Quantum Computer

Quantum computer 1 A Quantum Computer with spins as quantum bits was also formulated for use as a quantum space-time in

Quantum computer 1 Although Quantum Computing is still in its infancy, experiments have been carried out in which Quantum Computational operations were executed on a very small number of qubits (quantum bits). Both practical and theoretical research continues, and many national governments and military funding agencies support Quantum Computing research to develop Quantum Computers for both civilian and national security purposes, such as cryptanalysis.

Quantum computer 1 Large-scale Quantum Computers will be able to solve certain problems much more quickly than any classical computer using the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems

Quantum computer - Basis 1 A quantum computer operates by setting the qubits in a controlled initial state that represents the problem at hand and by manipulating those qubits with a fixed sequence of quantum logic gates

Quantum computer - Basis 1 An example of an implementation of qubits for a quantum computer could start with the use of particles with two spin states: "down" and "up" (typically written and, or and ). But in fact any system possessing an observable quantity A, which is conserved under time evolution such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit. This is true because any such system can be mapped onto an effective spin-1/2 system.

Quantum computer - Bits vs. qubits 1 A Quantum Computer with a given number of qubits is fundamentally different from a classical computer composed of the same number of classical bits

Quantum computer - Bits vs. qubits 1 The state of a three-qubit Quantum Computer is similarly described by an eight-dimensional vector (a,b,c,d,e,f,g,h), called a ket

Quantum computer - Operation 1 However, by repeatedly initializing, running and measuring the quantum computer, the probability of getting the correct answer can be increased.

Quantum computer - Operation 1 For more details on the sequences of operations used for various quantum algorithms, see universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch-Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.

Quantum computer - Potential 1 This ability would allow a Quantum Computer to decrypt many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem

Quantum computer - Potential 1 Lattice-based cryptosystems are also not known to be broken by Quantum Computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem

Quantum computer - Potential 1 For some problems, Quantum Computers offer a polynomial speedup

Quantum computer - Potential 1 For problems with all four properties, the time for a Quantum Computer to solve this will be proportional to the square root of the number of inputs. That can be a very large speedup, reducing some problems from years to seconds. It can be used to attack symmetric ciphers such as Triple DES and AES by attempting to guess the secret key.

Quantum computer - Potential 1 There are a number of technical challenges in building a large-scale Quantum Computer, and thus far Quantum Computers have yet to solve a problem faster than a classical computer. David DiVincenzo, of IBM, listed the following requirements for a practical Quantum Computer:

Quantum computer - Quantum decoherence 1 A very different approach to the stability- decoherence problem is to create a topological Quantum Computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.

Quantum computer - Developments 1 One-way Quantum Computer (computation decomposed into sequence of one-qubit measurements applied to a highly entangled initial state or cluster state)

Quantum computer - Developments 1 Adiabatic Quantum Computer or computer based on Quantum annealing (computation decomposed into a slow continuous transformation of an initial Hamiltonian into a final Hamiltonian, whose ground states contains the solution)

Quantum computer - Developments 1 Topological Quantum Computer (computation decomposed into the braiding of anyons in a 2D lattice)

Quantum computer - Developments 1 For physically implementing a Quantum Computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits):

Quantum computer - Developments 1 Superconductor-based Quantum Computers (including SQUID-based Quantum Computers) (qubit implemented by the state of small superconducting circuits (Josephson junctions))

Quantum computer - Developments 1 Trapped ion Quantum Computer (qubit implemented by the internal state of trapped ions)

Quantum computer - Developments 1 Electrically defined or self-assembled quantum dots (e.g. the Loss-DiVincenzo Quantum Computer or) (qubit given by the spin states of an electron trapped in the quantum dot)

Quantum computer - Developments 1 Quantum dot charge based semiconductor Quantum Computer (qubit is the position of an electron inside a double quantum dot)

Quantum computer - Developments 1 Solid-state NMR Kane Quantum Computers (qubit realized by the nuclear spin state of phosphorus donors in silicon)

Quantum computer - Developments 1 Electrons-on-helium Quantum Computers (qubit is the electron spin)

Quantum computer - Developments 1 Fullerene-based ESR Quantum Computer (qubit based on the electronic spin of atoms or molecules encased in fullerene structures)

Quantum computer - Developments 1 Optics-based Quantum Computer (Quantum optics) (qubits realized by appropriate states of different modes of the electromagnetic field, e.g.)

