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👩‍🎓 | The University of Tokyo and Quantum Computer ② Quantum Education


The University of Tokyo and Quantum Computer ② Quantum Education

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"Quantum computers on the cloud and quantum computers installed in Kawasaki are also practiced by throwing jobs and having them calculate, so the inside of the hardware where the calculations are done is a black box in a sense. is.

The University of Tokyo concludes an academic partnership with IBM in 2019 to bring human resources who can lead quantum technology in the world ... → Continue reading

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Quantum computer

Quantum computer (Ryoshi computer,British: quantum computer) (Quantum computer)Superposition,EntanglementSaidQuantum mechanicsIt is expected to solve problems that could not be solved in a realistic time and scale with a conventional computer using a conventional phenomenon.Computer. "Quantum gateThere is a lot of research on the principle of quantum computation using ", but other methods are also being researched and developed.

Conventional general such as so-called electronic type[1]The elements of a computer (hereinafter referred to as "classical computer") are情报About, you can only have one of the states that represents some binary value such as "0 or 1"bit”.Quantum computer is "Qubit'' (British: qubit; quantum bit, Cubit) bySuperpositionHandles information according to the state.

n If you have a qubitThe state of is calculated at the same time,You can get the result of superimposing pieces.However, even if the superimposed results are observed, only one randomly selected result can be obtained, which is not as fast as that of a classical computer.In order to obtain high speed, an algorithm dedicated to quantum computers that has been devised to obtain the desired answer with high probability is indispensable.If thousands of qubits of hardware are realized, using multiple qubits, a quantum computer will be of a scale that cannot be realized by a classical computer.Parallel computingIs said to be realized.

Regarding the capabilities of quantum computers, there are discussions on the theory of computation and on the actual machines that are actually being realized.#Computational powerSee section.About the capabilities of real machines#actualSee section.


1980 era

The history of quantum computers showed in 1980 that Paul Benioff could perform calculations in quantum systems without consuming energy.[2]In 1982,FeynmanAlso speculates that quantum computation is exponentially effective for classical computation.[3]..Following these, in 1985,DeutschIs "quantumComputation modelCan be said(English edition[4]Defined in 1989Quantum circuit[5]Invented.

1990 era

In 1992, with Deutsch(English editionIs a problem that quantum computers can solve faster than classical computersDeutsch-Jozsa's algorithmDevised[6].. In 1993,(English editionAnd student Ethan Bernstein(English edition(English editionInvented the algorithm of[7].

In 1994Peter shoreIs a practical algorithm "(English edition[8]], And ignited research on quantum computers.This is the quantum Fourier transform of Vazirani et al. And the study of Simon in the same year.[9]Is based on.Shor's algorithm, which is an algorithm peculiar to quantum computers, cannot be solved in a realistic time on classical computers.Prime factorizationBecause it can be executed in an extremely short time, we took advantage of the difficulty of prime factorization.RSA encryptionIt has been shown that the safety of is broken if a practical quantum computer is realized.

In 1995,Andrew Steane[10],Peter shore[11]Invented an algorithm for quantum error correction. In 1996,(English editionIs then applied to various algorithmsGrover's algorithm[12]Was devised.same year,Serge ArrocheBy experimental observationQuantum decoherenceProve and [13][14] It has been demonstrated that quantum decoherence is an obstacle to the realization of quantum computers. In 1997, by Edward Farhi and Sam GutmannQuantum walk[15](Continuous-time quantum walk, Abbreviation: CTQW) was devised. In 1998, QCL (QCL), a programming language for quantum computersQuantum Computation Language) Implementation has been published.

またHidetoshi Nishimoriby,Quantum annealing methodThe proposal was also in this era.

2000 era

hardwareSignificant progress has been made in development, in 2008Ion trapExpertDavid WinelandIs an individual ionLaser coolingAnd show that it can be captured individuallyEntanglementManipulate the ions in the state,Trapped ion quantum computerResearch has progressed.[16]

Shor's algorithm was introduced in 2001Nuclear magnetic resonance[17]By 2007Quantum optics[18]By light in 2009Integrated circuit[19]By 15Prime factorization (= 3 * 5) has been implemented.

