Quantum Computers – Implementations and Applications  

In General > s.a. black holes; spin chains.
* Issue: Efficient fault-tolerant quantum computation requires error probabilities for qubit manipulations below ~10−4, but quantum states are fragile with respect to decoherence (spontaneous radiation, vibrations, can't make a measurement before it's done!), and one needs error correction techniques.
* 1995: A single quantum logic gate has been made (but a useful computer would need thousands of them).
* 1998: 3-bit memory.
* 1999: First simulation, a truncated simple harmonic oscillator, with NMR-type (each qubit is the spin of a H or C atom in an external B-field).
* 2002: Physical realization of NOT operation – or something analogous for qubits [@ De Martini et al Nat(02)oct].
* 2003: Two qubits entangled in a solid-state device [@ Pashkin et al Nat(03)feb].
* 2007: Vancouver firm claims to have developed commercially viable quantum computer [@ news pw(07)feb], but Intel Corporation's Bourianoff estimates that we're at least 50 years away from a true quantum computer.
* 2008: Useful quantum computers are far beyond current technology, mainly because of the difficulties in maintaining coherence of all the qubits.
* 2011: Controlled entanglement of 14 qubits achieved [@ Monz et al PRL(11) + news physorg(11)apr].
* 2013: NASA buys into quantum computer [@ news bbc(13)may]; Pairs of linear equations solved [@ news pw(13)jun].
* 2014: Simon's algorithm run on a 6-qubit quantum computer.
* 2016: IBM makes the 5-qubit Quantum Experience available online for free.
* 2017: IBM creates a 16-qubit quantum computer and a 17-qubit prototype [@ news sn(17)jun]; 7-qubit machine used at IBM to simulate beryllium hydride.
* 2018: Entanglement of 20 individually controlled qubits [@ Friis et al PRX(18)]; IBM still working on 50-qubit computer.
* 2020: Supremacy achieved by light-based photonic quantum computer Jiuzhang.
* Simulation: A simple quantum computer can be simulated on a normal computer, but at around 50 qubits it becomes nearly impossible.
@ Overview: DiVincenzo FdP(00)qp; Stoneham Phy(09), Paraoanu PP(11)-a1110, Sevilla & Riedel a2009 [future assessment].
@ Experiment: Monroe et al PRL(95); Turchette et al PRL(95); Bose et al PTRS(98)gq/97-proc; Devitt PRA(16)-a1605 [in the cloud]; Santos RBEF(17)-a1610 [the IBM quantum computer]; Boixo et al nPhys(18)-a1608 [characterizing quantum supremacy]; Svozil a1911, Alicki a2001, Horner & Symons a2009-in [comments on quantum supremacy].
@ Errors: news pn(96)oct; DiVincenzo & Loss SM(98)cm/97-fs; Preskill PRS(98)qp/97, qp/97-in; Cory et al PRL(98); & R Laflamme.
@ Related topics: Trugenberger PRL(01)qp/00 [memory]; Anders & Browne PRL(09) [computational power of correlations]; Novais et al PRA(10)-a1004 [upper bound on the time available]; Steiger et al Quant(18)-a1612 [the ProjectQ open source software]; Kalai a1908-in [argument against feasibility]; Leymann et al a2003-proc [in the cloud]. Fox et al PRPER(20)-a2006 [education and the quantum industry]; Salehi et al IEEE(21)-a2010 [quantum programming workshop].

