History of Quantum Computing¶

Introduction¶

Quantum computing is a rapidly evolving field that leverages the principles of quantum mechanics to perform computations. This notebook explores the history and development of quantum computing.

Early Concepts and Theoretical Foundations¶

Conjugate Coding (1968)¶

Stephen Wiesner invents conjugate coding (published in ACM SIGACT News 15(1): 78–88).

No-Cloning Theorem (1970)¶

James Park articulates the no-cloning theorem.

Holevo's Theorem and Reversible Computation (1973)¶

Alexander Holevo publishes a paper showing that n qubits can carry more than n classical bits of information, but at most n classical bits are accessible (a result known as "Holevo's theorem" or "Holevo's bound"). Charles H. Bennett shows that computation can be done reversibly.

Thermodynamical Models of Information Processing (1975)¶

R. P. Poplavskii publishes "Thermodynamical models of information processing" (in Russian), which shows the computational infeasibility of simulating quantum systems on classical computers, due to the superposition principle.

Quantum Information Theory (1976)¶

Roman Stanisław Ingarden, a Polish mathematical physicist, publishes the paper "Quantum Information Theory" in Reports on Mathematical Physics, vol. 10, pp. 43–72, 1976 (The paper was submitted in 1975). It is one of the first attempts at creating a quantum information theory, showing that Shannon information theory cannot directly be generalized to the quantum case, but rather that it is possible to construct a quantum information theory, which is a generalization of Shannon's theory, within the formalism of a generalized quantum mechanics of open systems and a generalized concept of observables (the so-called semi-observables).

Quantum Mechanical Model of a Computer (1980)¶

Paul Benioff describes the first quantum mechanical model of a computer. In this work, Benioff showed that a computer could operate under the laws of quantum mechanics by describing a Schrödinger equation description of Turing machines, laying a foundation for further work in quantum computing. The paper was submitted in June 1979 and published in April 1980. Yuri Manin briefly motivates the idea of quantum computing. Tommaso Toffoli introduces the reversible Toffoli gate, which (together with initialized ancilla bits) is functionally complete for reversible classical computation.

Conference on the Physics of Computation (1981)¶

At the first Conference on the Physics of Computation, held at the Massachusetts Institute of Technology (MIT) in May, Paul Benioff and Richard Feynman give talks on quantum computing. Benioff's talk built on his earlier 1980 work showing that a computer can operate under the laws of quantum mechanics. The talk was titled “Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: application to Turing machines”. In Feynman's talk, he observed that it appeared to be impossible to efficiently simulate an evolution of a quantum system on a classical computer, and he proposed a basic model for a quantum computer.

Further Development of Quantum Mechanical Turing Machine (1982)¶

Paul Benioff further develops his original model of a quantum mechanical Turing machine. William Wootters and Wojciech Zurek, and independently Dennis Dieks, rediscover the no-cloning theorem of James Park.

Quantum Key Distribution (1984)¶

Charles Bennett and Gilles Brassard employ Wiesner's conjugate coding for distribution of cryptographic keys.

Universal Quantum Computer (1985)¶

David Deutsch, at the University of Oxford, describes the first universal quantum computer. Just as a Universal Turing machine can simulate any other Turing machine efficiently (Church–Turing thesis), so the universal quantum computer is able to simulate any other quantum computer with at most a polynomial slowdown. Asher Peres points out the need for quantum error correction schemes and discusses a repetition code for amplitude errors.

Physical Realization of a Quantum Computer (1988)¶

Yoshihisa Yamamoto and K. Igeta propose the first physical realization of a quantum computer, including Feynman's CNOT gate. Their approach uses atoms and photons and is the progenitor of modern quantum computing and networking protocols using photons to transmit qubits and atoms to perform two-qubit operations.

Quantum-Optical Realization of a Fredkin Gate (1989)¶

Gerard J. Milburn proposes a quantum-optical realization of a Fredkin gate. Bikas K. Chakrabarti & collaborators from Saha Institute of Nuclear Physics, Kolkata, India, propose that quantum fluctuations could help explore rugged energy landscapes by escaping from local minima of glassy systems having tall but thin barriers by tunneling (instead of climbing over using thermal excitations), suggesting the effectiveness of quantum annealing over classical simulated annealing.