2010 era

Suddenly in 2011カナダCompaniesD-Wave Systems Succeeded in building the quantum computer "D-Wave"Announced. D-Wave isn't a quantum-gate computer described in many parts of this article.Quantum annealing methodSpecialized in optimization calculation byDedicated computerIs.The original one was 128 qubits[20].. At first, there were many doubts as to whether D-Wave really realized quantum computing, but a research paper that certainly attributed it to quantum computing was published in the English scientific journal Nature.[21]As of January 2018, it has been firmly regarded as a venture company led by Google has started collaboration with D-Wave.

2012 years,Serge ArrocheDavid Wineland Nobel Prize in PhysicsWas awarded.The reason for the award is "Achievements on epoch-making experimental methods that enable measurement and control of individual quantum systems".

Edward SnowdenAccording to the disclosure document ofNSAIt is said that practical application for decryption is being researched in[22].

September 2014 USGoogleCompanyUCSBAnnounced that it will start its own development of quantum computer in collaboration with John Martinis of[23].

2016 year 5 month,IBMIs a 5 qubit quantum computer[24]Was published online.Tested by a professor at the University of Waterloo, David Corey, we were able to get almost the same results.[25].. In May 2017, IBM announced that it had developed a 5-qubit processor for IBM Q, its general-purpose quantum computer system.[26]

January 2019, 1, IBMCESAnnounced that it has developed the world's first commercial quantum computer (name: IBM Q System One).[27].

October 2019, 10, Google is the fastest in the worldSuper computerQuantum computer solves a computational problem that takes 1 yearsSycamore processorSucceeded in solving in 3 minutes and 20 secondsQuantum supremacyAnnounced that it was the first in the world to demonstrateThunder Pichai The地球First took off fromSpace rocketSaid that the result was comparable to[28][29].

2020 era



Quantum computer peculiaralgorithmAre known, and traditionally show the famous ones.Other thingsQuantum Algorithm Zoo[32]See also.

Shor's algorithm

(English edition(British: Shor's factorizationTomo) is a high-speed (tomo) factorization problem.Polynomial timeIt is an algorithm that can be solved.In classical computers, only algorithms that solve in unrealistic time () are known. In 1994Peter shoreDiscovered by[8][33]..The shore is this case,Nevanlinna PrizeGodel PrizeWas awarded.

Succeeded in factoring 2001 (= 12 × 7) on a 15 qubit quantum computer at IBM Research-Almaden Laboratory in December 3 (Nature, December 5 issue)[17]).

Discrete logarithm problem (DLP, ElGamal encryption,Elliptic curve cryptographyThe basis of safety) can also be solved in polynomial time.An extension of the basic idea of ​​this algorithm is the quantum algorithm for the commutative hidden subgroup problem.Currently, research is underway to extend this to the non-commutative hidden subgroup problem.

Shor's algorithm is a quantum computerDiscrete Fourier transformBy being able to execute at high speed.Also, the whole algorithm is stochastic (BQP), And try again and again until you get the correct answer.

N In factoringa The N AgainstVegetarianNumbera Mod N Order, min {x > 0 |ax Find = 1 (mod N)}.in short,ax Cycle r To ask.If the order is obtained at high speed, factorization can be performed at high speed.

For example,N = 15, a = 7.

70 = 1 (mod 15)
71 = 7 (mod 15)
72 = 4 (mod 15)
73 = 13 (mod 15)
74 = 1 (mod 15)
75 = 7 (mod 15)
76 = 4 (mod 15)
77 = 13 (mod 15)
78 = 1 (mod 15)
79 = 7 (mod 15)

A sequence of period 1,7,4,13,1,7,4,13,1,7 of 4, ... is generated.

Therefore, the cycle r = min {x > 0 | 7x = 1 (mod 15)} = 4

The outline of the procedure is the following two.

  1. All of x Is initialized so that the probabilities are even.And that ax against N Only have probabilities and convert them evenly.Although this calculation is quantum computer-like, the basic idea is the same as that of a classical computer.For that purpose, we prepare addition / subtraction of binary numbers and conditional branching by bits.
  2. ax against N Is the cycle r have.This is the order obtained by this cycle.Therefore, the result obtained in 1 is subjected to the discrete Fourier transform.Then the frequency 1 /r Since the probability of the place becomes large, when observing, there is a high probability r Is obtained.If it fails, repeat until it succeeds.

