8uO2/DJgoVIvMNs7k2mw3z4tq8CGYYmaQ/IJvk6M04icfJ4dvR/ofV8GyT5+QFeUUS8o7sk0/kgEwIJ0i+kx/kMrqKfka/ot/LaDRYnXlG1hD9+Q/DEQPN</latexit><latexit sha1_base64="3uD505hTeCdWQxuy/aEbnaDLkCw=">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</latexit><latexit sha1_base64="3uD505hTeCdWQxuy/aEbnaDLkCw=">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</latexit><latexit sha1_base64="3uD505hTeCdWQxuy/aEbnaDLkCw=">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</latexit>
![Page 10: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/10.jpg)
© 2019 1QB Information Technologies. All rights reserved.�10
A qubit is a 2 energy level quantum system.
|0i<latexit sha1_base64="yYj4HmDWx2VLt7LCBRh8Km+v7xU=">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</latexit>
|1i<latexit sha1_base64="iJffb1QG5R6plE8lC2zBaNMWJSs=">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</latexit>
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>
![Page 11: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/11.jpg)
© 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=">AAADIXicbVLLbtQwFPWEVxkebemSjcUIiQUaJdMRpbsKNiyL1GkrTcLIce6kVm0nsh2Y1MpvsAWJr+mu6g7xMeAkI9rJ9Ei2js459vXjxjln2vj+75537/6Dh482HvefPH32fHNr+8WxzgpFYUIznqnTmGjgTMLEMMPhNFdARMzhJD7/WPsnX0FplskjU+YQCZJKNmeUGCeFYcwLsEczO6qq2dbAH/oN8DoJlmSAljicbff+hklGCwHSUE60ngZ+biJLlGGUQ9UPCw05oeckhamjkgjQkW0OXeHXTknwPFNuSIMb9fYKS4TWpYhdUhBzprteLd7lTQszfx9ZJvPCgKRtoXnBsclw/QI4YQqo4aUjhCrmzorpGVGEGvdOfYfbhWLxFsexqHCDFUsrys3C3VLCN5oJQWRiQwVJNQ0iGxpYmOZOtpbsIKg6yVQByG62Fe9I1//UDTdam+2vpomrSL7YMCFpCqq7l15UbmKpcJHFmlnemOWaeXFjXjizaZn9wB/tvsMNGft7LQn2x/9b5ng0DHaHo8/jwcGHZfNsoJfoFXqDArSHDtAndIgmiKIcfUc/0E/vl3fpXXnXbdTrLdfsoBV4f/4BhfAI6Q==</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>
![Page 12: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/12.jpg)
© 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
![Page 13: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/13.jpg)
© 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
![Page 14: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/14.jpg)
© 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
![Page 15: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/15.jpg)
© 2019 1QB Information Technologies. All rights reserved. �15
![Page 16: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/16.jpg)
© 2019 1QB Information Technologies. All rights reserved. �16
![Page 17: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/17.jpg)
© 2019 1QB Information Technologies. All rights reserved. �17
![Page 18: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/18.jpg)
© 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
![Page 19: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/19.jpg)
© 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
![Page 20: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/20.jpg)
© 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
![Page 21: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/21.jpg)
© 2019 1QB Information Technologies. All rights reserved. �21
![Page 22: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/22.jpg)
© 2019 1QB Information Technologies. All rights reserved. �22
Variational Quantum Eigensolver
![Page 23: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/23.jpg)
© 2019 1QB Information Technologies. All rights reserved. �23
[1512.06860]Experimental result : Google
Hydrogen molecule
![Page 24: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/24.jpg)
© 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:
![Page 25: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/25.jpg)
© 2019 1QB Information Technologies. All rights reserved. �25
Experimental results: IBM [1704.05018]
Hardware-efficient ansatz
d=1
![Page 26: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/26.jpg)
© 2019 1QB Information Technologies. All rights reserved. �26
H = J
X
ij
(XiXj + YiYj + ZiZj) +B
X
i
Zi
<latexit sha1_base64="pt6ydlSIz00vbqzzCZT5qqMGCkc=">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</latexit>
Heisenberg model
![Page 27: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/27.jpg)
© 2019 1QB Information Technologies. All rights reserved. �27
[1803.11173]Concentration of measure
![Page 28: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/28.jpg)
© 2019 1QB Information Technologies. All rights reserved. �28
![Page 29: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/29.jpg)
© 2019 1QB Information Technologies. All rights reserved. �29
Schroedinger Equation
![Page 30: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/30.jpg)
© 2019 1QB Information Technologies. All rights reserved. �30
[1611.09301]
Hybrid method for solving Schroedinger Eq
Error
![Page 31: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/31.jpg)
© 2019 1QB Information Technologies. All rights reserved. �31
H2<latexit sha1_base64="eAUp7Vb4mEpx3S/qi0Fa6z9KfxA=">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</latexit><latexit sha1_base64="eAUp7Vb4mEpx3S/qi0Fa6z9KfxA=">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</latexit><latexit sha1_base64="eAUp7Vb4mEpx3S/qi0Fa6z9KfxA=">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</latexit><latexit sha1_base64="eAUp7Vb4mEpx3S/qi0Fa6z9KfxA=">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</latexit>
Imaginary time evolution
[1804.03023]
![Page 32: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/32.jpg)
© 2019 1QB Information Technologies. All rights reserved. �32
VQE
VQE
LiH
42 parameters: Hardware efficient circuit: Random initial values
![Page 33: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/33.jpg)
© 2019 1QB Information Technologies. All rights reserved. �33
![Page 34: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/34.jpg)
© 2019 1QB Information Technologies. All rights reserved. �34
![Page 35: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/35.jpg)
© 2019 1QB Information Technologies. All rights reserved. �35
Error Mitigation
![Page 36: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/36.jpg)
© 2019 1QB Information Technologies. All rights reserved. �36
Experimental results: IBM
Error mitigation[1805.04492]
![Page 37: Introduction to Quantum Computing...© 2019 1QB Information Technologies. All rights reserved. Gate Model Quantum Computing Quantum circuits, analogue to digital circuits 3 © 2019](https://reader033.vdocument.in/reader033/viewer/2022042309/5ed6e250df0eda5e752ae5a1/html5/thumbnails/37.jpg)
© 2019 1QB Information Technologies. All rights reserved. �37