Development of Quantum Algorithms¶

Entanglement-Based Secure Communication (1991)¶

Artur Ekert at the University of Oxford proposes entanglement-based secure communication.

Deutsch–Jozsa Algorithm and Bernstein–Vazirani Algorithm (1992)¶

David Deutsch and Richard Jozsa propose a computational problem that can be solved efficiently with the deterministic Deutsch–Jozsa algorithm on a quantum computer, but for which no deterministic classical algorithm is possible. Ethan Bernstein and Umesh Vazirani propose the Bernstein–Vazirani algorithm, a restricted version of the Deutsch–Jozsa algorithm designed to prove an oracle separation between complexity classes BQP and BPP. Research groups at Max Planck Institute of Quantum Optics and NIST experimentally realize the first crystallized strings of laser-cooled ions.

Simon's Problem (1993)¶

Dan Simon, at Université de Montréal, invents an oracle problem, Simon's problem, for which a quantum computer would be exponentially faster than a conventional computer. This algorithm introduces the main ideas which were then developed in Peter Shor's factorization algorithm.

Shor's Algorithm (1994)¶

Peter Shor, at AT&T's Bell Labs in New Jersey, publishes Shor's algorithm. It would allow a quantum computer to factor large integers quickly. The first United States Government workshop on quantum computing is organized by NIST in Gaithersburg, Maryland. Isaac Chuang and Yoshihisa Yamamoto propose a quantum-optical realization of a quantum computer to implement Deutsch's algorithm. Ignacio Cirac and Peter Zoller propose an experimental realization of the controlled-NOT gate with cold trapped ions.

Quantum Error Correction and Quantum Logic Gate (1995)¶

Peter Shor proposes the first schemes for quantum error correction. Christopher Monroe and David Wineland at NIST experimentally realize the first quantum logic gate – the controlled-NOT gate – with trapped ions, following the Cirac-Zoller proposal. Independently, Subhash Kak and Ronald Chrisley propose the first quantum neural network.

Grover's Algorithm (1996)¶

Lov Grover, at Bell Labs, invents the quantum database search algorithm. The United States Government issues the first public call for research proposals in quantum information processing. Andrew Steane designs Steane codes for error correction. David P. DiVincenzo, of IBM, proposes a list of minimal requirements for creating a quantum computer, now called DiVincenzo's criteria.

NMR Quantum Computing and Topological Quantum Computation (1997)¶

David Cory, Amr Fahmy, and Timothy Havel, and at the same time Neil Gershenfeld and Isaac L. Chuang at MIT publish the first papers realizing gates for quantum computers based on bulk nuclear spin resonance, or thermal ensembles. Alexei Kitaev describes the principles of topological quantum computation as a method for dealing with the problem of decoherence. Daniel Loss and David P. DiVincenzo propose the Loss-DiVincenzo quantum computer, using as qubits the intrinsic spin-1/2 degree of freedom of individual electrons confined to quantum dots.

Experimental Demonstration of Quantum Algorithms (1998)¶

The first experimental demonstration of a quantum algorithm is reported. A working 2-qubit NMR quantum computer was used to solve Deutsch's problem by Jonathan A. Jones and Michele Mosca at Oxford University and shortly after by Isaac L. Chuang at IBM's Almaden Research Center, in California, and Mark Kubinec and the University of California, Berkeley together with coworkers at Stanford University and MIT. The first working 3-qubit NMR computer is reported. Bruce Kane proposes a silicon-based nuclear spin quantum computer. The first execution of Grover's algorithm on an NMR computer is reported. Hidetoshi Nishimori & colleagues from Tokyo Institute of Technology show that a quantum annealing algorithm can perform better than classical simulated annealing under certain conditions. Daniel Gottesman and Emanuel Knill independently prove that a certain subclass of quantum computations can be efficiently emulated with classical resources (Gottesman–Knill theorem).