Grover's algorithm

n Specific data from among the individual data n Algorithms that can be obtained in steps.To be exact, from 1 N One value of, the oracle function f(z) Becomes 1, otherwise f(z) = 0, Oracle function f Atf(z) = 1 z The problem of seeking.An oracle function is a function with zero complexity.Approximately on a classical computer n/ 2 steps are required. In 1996(English editionAnnounced by[12][34]..Very wide varietyProbabilistic algorithmIn combination with or quantum algorithms, the calculation time can be reduced to its square root.Its effect is not as dramatic as Shor's algorithm, but it is characterized by its wide range of applications.The search conditions and search targets have been improved.

This algorithm assumes that you have enough qubits to match the number of data, but if you have enough parallelism to match the data on a classical computer,f(z) = 1 to look for O(1), the problem of finding the minimum value of the function isO(log log n).

Deutsch-Jozsa's algorithm

Quantum walk

Random walkIs executed on a quantum computer.Several algorithms have been created using this.

Discrete Fourier transform

Against amplitudeDiscrete Fourier transformHowever, it should be noted that the amplitude cannot be observed directly.Used in Shor's algorithm. The source code in QCL is as follows.The variable q is subjected to a discrete Fourier transform. V is conditional phase, H isHadamard transform.

for i = 1 to #q {
 for j = 1 to i - 1 {
  V(pi / 2^(i - j), q[#q - i] & q[#q - j]);
 H(q[#q - i]);

Programming language

For quantum computersProgramming languageAnd itsProcessing systemMany implementation methods of QCL have been proposed.[35]and so on.Detail is,Quantum programming language See.


Many simulators have been created to execute quantum computer algorithms by simulation.For the list,List of QC simulators[36]See.


The hardware is physically equivalent to a quantum gateNuclear magnetic resonance,Quantum optics,Quantum dot,Superconductivityelement,Laser coolingSince it can be configured by such means, various experimental hardware implementation methods are being researched.

Nuclear magnetic resonance / electron spin resonance

in recent years,Nuclear magnetic resonance(NMR) andElectron spin resonanceQuantum computer research and development using[17][37][38][39][40].

In 2001, prime factorization by a 7-qubit quantum computer was implemented.[17][37]..1998 qubits in 2, 1999 qubits in 3, 2000 qubits in 5, 2001 qubits in 7 by nuclear magnetic resonance (NMR)[38], 2005 8 qubit[39], 2006 12 qubits[40]Was realized. The degree of parallelism doubles with each additional qubit.

Osaka University in Japan[41]And Okinawa Institute of Science and Technology Graduate University[42]Is the main research base, and experiments on quantum information processing using nuclear spins and electron spins are being conducted.

Nitrogen vacancy defect spin / Silicon nuclear spin

Yokohama National University in Japan[43], Kyoto University[44]Is the main research base, and experiments on quantum media conversion and quantum information processing using nitrogen vacancy defects are being conducted.Also Keio University[45] Is conducting a quantum information processing experiment using nuclear spins in silicon.

Quantum dot

RIKEN in Japan[46], The University of Tokyo[47]Is the main research base, and efforts are being made toward the realization of quantum computers.

Quantum optics

In particularPhotonThose usingPhoton computer,Photon computerAlso called. 2001,Nonlinear opticsA method was devised to create a quantum computer without using[48]..Linear photon computer (British: linear optical quantum computer, LOQC), and later became the mainstream of photon computers.

2007 years,PhotonWas implemented in prime factorization by a 4qubit quantum computer[18]..Furthermore, in 2009, prime factorization by a 4qubit quantum computer was implemented on an optical integrated circuit (silicon photonics).[19].

September 2017, Graduate School of Engineering, The University of TokyoAkira FurusawaProfessor and Assistant Professor Shuntaro Takeda invent and announce large-scale photon computer realization method[49].

2020 ChineseNine chaptersRealized the world's first quantum feasibility in a computer using photons and became a hot topic all over the world.[50].

The University of Tokyo is the main research base in Japan[51]And Tokyo University of Science[52]Is mentioned.

Superconducting element

The qubit of a quantum computer using a superconducting element isJosephson JunctionIt is composed of a superconducting circuit using[53][54][55][56]..Charges in superconducting circuits (Cooper vs.A qubit using the degrees of freedom of) is called a charge qubit or a Cooper pair box. 1999,NECRealized by Nakamura, Pashkin, Cai and others in[53]..The coherence time of qubits at that time was about 1 nanosecond.Superconducting qubits(English editionIn 2004, a strong coupling between a superconducting resonator implemented by a Coplanar waveguide and a charge qubit was observed.[57]..Circuit quantum electrodynamics, which combines resonators and waveguides, is a very good tool for performing interactions between superconducting qubits and quantum nondemolition measurements.