Quantum computer - Developments 1 Diamond-based Quantum Computer (qubit realized by the electronic or nuclear spin of Nitrogen-vacancy centers in diamond)

Quantum computer - Developments 1 Bose–Einstein condensate-based Quantum Computer

Quantum computer - Developments 1 Transistor-based Quantum Computer – string Quantum Computers with entrainment of positive holes using an electrostatic trap

Quantum computer - Developments 1 Rare-earth-metal-ion-doped inorganic crystal based Quantum Computers (qubit realized by the internal electronic state of dopants in optical fibers)

Quantum computer - Developments 1 This approach was liked by investors more than by some academic critics, who said that D-Wave had not yet sufficiently demonstrated that they really had a Quantum Computer

Quantum computer - Developments 1 In September 2011 researchers also proved that a Quantum Computer can be made with a Von Neumann architecture (separation of RAM).

Quantum computer - Developments 1 In April 2012 a multinational team of researchers from the University of Southern California, Delft University of Technology, the Iowa State University of Science and Technology, and the University of California, Santa Barbara, constructed a two-qubit Quantum Computer on a crystal of diamond doped with some manner of impurity, that can easily be scaled up in size and functionality at room temperature

Quantum computer - Developments 1 In September 2012, Australian researchers at the University of New South Wales said the world's first Quantum Computer was just 5 to 10 years away, after announcing a global breakthrough enabling manufacture of its memory building blocks. A research team led by Australian engineers created the first working "quantum bit" based on a single atom in silicon, invoking the same technological platform that forms the building blocks of modern day computers, laptops and phones.

Quantum computer - Developments 1 In February 2013, a new technique Boson Sampling was reported by two groups using photons in an optical lattice that is not a universal Quantum Computer but which may be good enough for practical problems. Science Feb 15,

Quantum computer - Developments 1 In May 2013, Google Inc announced that it was launching the Quantum Artificial Intelligence Lab, to be hosted by NASA’s Ames Research Center. The lab will house a 512-qubit Quantum Computer from D- Wave Systems, and the USRA (Universities Space Research Association) will invite researchers from around the world to share time on it. The goal being to study how Quantum Computing might advance machine learning

Quantum computer - Relation to computational complexity theory 1 A quantum computer is said to "solve" a problem if, for every instance, its answer will be right with high probability

Quantum computer - Relation to computational complexity theory 1 BQP is suspected to be disjoint from NP- complete and a strict superset of P, but that is not known. Both integer factorization and discrete log are in BQP. Both of these problems are NP problems suspected to be outside BPP, and hence outside P. Both are suspected to not be NP-complete. There is a common misconception that quantum computers can solve NP-complete problems in polynomial time. That is not known to be true, and is generally suspected to be false.

Quantum computer - Relation to computational complexity theory 1 The capacity of a quantum computer to accelerate classical algorithms has rigid limits—upper bounds of quantum computation's complexity. The overwhelming part of classical calculations cannot be accelerated on a quantum computer. A similar fact takes place for particular computational tasks, like the search problem, for which Grover's algorithm is optimal.

Quantum computer - Relation to computational complexity theory 1 The existence of "standard" quantum computers does not disprove the Church–Turing thesis

Adiabatic quantum computation - D-Wave Quantum Computers 1 The D-Wave is an adiabatic quantum computer made by a Canadian company of the same name. Lockheed-Martin purchased one for $10 million in 2011 and Google purchased a Model 2 D-Wave in May 2013 with 512 qubits.

Nuclear magnetic resonance quantum computer 1 NMR Quantum Computing uses the spin states of molecules as qubits. NMR differs from other implementations of Quantum Computers in that it uses an ensemble of systems, in this case molecules. The ensemble is initialized to be the thermal equilibrium state (see quantum statistical mechanics). In mathematical parlance, this state is given by the density matrix:

Nuclear magnetic resonance quantum computer 1 Some early success was obtained in performing quantum algorithms in NMR systems due to the relative maturity of NMR technology. For instance, in 2001 researchers at IBM reported the successful implementation of Shor's algorithm in a 7-qubit NMR Quantum Computer.

Nuclear magnetic resonance quantum computer 1 Hence NMR Quantum Computing experiments are likely to have been only classical simulations of a Quantum Computer.

One-way quantum computer 1 The one-way or measurement based Quantum Computer is a method of Quantum Computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.