Quantum Annealing and Superconducting Qubits (1999)¶

Samuel L. Braunstein and collaborators show that none of the bulk NMR experiments performed to date contain any entanglement; the quantum states being too strongly mixed. Gabriel Aeppli, Thomas Felix Rosenbaum and colleagues demonstrate experimentally the basic concepts of quantum annealing in a condensed matter system. Yasunobu Nakamura and Jaw-Shen Tsai demonstrate that a superconducting circuit can be used as a qubit.

Development of Quantum Algorithms in the 2000s¶

Quantum No-Deleting Theorem and NMR Quantum Computers (2000)¶

Arun K. Pati and Samuel L. Braunstein prove the quantum no-deleting theorem, which shows that one cannot delete a copy of an unknown qubit. The first working 5-qubit NMR computer is demonstrated at the Technical University of Munich, Germany. The first execution of order finding (part of Shor's algorithm) at IBM's Almaden Research Center and Stanford University is demonstrated. The first working 7-qubit NMR computer is demonstrated at the Los Alamos National Laboratory in New Mexico. The textbook, Quantum Computation and Quantum Information, by Michael Nielsen and Isaac Chuang is published.

Execution of Shor's Algorithm and Linear Optical Quantum Computing (2001)¶

The first execution of Shor's algorithm at IBM's Almaden Research Center and Stanford University is demonstrated. Noah Linden and Sandu Popescu prove that the presence of entanglement is a necessary condition for a large class of quantum protocols. Emanuel Knill, Raymond Laflamme, and Gerard Milburn show that optical quantum computing is possible with single-photon sources, linear optical elements, and single-photon detectors. Robert Raussendorf and Hans Jürgen Briegel propose measurement-based quantum computation.

Quantum Information Science and Technology Roadmap (2002)¶

The Quantum Information Science and Technology Roadmapping Project lays out the Quantum computation roadmap. The Institute for Quantum Computing is established at the University of Waterloo in Waterloo, Ontario. A group led by Gerhard Birkl demonstrates the first 2D array of optical tweezers with trapped atoms for quantum computation with atomic qubits.

Implementation of Deutsch–Jozsa Algorithm and Quantum Networks (2003)¶

Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer at the University of Innsbruck is reported. Todd D. Pittman and collaborators, and independently Jeremy L. O'Brien and collaborators, demonstrate quantum controlled-not gates using only linear optical elements. The first implementation of a CNOT quantum gate, according to the Cirac–Zoller proposal, is reported by a team at the University of Innsbruck. The DARPA Quantum Network becomes fully operational. The Institute for Quantum Optics and Quantum Information (IQOQI) is established in Innsbruck and Vienna, Austria.

Pure State NMR Quantum Computer and Quantum Teleportation (2004)¶

The first working pure state NMR quantum computer is demonstrated at Oxford University and University of York. Physicists at the University of Innsbruck show deterministic quantum-state teleportation between a pair of trapped calcium ions. The first five-photon entanglement is demonstrated by Jian-Wei Pan's team at the University of Science and Technology of China.

Quantum Entanglement and Josephson Junctions (2005)¶

University of Illinois at Urbana–Champaign scientists demonstrate quantum entanglement of multiple characteristics. Two teams of physicists measure the capacitance of a Josephson junction for the first time. W-states of quantum registers with up to 8 qubits are demonstrated at the Institute for Quantum Optics and Quantum Information and the University of Innsbruck. Harvard University and Georgia Institute of Technology researchers succeed in transferring quantum information between "quantum memories".

Quantum Error Correction and Quantum Telecloning (2006)¶

The Materials Science Department of Oxford University demonstrates quantum "bang-bang" error correction. Researchers from the University of Illinois at Urbana–Champaign use the Zeno Effect for counterfactual quantum computation. Vlatko Vedral and colleagues find that photons in ordinary laser light can be entangled with the vibrations of a macroscopic mirror. Samuel L. Braunstein and collaborators give the first experimental demonstration of quantum telecloning. Professors at the University of Sheffield develop a means to efficiently produce and manipulate individual photons at room temperature. The first 12-qubit quantum computer is benchmarked by researchers at the Institute for Quantum Computing and the Perimeter Institute for Theoretical Physics. A two-dimensional ion trap is developed for quantum computing. Seven atoms are placed in a stable line at the University of Bonn. A team at Delft University of Technology creates a device that can manipulate the "up" or "down" spin-states of electrons on quantum dots. The University of Arkansas develops quantum dot molecules. The University of Copenhagen develops quantum teleportation between photons and atoms. University of Camerino scientists develop a theory of macroscopic object entanglement. Tai-Chang Chiang finds that quantum coherence can be maintained in mixed-material systems. Cristophe Boehme demonstrates the feasibility of reading data using the nuclear spin on a silicon-phosphorus Kane quantum computer.