SQUIDQuantum bit using the superposition state of magnetic flux quantum including(English editionCalled. Realized by Chiorescu, Nakamura, Harmans, Mooij and others at Delft University of Technology in 2003[54].. They areDWAVECompany developedQuantum annealing methodOptimization method by[20][21]Has been adopted by.

In 2007, a qubit that avoids charge fluctuation noise in charge qubits was proposed.(English editionと 呼 ば れ る[58]..Long coherence time is realized with a relatively simple structure, and research is being actively promoted mainly in the United States. In 2011, a single trial essential for quantum computation and quantum error correction(English editionHas been realized, and the quantum jump of the Transmon-type superconducting qubit has been observed.[59]..Behind these technologies is the realization of a low noise amplifier (Josephson parametric amplifier) ​​that achieves a noise figure close to the standard quantum limit.[60][61].. 2013, with the above basic technologyFPGAQuantum teleportation by high-speed feedback processing by[62]Experiments were carried out, and state transfer between spatially separated qubits was realized. A coherence time of 2014 microseconds was achieved in 160[63]In the 1999 years since its discovery in 15, a dramatic improvement of about 10 times has been made.same year,GoogleJohn Martinis[64]These groups are one of the error tolerance codes(English editionAchieves a high fidelity basic quantum gate below the error threshold of[65]..As a result, error-tolerant quantum calculations will become a reality, and the development of quantum computers using superconducting qubits will be further accelerated. 2015, by 9 qubits(English editionSucceeded in reducing the error probability of the logical qubit to about 1/8 of that of the physical qubit.[66]..In the same year, a digital quantum simulation of fermions, which dramatically accelerates the development of new functional materials, was implemented in a small system.[67]..Efforts for large scale have begun, and implementation by 2016D integration technology is being discussed in XNUMX.[68].

The University of Tokyo in Japan[69]And RIKEN[70]Researches on quantum computers and quantum information processing, NTT Basic Research Laboratories[71], National Institute of Information and Communications Technology[72]Is conducting research on quantum physics and is the main research base.

Google overseas[64], IBM[73], Delft University of Technology (supported by Intel Microsoft)[74], Massachusetts Institute of Technology[75], ETH Zurich[76]Is the main research base.

Ion trap

Ion trapIn a quantum computer that usesLaser coolingIons are captured and manipulated by.Osaka University in Japan[77]Research on quantum simulators and quantum computers is being conducted at.


Quantum circuit

It is one of the methods to describe a quantum algorithm by a quantum computer. In the case of an algorithm using N qubits, N lines are drawn and quantum operations (initial value setting, quantum operation, measurement) for the qubits are described in chronological order from left to right.

Generally, "initial value setting" is performed at the left end, and "measurement" is performed to read out qubit information explicitly or implicitly at the right end. The value obtained as a result of "measurement" is 0 or 1, and the quantum superposition state is destroyed at the moment of "measurement", and after that, it becomes a simple 0 or 1 state read out.

Difference in meaning from classical logic circuits

It's easy to think that a quantum computer is made up of quantum circuits, but it's not.Unlike logic gates that operate without adjustment, quantum gates require control and adjustment at all times during operation, and therefore require control lines from outside the quantum chip for each quantum gate.Therefore, in order to connect a plurality of quantum gates having a fixed function in a longitudinal manner, a large number of control signals are required between the quantum chip and an external circuit for controlling the quantum gate, which is difficult to implement.

In the actually made IBM and Google chips, qubits that are close to each other are connected by a small number of gates that can realize various gate functions with parameters, and the parameters are changed as the algorithm is executed. The algorithm expressed by is realized.In this way, the quantum circuit is for describing the quantum algorithm, and its position is different from that of the logic circuit, which is closely related to the hardware structure.

Quantum gate

Calculations on a classical computerBoolean logicBased onLogic gatebyLogical operationIt is done based on.On the other hand, in the quantum circuit of a quantum computer, the function of performing operations corresponding to the operators of quantum operations is called a quantum gate.Unitary matrixCan be described with.The unitary matrix for any one qubit is expressed in the following format.Reversible computingIt is also a feature.As you can see from this equation, the quantum gate is essentially analog signal processing, and differs from logical operations in that the error associated with analog processing becomes a problem.This is the biggest problem in realizing a quantum computer.

It is known that an arbitrary unitary transformation of n qubits can be constructed by combining a unitary transformation for one qubit and a CNOT gate.


