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[47] R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T.C. White, et al., 2014, Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature 508(7497):500.

[48] L. DiCarlo, J.M. Chow, J.M. Gambetta, L.S. Bishop, B.R. Johnson, D.I. Schuster, J. Majer, A. Blais, L. Frunzio, S.M. Girvin, and R.J. Schoelkopf, 2009, Demonstration of two-qubit algorithms with a superconducting quantum processor, Nature 460:240-244.

[49] E. Lucero, R. Barends, Y. Chen, J. Kelly, M. Mariantoni, A. Megrant, P. OMalley, et al., 2012, Computing prime factors with a Josephson phase qubit quantum processor, Nature Physics 8:719-723.

[50] P.J.J. OMalley, R. Babbush, I.D. Kivlichan, J. Romero, J.R. McClean, R. Barends, J. Kelly, et al., 2016, Scalable quantum simulation of molecular energies, Physical Review X 6:031007.

[51] N.K. Langford, R. Sagastizabal, M. Kounalakis, C. Dickel, A. Bruno, F. Luthi, D.J. Thoen, A. Endo, and L. DiCarlo, 2017, Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling, Nature Communications 8:1715.

[52] M.D. Reed, L. DiCarlo, S.E. Nigg, L. Sun, L. Frunzio, S.M. Girvin, and R.J. Schoelkopf, 2012, Realization for three-qubit quantum error correction with superconducting circuits, Nature 482:382-385.

[53] J. Kelly, R. Barends, A.G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, et al., 2015, State preservation by repetitive error detection in a superconducting quantum circuit, Nature 519:66-69.

[54] A.D. Crcoles, E. Magesan, S.J. Srinivasan, A.W. Cross, M. Steffen, J.M. Gambetta, and J.M. Chow, 2015, Demonstration of a quantum error detection code using a square lattice of four superconducting qubits, Nature Communications 6:6979.

[55] D. Rist, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, 2015, Detecting bit-flip errors in a logical qubit using stabilizer measurements, Nature Communications 6:6983.

[56] N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, et al., 2016, Extending the lifetime of a quantum bit with error correction in superconducting circuits, Nature 536:441-445.

[57] IBM Q Team, 2018, IBM Q 5 Yorktown Backend Specification V1.1.0, https://ibm.biz/qiskit-yorktown; IBM Q Team, 2018, IBM Q 5 Tenerife backend specification V1.1.0, https://ibm.biz/qiskit-tenerife.

[58] Ibid.

[59] M.W. Johnson, M.H.S. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, et al., 2011, Quantum annealing with manufactured spins, Nature 473:194-198.

[60] D Wave, Technology Information, http://dwavesys.com/resources/publications.

[61] John Martinis, private conversation.

[62] W.D. Oliver and P.B. Welander, 2013, Materials in superconducting qubits, MRS Bulletin 38:816.

[63] D. Rosenberg, D.K. Kim, R. Das, D. Yost, S. Gustavsson, D. Hover, P. Krantz, et al., 2017, 3D integrated superconducting qubits, npj Quantum Information 3:42.

[64] B. Foxen, J.Y. Mutus, E. Lucero, R. Graff, A. Megrant, Y. Chen, C. Quintana, et al., 2017, Qubit Compatible Superconducting Interconnects, arXiv:1708.04270.

[65] J.M. Chow, J.M. Gambetta, A.D. Corcoles, S.T. Merkel, J.A. Smolin, C. Rigetti, S. Poletto, G.A. Keefe, M.B. Rothwell, J.R. Rozen, M.B. Ketchen, and M. Steffen, 2012, Universal quantum gate set approaching fault-tolerant thresholds with superconducing qubits, Physical Review Letters 109:060501.

[66] See, for example, J.W. Silverstone, D. Bonneau, J.L. OBrien, and M.G. Thompson, 2016, Silicon quantum photonics, IEEE Journal of Selected Topics in Quantum Electronics 22:390-402;

T. Rudolph, 2017, Why I am optimistic about the silicon-photonic route to quantum computing?, APL Photonics 2:030901.

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5 Essential Hardware Components of a Quantum Computer | Quantum ...

The Quantinuum quantum computer.

Quantinuums quantum computer, which was used in the recent discovery.