Quantum Waveguides and One-Way Quantum Computers (2007)¶

Subwavelength waveguide is developed for light. A single-photon emitter for optical fibers is developed. The first one-way quantum computers are built and shown to perform simple computations. A new material is proposed for quantum computing. A single-atom single-photon server is devised. The University of Cambridge develops an electron quantum pump. A superior method of qubit coupling is developed. A successful demonstration of controllably coupled qubits is reported. A breakthrough in applying spin-based electronics to silicon is reported. Scientists demonstrate a quantum state exchange between light and matter. A diamond quantum register is developed. Controlled-NOT quantum gates on a pair of superconducting quantum bits are realized. Scientists contain and study hundreds of individual atoms in a 3D array. Nitrogen in a buckyball molecule is used in quantum computing. A large number of electrons are quantum coupled. Spin–orbit interaction of electrons is measured. Atoms are quantum manipulated in laser light. Light pulses are used to control electron spins. Quantum effects are demonstrated across tens of nanometers. Light pulses are used to accelerate quantum computing development. A quantum RAM blueprint is unveiled. A model of a quantum transistor is developed. Long distance entanglement is demonstrated. Photonic quantum computing is used to factor a number by two independent labs. A quantum bus is developed by two independent labs. A superconducting quantum cable is developed. The transmission of qubits is demonstrated. Superior qubit material is devised. A single-electron qubit memory is reported. Bose–Einstein condensate quantum memory is developed. D-Wave Systems demonstrates use of a 28-qubit quantum annealing computer. A new cryonic method reduces decoherence and increases interaction distance, and thus quantum computing speed. A photonic quantum computer is demonstrated. Graphene quantum dot spin qubits are proposed.

HHL Algorithm and Quantum Bit Storage (2008)¶

The HHL algorithm for solving linear equations is published. Graphene quantum dot qubits are described. Scientists succeed in storing a quantum bit. 3D qubit-qutrit entanglement is demonstrated. Analog quantum computing is devised. Control of quantum tunneling is devised. Entangled memory is developed. A superior NOT gate is developed. Qutrits are developed. Quantum logic gate in optical fiber. A superior quantum Hall Effect is discovered. Enduring spin states in quantum dots are reported. Molecular magnets are proposed for quantum RAM. Quasiparticles offer hope of stable quantum computers. Image storage may have better storage of qubits is reported. Quantum entangled images are reported. Quantum state is intentionally altered in a molecule. Electron position is controlled in a silicon circuit. A superconducting electronic circuit pumps microwave photons. Amplitude spectroscopy is developed. A superior quantum computer test is developed. An optical frequency comb is devised. The concept of Quantum Darwinism is supported. Hybrid qubit memory is developed. A qubit is stored for over 1 second in an atomic nucleus. Faster electron spin qubit switching and reading is developed. The possibility of non-entanglement quantum computing is described. D-Wave Systems claim to have produced a 128 qubit computer chip, though this claim had yet to be verified.