NOT is also one of Pauli matrices.


Control NOT

Called CNOT. Corresponds to XOR.

Pauli matrices

Hadamard transform

TheHadamard matrix.

Conditional Phase

It is called CPhase.

In the case of 1 qubit, it is as follows.


Toffoli gate

Fredkin Gate

Computational power


Vazirani et al. Of quantum Turing machines and classic Turing machinesComputabilityWas shown to be equivalent.Therefore, in terms of computability, all existing computers and quantum Turing machines are no different.In other words, a problem that is "computable" in a quantum Turing machine is "computable" in a classical Turing machine, and a problem that is not "computable" in a classical Turing machine is not "computable" in a quantum Turing machine. (Note that "computable" is a technical term in theory of computation, and the simple impression that ordinary people imagine from expressions such as "cannot be solved in principle" is probably the most common. Is not accurate)

That's all for the theory of computability, butComputational complexity theoryWhat about it?

Quantum computer easily makes a classic computeremulateA problem that can be solved quickly by a classical computer (general-purpose problem) can be solved by a quantum computer as quickly as possible.Therefore, for general-purpose problems, quantum computers have more powerful computing speed than classical computers.However, even if the same is possible, it is not clear whether it is "greater than".

Related to quantum computersComplexity classToBQPThere is. The relationship between BQP and NP is not clear, but it is thought that BQP will be larger, including NP from around the 2010s.PHSome results have been shown suggesting that BQP is not included in.

In fact

It is said that the quantum gate machine can theoretically simulate a classical computer, but in reality, it cannot simulate a small-scale arithmetic unit with a classical gate.Furthermore, the time required for quantum gate processing is overwhelmingly slower than that of logic circuits, making it impossible to replace classical computers.Therefore, it is realistic to use the quantum gate machine as an additional device for solving a certain problem at high speed for a classical computer together with the development of a dedicated algorithm.

Google predicted that quantum gate machine speed will be demonstrated by the end of 2017[78]..That there is a problem that can be solved faster by an actual quantum gate machine than by a classical computer.Quantum supremacyThe search for such a problem is continuing. On October 2019, 10, Google announced that it has demonstrated quantum transcendence in the problem of estimating the output result of a randomly created quantum circuit.[79].

In 2001, IBM succeeded in decomposing 15 (= 3 × 5) for the first time in the world for Shor's algorithm that performs prime factorization on a quantum gate machine.[17].. In 2012, the University of Bristol performed a prime factorization of 21 (= 3 × 7) and set a new record.[80], There are no reports of prime factorization of numbers greater than 22 (as of September 2019).

IBM Q starting as of 2017[81]Can handle only a very limited number of qubits.Quantum memory that keeps the superposition state and stores data has not been realized,No-cloning theoremAs a result, the calculation results cannot be reused, the technology for connecting multiple quantum computers to increase the calculation scale has not been realized, and errors due to quantum gates accumulate. Have difficulty.Therefore, at present, it is not the state used to solve a given problem, but the search for a useful problem that can be solved by a quantum computer continues, starting from the demonstration of a small-scale quantum algorithm that has already been proposed.

As a quantum computer, in addition to the quantum gate type, D-Wave etc.Quantum annealingAnd several other types have been proposed, the quantum Ising machine is QUBO (optimization of unconstrained quadratic unconstrained expressions) (English edition) SpecializedDedicated computerIt can be said.


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Related item

Related books

The list below lists books on quantum computers and their mathematics in chronological order.Of course it is not perfect.