A team of physicists say they managed to create a new phase of matter by shooting laser pulses reading out the Fibonacci sequence to a quantum computer in Colorado. The matter phase relies on a quirk of the Fibonacci sequence to remain in a quantum state for longer.

Just as ordinary matter can be in a solid, liquid, gas, or superheated plasmic phase (or state), quantum materials also have phases. The phase refers to how the matter is structured on an atomic levelthe arrangement of its atoms or its electrons, for example. Several years ago, physicists discovered a quantum supersolid, and last year, a team confirmed the existence of quantum spin liquids, a long-suspected phase of quantum matter, in a simulator. The recent team thinks theyve discovered another new phase.

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Quantum bits, or qubits, are like ordinary computer bits in that their values can be 0 or 1, but they can also be 0 or 1 simultaneously, a state of ambiguity that allows the computers to consider many possible solutions to a problem much faster than an ordinary computer. Quantum computers should eventually be able to solve problems that classical computer cant.

Qubits are often atoms; in the recent case, the researchers used 10 ytterbium ions, which were controlled by electric fields and manipulated using laser pulses. When multiple qubits states can be described in relation to one another, the qubits are considered entangled. Quantum entanglement is a delicate agreement between multiple qubits in a system, and the agreement is dissolved the moment any one of those bits values is certain. At that moment, the system decoheres, and the quantum operation falls apart.

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A big challenge of quantum computing is maintaining the quantum state of qubits. The slightest fluctuations in temperature, vibrations, or electromagnetic fields can cause the supersensitive qubits to decohere and their calculations to fall apart. Since the longer the qubits stay quantum, the more you can get done, making computers quantum states persist for as long as possible is a crucial step for the field.

In the recent research, pulsing a laser periodically at the 10 ytterbium qubits kept them in a quantum statemeaning entangledfor 1.5 seconds. But when the researchers pulsed the lasers in the pattern of the Fibonacci sequence, they found that the qubits on the edge of the system remained in a quantum state for about 5.5 seconds, the entire length of the experiment (the qubits could have remained in a quantum state for longer, but the team ended the experiment at the 5.5-second mark). Their research was published this summer in Nature.

You can think of the Fibonacci sequence laser pulses as two frequencies that never overlap. That makes the pulses a quasicrystal: a pattern that has order, but no periodicity.

The key result in my mind was showing the difference between these two different ways to engineer these quantum states and how one was better at protecting it from errors than the other, said study co-author Justin Bohnet, a quantum engineer at Quantinuum, the company whose computer was used in the recent experiment.

The Fibonacci sequence is a numeric pattern in which each number is the sum of the two previous numbers (so 1, 1, 2, 3, 5, 8, 13, and so on). Its history goes back over 2,000 years and is connected to the so-called golden ratio. Now, the unique series may have quantum implications.

It turns out that if you engineer laser pulses in the correct way, your quantum system can have symmetries that come from time translation,said Philipp Dumitrescu, the papers lead author and a quantum physicist who conducted the work while at the Flatiron Institute. A time-translation symmetry means that an experiment will yield the same result, regardless of whether it takes place today, tomorrow, or 100 years from now.

What we realized is that by using quasi-periodic sequences based on the Fibonacci pattern, you can have the system behave as if there are two distinct directions of time, Dumitrescu added.

Shooting the qubits with laser pulses with a periodic (a simple A-B-A-B) pattern didnt prolong the systems quantum state. But by pulsing the laser in a Fibonacci sequence (A-AB-ABA-ABAAB, and so on), the researchers gave the qubits a non-repeating, or quasi-periodic, pattern.

Its similar to the quasicrystals from the Trinity nuclear test site, but instead of being a three-dimensional quasicrystal, the physicists made a quasicrystal in time. In both cases, symmetries that exist at higher dimensions can be projected in a lower dimension, like the tessellated patterns in a two-dimensional Penrose tiling.

With this quasi-periodic sequence, theres a complicated evolution that cancels out all the errors that live on the edge, Dumitrescu said in a Simons Foundation release. By on the edge, hes referring to the qubits farthest from the center of their configuration at any one time. Because of that, the edge stays quantum-mechanically coherent much, much longer than youd expect. The Fibonacci-pattern laser pulses made the edge qubits more robust.

More robust, longer-lived quantum systems are a vital need for the future of quantum computing. If it takes shooting qubits with a very specific mathematical rhythm of laser pulses to keep a quantum computer in an entangled state, then physicists had better start blasting.