Extended Qubit Lifetime and Quantum Processor (2009)¶

Carbon 12 is purified for longer coherence times. The lifetime of qubits is extended to hundreds of milliseconds. Improved quantum control of photons is reported. Quantum entanglement is demonstrated over 240 micrometres. Qubit lifetime is extended by a factor of 1000. The first electronic quantum processor is created. Six-photon graph state entanglement is used to simulate the fractional statistics of anyons living in artificial spin-lattice models. A single-molecule optical transistor is devised. NIST reads and writes individual qubits. NIST demonstrates multiple computing operations on qubits. The first large-scale topological cluster state quantum architecture is developed for atom-optics. A combination of all of the fundamental elements required to perform scalable quantum computing through the use of qubits stored in the internal states of trapped atomic ions is shown. Researchers at University of Bristol demonstrate Shor's algorithm on a silicon photonic chip. Quantum Computing with an Electron Spin Ensemble is reported. A so-called photon machine gun is developed for quantum computing. The first universal programmable quantum computer is unveiled. Scientists electrically control quantum states of electrons. Google collaborates with D-Wave Systems on image search technology using quantum computing. A method for synchronizing the properties of multiple coupled CJJ rf-SQUID flux qubits with a small spread of device parameters due to fabrication variations is demonstrated. Universal Ion Trap Quantum Computation with decoherence free qubits is realized. The first chip-scale quantum computer is reported.

Development of Quantum Algorithms in the 2010s¶

Optical Traps and Quantum Computers (2010)¶

Ions were trapped in an optical trap. An optical quantum computer with three qubits calculated the energy spectrum of molecular hydrogen to high precision. The first germanium laser advanced the state of optical computers. A single-electron qubit was developed. The quantum state in a macroscopic object was reported. A new quantum computer cooling method was developed. Racetrack ion trap was developed. Evidence for a Moore-Read state in the ν=5/2 quantum Hall plateau, suitable for topological quantum computation, was reported. A quantum interface between a single photon and a single atom was demonstrated. LED quantum entanglement was demonstrated. Multiplexed design increased the speed of transmission of quantum information through a quantum communications channel. A two-photon optical chip was reported. Microfabricated planar ion traps were tested. A boson sampling technique was proposed by Aaronson and Arkhipov. Quantum dot qubits were manipulated electrically, not magnetically.

Solid-State Spin Ensemble and Quantum Antenna (2011)¶

Entanglement in a solid-state spin ensemble was reported. NOON photons in a superconducting quantum integrated circuit were reported. A quantum antenna was described. Multimode quantum interference was documented. Magnetic Resonance applied to quantum computing was reported. The quantum pen for single atoms was documented. Atomic "Racing Dual" was reported. A 14 qubit register was reported. D-Wave claimed to have developed quantum annealing and introduced their product called D-Wave One, the first commercially available quantum computer. Repetitive error correction was demonstrated in a quantum processor. Diamond quantum computer memory was demonstrated. Qmodes were developed. Decoherence was demonstrated as suppressed. Simplification of controlled operations was reported. Ions entangled using microwaves were documented. Practical error rates were achieved. A quantum computer employing Von Neumann architecture was described. A quantum spin Hall topological insulator was reported. The concept of two diamonds linked by quantum entanglement could help develop photonic processors was described.

Quantum Computation and Transistors (2012)¶

D-Wave claimed a quantum computation using 84 qubits. Physicists created a working transistor from a single atom. A method for manipulating the charge of nitrogen vacancy-centres in diamond was reported. Creation of a 300 qubit/particle quantum simulator was reported. Demonstration of topologically protected qubits with an eight-photon entanglement was reported. 1QB Information Technologies (1QBit) was founded, the world's first dedicated quantum computing software company. The first design of a quantum repeater system without a need for quantum memories was reported. Decoherence suppressed for 2 seconds at room temperature by manipulating Carbon-13 atoms with lasers was reported. The theory of Bell-based randomness expansion with reduced assumption of measurement independence was reported. New low overhead method for fault-tolerant quantum logic was developed called lattice surgery.

Coherence Time and Quantum Algorithm Resource Analysis (2013)¶

Coherence time of 39 minutes at room temperature (and 3 hours at cryogenic temperatures) was demonstrated for an ensemble of impurity-spin qubits in isotopically purified silicon. Extension of time for a qubit maintained in superimposed state for ten times longer than what has ever been achieved before was reported. The first resource analysis of a large-scale quantum algorithm using explicit fault-tolerant, error-correction protocols was developed for factoring.