  • Tetsuro Nishino: "Introduction to Quantum Computers", Tokyo Denki University Press,ISBN-978 4501526504(June 1997, 3).
  • Masanori Ohya: "Mathematical Computers", Maruzen,ISBN-978 4621046074 (May 1999, 5).
  • Yoshinori Uesaka: "Basic Mathematics of Quantum Computers", Corona Publishing Co., Ltd.ISBN-978 4339023763(June 2000, 5).
  • CP Williams, SH Clearwater (co-authored), Tetsuro Nishino, Takashi Arai, Noboru Watanabe (co-translated): "Quantum Computing: Toward the Realization of Quantum Computers", Springer Fairlark Tokyo,ISBN-978 4431708698(June 2000, 6).
  • Tetsuro Nishino: "Quantum Computer and Quantum Cryptography", Iwanami Lecture The World of Physics Physics and Information (Volume 4), Iwanami Shoten,ISBN-978 4000111591(June 2002, 3).
  • Osamu Hirota: "Basics of Quantum Information Science: Approach to Quantum Computers", Morikita Publishing,ISBN-978 4627827417 (May 2002, 4).
  • A.Yu.Kitaev, AHShen, MNVyalyi: "Classical and Quantum Computation", American Mathematical Society,ISBN-978 0821832295(June 2002, 7).
  • Genadi P. Bellman, Ronnie Mainieri: "Introduction to Quantum Computers", Personal Media,ISBN-978 4893621924 (November 2002).
  • Tetsuro Nishino: "Theory of Quantum Computers: An Introduction to Quantum Computing", Baifukan,ISBN-978 4563015510 (May 2002, 12).
  • G. Milburn, Hayashi Ichi (Translation): "Fineman Processor: Dream Quantum Computer", Iwanami Shoten,ISBN-978 4000059497(June 2003, 1).
  • Jozef Gruska (Author), Masami Ito, Katsunori Imai, Sozo Iwamoto, Masafumi Toyama, Kenichi Morita (Co-translation): "Quantum Computing", Morikita Publishing,ISBN-978 4627827912(June 2003, 11).
  • Michael A. Nielsen, Issac L. Chuang (co-authored), Tatsuya Kimura (translation): "Quantum Computer and Quantum Communication (I)", Ohmsha, Inc.ISBN-4 274-20007-8(December 2004, 12). * All 20 volumes
  • Shigeru Ishii: "Invitation to Quantum Computers: Why Can We Calculate with Whimsical Quantum?", Nikkei BP, Inc.ISBN-978 4822282110(June 2004, 12).
  • Michael A. Nielsen, Issac L. Chuang (co-authored), Tatsuya Kimura (translation): "Quantum Computer and Quantum Communication (II)", Ohmsha, Inc.ISBN-4 274-20008-6(December 2005, 1). * All 10 volumes
  • Michael A. Nielsen, Issac L. Chuang (co-authored), Tatsuya Kimura (translation): "Quantum Computer and Quantum Communication (III)", Ohmsha, Inc.ISBN-4 274-20009-4(December 2005, 1). * All 10 volumes
  • Shigeki Takeuchi: "Quantum Computer: Mechanism of Super-Parallel Computation" Kodansha (Blue Bucks),ISBN-978 4062574693(June 2005, 2).
  • Akira Furusawa: "Quantum Optics and Quantum Information Science", Mathematical Engineering Co., Ltd.ISBN-4 901683-23-3(June 2005, 4).
  • D.Bouwmeester, A.Ekert, A.Zeilinger (eds.): "Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation", Kyoritsu Shuppan,ISBN 978-4-320-03431-0 (May 2007, 5).
  • Tetsuro Nishino: "(Illustrated Trivia) Quantum Computer", Natsumesha, Inc.ISBN-978 4816341311 (May 2007, 7).
  • N. David Mermin: "Quantum Computer Science: An Introduction", Cambridge University Press,ISBN-978 0521876582 (May 2007, 8).
  • Kenjiro Miyano, Akira Furusawa: "Introduction to Quantum Computers", Nihon Hyoronsha,ISBN-978 4535784796 (May 2008, 3).
  • Noson S. Yanofsky, Mirco A. Mannucci: "Quantum Computing for Computer Scientists", Cambridge University Press,ISBN-978 0521879965 (May 2008, 8).
  • G. Benenti, G. Gazati, G. Sturini, Hajime Hirooka (Translation): "Principles of Quantum Calculation and Quantum Information", Springer Japan,ISBN-978 4431100096 (November 2009).
  • ND Marmin, Gen Kimura (Translation): "Basics of Marmin Quantum Computer Science", Maruzen,ISBN-978 4621081464(June 2009, 7).
  • George Johnson: "What is a Quantum Computer?", Hayakawa Publishing (Hayakawa Bunko NF-A series of enjoying mathematics),ISBN-978 4150503611 (May 2009, 12).