One-way quantum computer - Implementations 1 One-way quantum computation has been demonstrated by running the 2 qubit Grover's algorithm on a 2x2 cluster state of photons. A linear optics quantum computer based on one-way computation has been proposed.

Kane quantum computer 1 The Kane Quantum Computer is a proposal for a scalable Quantum Computer proposed by Bruce Kane in 1998, then at the University of New South Wales. Often thought of as a hybrid between quantum dot and NMR Quantum Computers, the Kane computer is based on an array of individual phosphorus donor atoms embedded in a pure silicon lattice. Both the nuclear spins of the donors and the spins of the donor electrons participate in the computation.

Kane quantum computer 1 Nuclear spin is useful to perform single- qubit operations, but to make a Quantum Computer, two-qubit operations are also required

Kane quantum computer 1 Unlike many Quantum Computation schemes, the Kane Quantum Computer is in principle scalable to an arbitrary number of qubits. This is possible because qubits may be individually addressed by electrical means.

Kane quantum computer 1 The group remains optimistic that a practical large- scale Quantum Computer can be built.

Non-deterministic Turing machine - Comparison with quantum computers 1 It is a common misconception that quantum computers are NTMs. It is believed but has not been proven that the power of quantum computers is incomparable to that of NTMs. That is, problems likely exist that an NTM could efficiently solve that a quantum computer cannot. A likely example of problems solvable by NTMs but not by quantum computers in polynomial time are NP- complete problems.

Trapped ion quantum computer 1 A trapped ion Quantum Computer is a type of Quantum Computer

Trapped ion quantum computer 1 This makes the trapped ion Quantum Computer system one of the most promising architectures for a scalable, universal Quantum Computer

Topological quantum computer 1 To live up to its name, a topological Quantum Computer must provide the unique computation properties promised by a conventional Quantum Computer design, which uses trapped quantum particles. Fortunately in 2002, Michael H. Freedman along with Zhenghan Wang, both with Microsoft, and Michael Larsen of Indiana University proved that a topological Quantum Computer can, in principle, perform any computation that a conventional Quantum Computer can do.

Topological quantum computer 1 However, any level of precision for the answer can be obtained by adding more braid twists (logic circuits) to the topological Quantum Computer, in a simple linear relationship

Loss-DiVincenzo quantum computer 1 This was done in a way that fulfilled DiVincenzo Criteria for a scalable Quantum Computer,D

Loss-DiVincenzo quantum computer 1 A candidate for such a Quantum Computer is a lateral quantum dot system.

Loss-DiVincenzo quantum computer - Implementation of the two-qubit gate 1 The Loss–DiVincenzo quantum computer operates, basically, using inter-dot gate voltage for implementing Swap (computer science) operations and local magnetic fields (or any other local spin manipulation) for implementing the Controlled NOT gate (CNOT gate).

Diamond-based quantum computer 1 An individual N-V center can be viewed as a basic unit of a Quantum Computer, and it has potential applications in novel, more efficient fields of electronics and computational science including quantum cryptography and spintronics.

Diamond-based quantum computer - Energy level structure and its manipulation by external fields 1 The first pulse coherently excites the electron spins, and this coherence is then manipulated and probed by the subsequent pulses. Those dynamic effects are rather important for practical realization of quantum computers, which ought to work at high frequency.

Nanoelectronics - Quantum computers 1 Entirely new approaches for computing exploit the laws of quantum mechanics for novel quantum computers, which enable the use of fast quantum algorithms. The Quantum computer has quantum bit memory space termed Qubit for several computations at the same time. This facility may improve the performance of the older systems.

Quantum computers 1 A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in

Quantum computers 1 quantum computing is still in its infancy but experiments have been carried out in which quantum computational operations were executed on a very small number of qubits (quantum bits).[ bodes-future-quantum.html New qubit control bodes well for future of quantum computing] Both practical and theoretical research continues, and many national governments and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.[ ap.shtml Quantum Information Science and Technology Roadmap] for a sense of where the research is heading.

Quantum computers 1 Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computer using the best currently known algorithms, like integer factorization using Shor's algorithm or the Quantum algorithm#Quantum simulation|simulation of quantum many- body systems

Search algorithm - For quantum computers 1 There are also search methods designed for quantum computers, like Grover's algorithm, that are theoretically faster than linear or brute-force search even without the help of data structures or heuristics.

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