Quantum Computing Architecture and Teleportation (2014)¶

Documents leaked by Edward Snowden confirmed the Penetrating Hard Targets project by the NSA to develop a quantum computing capability for cryptography purposes. Researchers in Japan and Austria published the first large-scale quantum computing architecture for a diamond-based system. Scientists at the University of Innsbruck performed quantum computations on a topologically encoded qubit. Scientists transferred data by quantum teleportation over a distance of 10 feet with zero percent error rate, a vital step towards a quantum Internet.

Optically Addressable Nuclear Spins and Quantum Error Detection (2015)¶

Optically addressable nuclear spins in a solid with a six-hour coherence time were documented. Quantum information encoded by simple electrical pulses was documented. Quantum error detection code using a square lattice of four superconducting qubits was documented. D-Wave Systems Inc. announced on June 22 that it had broken the 1,000-qubit barrier. A two-qubit silicon logic gate was successfully developed.

Shor's Algorithm and Quantum Experience (2016)¶

Physicists led by Rainer Blatt joined forces with scientists at MIT to efficiently implement Shor's algorithm in an ion-trap-based quantum computer. IBM released the Quantum Experience, an online interface to their superconducting systems. Google, using an array of 9 superconducting qubits, simulated a hydrogen molecule. Scientists in Japan and Australia invented a quantum version of a Sneakernet communications system.

D-Wave 2000Q and Quantum Programming Language (2017)¶

D-Wave Systems Inc. announced general commercial availability of the D-Wave 2000Q quantum annealer. A blueprint for a microwave trapped ion quantum computer was published. IBM unveiled a 17-qubit quantum computer and a better way of benchmarking it. Scientists built a microchip that generates two entangled qudits each with 10 states, for 100 dimensions total. Microsoft revealed Q#, a quantum programming language integrated with its Visual Studio development environment. IBM revealed a working 50-qubit quantum computer. The first teleportation using a satellite, connecting ground stations over a distance of 1400 km apart, was announced.

Noisy Intermediate-Scale Quantum (NISQ) Era and Quantum Chips (2018)¶

John Preskill introduces the concept of noisy intermediate-scale quantum (NISQ) era. MIT scientists reported the discovery of a new triple-photon form of light. Oxford researchers successfully use a trapped-ion technique to speed up logic gates by a factor of 20 to 60 times. QuTech successfully tested a silicon-based 2-spin-qubit processor. Google announced the creation of a 72-qubit quantum chip, called "Bristlecone". Intel began testing a silicon-based spin-qubit processor. Intel confirmed development of a 49-qubit superconducting test chip, called "Tangle Lake". Japanese researchers demonstrated universal holonomic quantum gates. An integrated photonic platform for quantum information with continuous variables was documented. IonQ introduced the first commercial trapped-ion quantum computer. The National Quantum Initiative Act was signed into law by President Donald Trump.

IBM Q System One and Quantum Supremacy (2019)¶

IBM unveiled its first commercial quantum computer, the IBM Q System One. Austrian physicists demonstrated self-verifying, hybrid, variational quantum simulation of lattice models. Griffith University, UNSW and UTS developed noise cancelling for quantum bits via machine learning. Quantum Darwinism was observed in diamond at room temperature. Google revealed its Sycamore processor, consisting of 53 qubits, claiming quantum supremacy. Google also developed a cryogenic chip for controlling qubits from within a dilution refrigerator. University of Science and Technology of China researchers demonstrated boson sampling with 14 detected photons.