Approaches > s.a. quantum computing [specific physical theories, status].
* Types: NMR-type; Josephson junctions (1997); Quantum dots (1998); Ion trap-type (1998, 5 ions trapped); Photons (trapped between mirrors); Geometric or holonomic quantum computation (based on geometric phases); Other (e.g., states of P impurities in Si); 2018, IBM's computer uses superconducting circuits in which two distinct current states make up a qubit; These qubits are easier to manipulate and less delicate than individual photons or ions, and the hardware can be made using well-established manufacturing methods.
* Counterfactual computation: An approach in which the result of a computation may be learned 'without actually running the computer'.
* Difficulty: It is devilishly difficult to maintain qubits for any length of time, because they tend to decohere.
@ With entangled states: Wootters CM(02)qp/00 [qubit chains]; Jozsa & Linden PRS(03)qp/02.
@ With molecules: Gershenfeld & Chuang SA(98)jun; Hosaka et al PRL(10) + Walmsley Phy(10).
@ Fault-tolerant: Kitaev AP(03)qp/97 [with anyons]; Preskill PT(99)jun; Knill Nat(05)mar; Gottesman qp/07 [rev]; Barrett & Stace PRL(10) + news(10)nov; Vijay et al PRX(15) [anyon excitations from Majorana fermions arranged on a 2D lattice].
@ Counterfactual computation: Hosten et al Nat(06)feb; Vaidman PRL(07); Kong et al PRL(15) + news PhysOrg(15)aug.
@ Quantum networks: Elliott qp/04, et al qp/05-conf [DARPA]; news pw(05)dec.
@ Optical: Kok LNP(09)-a0705; O'Brien Sci(07)-a0803 [rev]; Li et al PRX(15) [resource costs]; news sn(20)dec [photonic quantum computer supremacy].
@ Geometric phase: Mitchell qp/05; news pw(07)nov [qubit based on Berry's phase]; Sjöqvist Phy(08); Sjöqvist et al QIP(16)-a1311.
@ Achievements: news sn(14)nov [Simon's algorithm implemented]; news pw(16)jun [universal quantum computer prototype].
@ Related topics: Shnirman et al PRL(97) [Josephson junctions]; Loss & DiVincenzo PRA(98) [quantum dots]; Moore & Nilsson qp/98, qp/98 [parallel]; Karafyllidis PLA(03) [cellular architecture]; Häffner et al PRP(08) [trapped ions]; Byrnes et al PRA(12)-a1103 [using Bose-Einstein condensates]; Araújo et al PRA(17)-a1706 [with indefinite causal structures]; Weiss & Saffman PT(17)jul [with neutral atoms].

Topological Quantum Computing > s.a. generalized particle statistics.
* Idea: A proposal that uses topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but particles obeying non-Abelian anyon statistics; Quantum information is stored in states with multiple quasiparticles which have a topological degeneracy, and the unitary gate operations necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states; It has emerged as a promising approach to constructing a fault-tolerant quantum computer, because the non-local encoding of the quasiparticle states makes them immune to errors caused by local perturbations; 2008, To date, the only such topological states thought to have been found in nature are fractional quantum Hall states.
@ References: Collins SA(06)apr; Das Sarma et al PT(06)jul; Brennen & Pachos PRS(08)-a0704 [intro]; Nayak et al RMP(08) [rev]; Thompson a1012; Cesare et al PRA(15)-a1406 [adiabatic]; Pachos & Simon NJP(14)-a1406 [focus issue]; Roy & DiVincenzo a1701-ln; Lahtinen & Pachos SPP(17)-a1705 [intro]; Rowell & Wang a1705 [conceptual development]; news cosmos(17)nov.

Applications > s.a. game theory.
@ Searching: Chuang et al PRL(98) + pn(98)apr [experiment]; Lomonaco qp/00-ln; Grover AJP(01)jul [algorithm]; Montanaro QIC(09)qp/07 [search of partially ordered sets]; Dohotaru & Hoyer QIC(09)-a0810 [lower bound].
@ Application to classical evolution: Meyer qp/01 [solving classical evolutions]; Georgeot & Shepelyansky qp/03 [chaotic evolution]; Margolus a1109 [quantum emulation of classical dynamics]; Bogdanov & Bogdanova a1412-conf [Lorenz and Rössler strange attractors]; Linden et al a2004 [solving the heat equation].
@ Other physics problems: Somaroo et al PRL(99) + pn(99)jul [simulating another quantum system]; Joseph et al a2105 [cosmology]; > s.a. computational physics [quantum simulation]; ising model; lattice field theories [lattice fermions]; lattice gauge theories; quantum cosmology; quantum gravity; SU(2); topological field theories; Wavelets.
@ Other applications: Becker a1910 [game, Flying Unicorn]; Zhu et al a2005 [combinatorial problems]; Miranda a2006 [quantum computing tools for music].

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