  • Seiki Akama: "Books for Understanding Quantum Computers", Kogakusha,ISBN-978 4777515141 (May 2010, 4).
  • Michael A. Nielsen, Isaac L. Chuang: "Quantum Computation and Quantum Information: 10th Anniversary Edition", Cambridge University Press,ISBN-978 1107002173(June 2010, 12).
  • Colin P. Williams: "Explorations in Quantum Computing" (2nd Ed.), Springer,ISBN-978 1846288869 (May 2010, 12).
  • Willi-Hans Steeb, Yorick Hardy: "Problems and Solutions in Quantum Computing and Quantum Information" (3rd Ed.), World Scientific Pub,ISBN-978 9814366328 (May 2011, 9).
  • Jiannis K. Pachos: "Introduction to Topological Quantum Computation", Cambridge Univ. Press,ISBN-978 1107005044(June 2012, 4).
  • G. Benenti, G. Gazati, G. Sturini, Hajime Hirooka (Translation): "Principles of Quantum Calculation and Quantum Information", Maruzen Publishing Co., Ltd.,ISBN-978 4621062272(June 2012, 6). * Republishing of a book from Springer Japan.
  • Satoshi Ishizaka, Tomohiro Ogawa, Ryoshu Kawauchi, Gen Kimura, Masato Hayashi: "Introduction to Quantum Information Science", Kyoritsu Shuppan,ISBN-978 4320122994 (May 2012, 6).
  • John Gribbin, Shunsuke Matsuura (Translation): "Schradinger's cat becomes a quantum computer.", Seitosha,ISBN-978 4791767717 (May 2014, 3).
  • Information Processing Society of Japan (ed.): Information Processing Society of Japan, July 2014 issue, reprint "<< Special Feature >> Quantum Computer", Information Processing Society of Japan,ISBN-978 4907626013(June 2014, 6).
  • Eleanor G. Rieffel, Wolfgang H. Polak: "Quantum Computing: A Gentle Introduction", MIT Press,ISBN-978 0262526678(June 2014, 8).
  • Shigeru Nakayama: "Quantum Algorithm", Gihodo Publishing,ISBN-978 4765533430 (May 2014, 10).
  • Richard J. Lipton, Kenneth W. Regan: "Quantum Algorithms via Linear Algebra: A Primer", MIT Press,ISBN-978 0262028394(June 2014, 12).
  • Kaoru Takeuchi: "Quantum computer is really amazing", PHP Institute,ISBN-978 4569824987(June 2015, 5).
  • Tetsuro Nishino, Tatsuaki Okamoto, Takashi Mihara: "Quantum Computing" (Natural Computing Series Volume 6), Modern Science Co., Ltd.ISBN-978 4764904866 (May 2015, 10).
  • Tomonori Nishino: "Quantum computer that can be understood this time", Kodansha,ISBN-978 4061566057(June 2015, 10).
  • Keisuke Fujii: "Quantum Computation with Topological Codes: From Qubit to Topological Fault-Tolerance", Springer,ISBN-978 9812879950(June 2016, 1).
  • Kenjiro Miyano, Akira Furusawa: "Introduction to Quantum Computers" (2nd Edition), Nihon Hyoronsha,ISBN-978 4535788053(June 2016, 3).
  • Shigeru Nakayama: "Introduction to Cloud Quantum Computing: IBM's Quantum Simulation and Quantum Computer", Cut System,ISBN-978 4877834081(May 2016, 9).
  • Tudor D. Stanescu: "Introduction to Topological Quantum Matter & Quantum Computation", CRC Press,ISBN-978 1482245936 (May 2016, 12).
  • Hidetoshi Nishimori, Masayuki Ozeki: "Quantum Computer Accelerates Artificial Intelligence", Nikkei BP, Inc.ISBN-978 4822251895(June 2016, 12).
  • Takeshi Koshiba, Keisuke Fujii, Tomoyuki Morimae: "Quantum Calculation Based on Observation", Corona Publishing Co., Ltd.ISBN-978 4339028706(May 2017, 3).
  • Akihisa Tomita: "Quantum Information Engineering", Morikita Publishing,ISBN-978 4627853812 (June 2017, 3).
  • Mingsheng Ying, Haruyuki Kawabe (Translation): "Basics of Quantum Programming", Kyoritsu Shuppan,ISBN-978 4320124059(June 2017, 3).
  • Tomoyuki Morimae: "Quantum Computation Theory: Principles of Quantum Computers", Morikita Publishing,ISBN-978 4627854017(June 2017, 11).
  • Shigeru Nakayama: "Cloud Quantum Computing: An Introduction to Quantum Assembler", Next Publishing Authors Press, On-Demand Print Book (January 2018, 1).