References¶

Feynman, R. P. (1982). Simulating physics with computers. International Journal of Theoretical Physics, 21(6-7), 467-488.
Deutsch, D. (1985). Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 400(1818), 97-117.
Shor, P. W. (1994). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings 35th Annual Symposium on Foundations of Computer Science.
Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proceedings of the twenty-eighth annual ACM symposium on Theory of computing.
Wiesner, S. (1968). Conjugate coding. ACM SIGACT News, 15(1), 78-88.
Park, J. (1970). The no-cloning theorem.
Holevo, A. (1973). Bounds for the quantity of information transmitted by a quantum communication channel.
Bennett, C. H. (1973). Logical reversibility of computation. IBM Journal of Research and Development, 17(6), 525-532.
Poplavskii, R. P. (1975). Thermodynamical models of information processing.
Ingarden, R. S. (1976). Quantum Information Theory. Reports on Mathematical Physics, 10, 43-72.
Benioff, P. (1980). The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. Journal of Statistical Physics, 22(5), 563-591.
Manin, Y. (1980). Computable and Uncomputable. Sovetskoye Radio.
Toffoli, T. (1980). Reversible computing. In Automata, Languages and Programming (pp. 632-644). Springer, Berlin, Heidelberg.
Bennett, C. H., & Brassard, G. (1984). Quantum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (pp. 175-179).
Deutsch, D. (1985). Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 400(1818), 97-117.
Peres, A. (1985). Reversible logic and quantum computers. Physical Review A, 32(6), 3266.
Yamamoto, Y., & Igeta, K. (1988). Proposal for a quantum computer. Physical Review Letters, 60(22), 2202-2205.
Milburn, G. J. (1989). Quantum optical Fredkin gate. Physical Review Letters, 62(18), 2124-2127.
Chakrabarti, B. K., & Das, A. (1989). Quantum annealing in a glassy system. Physical Review B, 39(16), 11943-11946.
Ekert, A. (1991). Quantum cryptography based on Bell's theorem. Physical Review Letters, 67(6), 661-663.
Deutsch, D., & Jozsa, R. (1992). Rapid solution of problems by quantum computation. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 439(1907), 553-558.
Bernstein, E., & Vazirani, U. (1992). Quantum complexity theory. SIAM Journal on Computing, 26(5), 1411-1473.
Simon, D. R. (1994). On the power of quantum computation. SIAM Journal on Computing, 26(5), 1474-1483.
Chuang, I. L., & Yamamoto, Y. (1994). Simple quantum computer. Physical Review A, 50(4), 2738.
Cirac, J. I., & Zoller, P. (1995). Quantum computations with cold trapped ions. Physical Review Letters, 74(20), 4091.
Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52(4), R2493.
Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M., & Wineland, D. J. (1995). Demonstration of a fundamental quantum logic gate. Physical Review Letters, 75(25), 4714.
Kak, S., & Chrisley, R. (1995). Artificial neural networks with quantum weights. Physics Letters A, 197(5-6), 307-310.
Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proceedings of the twenty-eighth annual ACM symposium on Theory of computing.
Steane, A. M. (1996). Error correcting codes in quantum theory. Physical Review Letters, 77(5), 793.
DiVincenzo, D. P. (1996). Topics in quantum computers. In Mesoscopic Electron Transport (pp. 657-677). Springer, Dordrecht.
Cory, D. G., Fahmy, A. F., & Havel, T. F. (1997). Ensemble quantum computing by NMR spectroscopy. Proceedings of the National Academy of Sciences, 94(5), 1634-1639.
Kitaev, A. Y. (1997). Fault-tolerant quantum computation by anyons. Annals of Physics, 303(1), 2-30.
Loss, D., & DiVincenzo, D. P. (1998). Quantum computation with quantum dots. Physical Review A, 57(1), 120.
Jones, J. A., & Mosca, M. (1998). Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer. Journal of Chemical Physics, 109(5), 1648-1653.
Kane, B. E. (1998). A silicon-based nuclear spin quantum computer. Nature, 393(6681), 133-137.
Chuang, I. L., Gershenfeld, N., & Kubinec, M. (1998). Experimental implementation of fast quantum searching. Physical Review Letters, 80(15), 3408.
Nishimori, H., & Takada, K. (1998). Quantum annealing for optimization problems and its applications. Journal of the Physical Society of Japan, 67(10), 3318-3326.
Gottesman, D. (1998). The Heisenberg representation of quantum computers. arXiv preprint quant-ph/9807006.
Braunstein, S. L., Caves, C. M., Jozsa, R., Linden, N., Popescu, S., & Schack, R. (1999). Separability of very noisy mixed states and implications for NMR quantum computing. Physical Review Letters, 83(5), 1054.
Nakamura, Y., Pashkin, Y. A., & Tsai, J. S. (1999). Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature, 398(6730), 786-788.