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QUANTUM COMPUTING INC. Management's Discussion and Analysis of Financial Condition and Results of Operations, (form 10-Q)  Marketscreener.com

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Model of quantum computation

A quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer. It provides a simple model that captures all of the power of quantum computationthat is, any quantum algorithm can be expressed formally as a particular quantum Turing machine. However, the computationally equivalent quantum circuit is a more common model.[1][2]:2

Quantum Turing machines can be related to classical and probabilistic Turing machines in a framework based on transition matrices. That is, a matrix can be specified whose product with the matrix representing a classical or probabilistic machine provides the quantum probability matrix representing the quantum machine. This was shown by Lance Fortnow.[3]

A way of understanding the quantum Turing machine (QTM) is that it generalizes the classical Turing machine (TM) in the same way that the quantum finite automaton (QFA) generalizes the deterministic finite automaton (DFA). In essence, the internal states of a classical TM are replaced by pure or mixed states in a Hilbert space; the transition function is replaced by a collection of unitary matrices that map the Hilbert space to itself.[4]

That is, a classical Turing machine is described by a 7-tuple M = Q , , b , , , q 0 , F {displaystyle M=langle Q,Gamma ,b,Sigma ,delta ,q_{0},Frangle } .

For a three-tape quantum Turing machine (one tape holding the input, a second tape holding intermediate calculation results, and a third tape holding output):

The above is merely a sketch of a quantum Turing machine, rather than its formal definition, as it leaves vague several important details: for example, how often a measurement is performed; see for example, the difference between a measure-once and a measure-many QFA. This question of measurement affects the way in which writes to the output tape are defined.

In 1980 and 1982, physicist Paul Benioff published articles[5][6] that first described a quantum mechanical model of Turing machines. A 1985 article written by Oxford University physicist David Deutsch further developed the idea of quantum computers by suggesting that quantum gates could function in a similar fashion to traditional digital computing binary logic gates.[4]

Iriyama, Ohya, and Volovich have developed a model of a linear quantum Turing machine (LQTM). This is a generalization of a classical QTM that has mixed states and that allows irreversible transition functions. These allow the representation of quantum measurements without classical outcomes.[7]

A quantum Turing machine with postselection was defined by Scott Aaronson, who showed that the class of polynomial time on such a machine (PostBQP) is equal to the classical complexity class PP.[8]

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Aspect of physics

In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization".[1] This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.

For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.

The word quantum is the neuter singular of the Latin interrogative adjective quantus, meaning "how much". "Quanta", the neuter plural, short for "quanta of electricity" (electrons), was used in a 1902 article on the photoelectric effect by Philipp Lenard, who credited Hermann von Helmholtz for using the word in the area of electricity. However, the word quantum in general was well known before 1900,[2] e.g. quantum was used in E.A. Poe's Loss of Breath. It was often used by physicians, such as in the term quantum satis, "the amount which is enough". Both Helmholtz and Julius von Mayer were physicians as well as physicists. Helmholtz used quantum with reference to heat in his article[3] on Mayer's work, and the word quantum can be found in the formulation of the first law of thermodynamics by Mayer in his letter[4] dated July 24, 1841.

In 1901, Max Planck used quanta to mean "quanta of matter and electricity",[5] gas, and heat.[6] In 1905, in response to Planck's work and the experimental work of Lenard (who explained his results by using the term quanta of electricity), Albert Einstein suggested that radiation existed in spatially localized packets which he called "quanta of light" ("Lichtquanta").[7]

The concept of quantization of radiation was discovered in 1900 by Max Planck, who had been trying to understand the emission of radiation from heated objects, known as black-body radiation. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called "bundles", or "energy elements"),[8] Planck accounted for certain objects changing color when heated.[9] On December 14, 1900, Planck reported his findings to the German Physical Society, and introduced the idea of quantization for the first time as a part of his research on black-body radiation.[10] As a result of his experiments, Planck deduced the numerical value of h, known as the Planck constant, and reported more precise values for the unit of electrical charge and the AvogadroLoschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.

While quantization was first discovered in electromagnetic radiation, it describes a fundamental aspect of energy not just restricted to photons.[11]In the attempt to bring theory into agreement with experiment, Max Planck postulated that electromagnetic energy is absorbed or emitted in discrete packets, or quanta.[12]

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