  • Shigeru Nakayama: "Python Cloud Quantum Computing QISKIT Bible", self-published on-demand (May 2018, 5).
  • Hidetoshi Nishimori, Masayuki Ozeki: "Basics of Quantum Annealing", Kyoritsu Shuppan,ISBN-978 4320035386(June 2018, 5).
  • Shigeru Nakayama: "Introduction to Python Quantum Programming", self-published on-demand (June 2018, 6).
  • Kengo Nagahashi: "Introduction to Illustrated Basics and Mechanisms of the Latest Quantum Computers", Shuwa System,ISBN-978 4798054551(June 2018, 9).
  • Shigeru Nakayama: "Introduction to Python Quantum Programming 2", self-published on-demand (October 2018, 10).
  • "Quantum Computer / Ising Computer Research and Development Frontline", Information Organization Co., Ltd.ISBN 978-4-86502-165-3 (February 2019).
  • Akira Furusawa: "Quantum Computer of Light", Shueisha International (International Shinsho),ISBN-978 4797680355(June 2019, 2).
  • Shigeru Nakayama: "Introduction to Qiskit Quantum Programming", self-published on-demand (February 2019, 2).
  • Yuichiro Minato: "The Easiest Quantum Computer Textbook", Impress, ISBN-13: 978-4295006077 (May 2019, 5).
  • Ken Utsuki, Hiromi Tokunaga (supervised): "Mechanism of quantum computer that can be seen in pictures", Shoeisha,ISBN-978 4798157467 (June 2019, 7).
  • Tsuyoshi Takagi: "Cryptography and Quantum Computers: Introduction to Quantum Resistant Computer Cryptography", Ohmsha, Inc.ISBN-978 4274224102(2019 8 年 月 日 25)
  • Emily Grumbling and Mark Horowitz (Eds): "Quantum Computing: Progress and Prospects (2019)", The National Academies Press, Washington, DC, ISBN 978-0-309-47969-1 (Sep, 4th, 2019).
  • Jack D. Hidary: "Quantum Computing: An Applied Approach", Springer,ISBN-978 3030239213 (May 2019, 9).
  • Hiroyuki Sagawa, Nobuaki Yoshida: "Quantum Information Theory 3rd Edition", Maruzen Publishing,ISBN-978 4621304167(June 2019, 10).
  • Keisuke Fujii: "Amazing Quantum Computer: Challenge to the Strongest Machine in Space", Iwanami Shoten (Iwanami Science Library),ISBN-978 4000296892(June 2019, 11).
  • Emily Grumbling, Mark Horowitz ed .: "Advances and Prospects of Quantum Computers by the American Academy of Science, Engineering and Medicine," Kyoritsu Shuppan,ISBN 978-4-320-12455-4 (September 2020, 1).
  • Chris Bernhardt, Yuichiro Minato (translated), Masahide Nakata (translated): "Minna no Quantum Computer", Shoeisha,ISBN-978 4798163574(June 2020, 1).
  • Shuntaro Takeda: "I really understand quantum computers! -Mechanisms and possibilities that front-line developers can easily reveal", Gijutsu-Hyoronsha,ISBN-978 4297111359(June 2020, 2).
  • Rihei Endo: "Quantum computer made in 14 days: Numerical simulation of quantum bits, quantum gates, and quantum entanglements with Schrodinger equation Python version", Cut systemISBN-978 4877834715(June 2020, 5).
  • Koji Sueda: "Quantum Resistant Computer Code", Morikita Publishing,ISBN-978 4627872110 (May 2020, 8).
  • Eric R. Johnston, Nic Harrigan, Mercedes Gimeno-Segovia: "Move and Learn Quantum Computer Programming", O'Reilly Japan,ISBN-978 4873119199 (June 2020, 8).
  • Maria Schuld, Francesco Petruccione, Masayuki Ozeki (Translated): "Machine Learning with Quantum Computers", Kyoritsu Shuppan,ISBN-978 4320124622(June 2020, 8).
  • Yoshiaki Shimada: "From basic algorithms for quantum computing to quantum machine learning," Ohmsha, Inc.ISBN 978-4-274-22621-2(June 2020, 11).
  • Kenji Sugisaki: "Introduction to Quantum Chemical Calculation by Quantum Computer", Kodansha,ISBN-978 4065218273(June 2020, 12).
  • Yuichiro Minato, Takumi Kato, Keiichiro Higa, Ryutaro Nagai: "Quantum Computers Learned with IBM Quantum", Shuwa System, ISBN-13: 978-4798062808 (March 2021, 3).

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