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.

* __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 [future assessment].

@ __Experiment__: Monroe et al PRL(95);
Turchette et al PRL(95);
Bose et al PTRS(98)gq/97-proc;
Devitt a1605 [in the cloud];
Santos RBEF(17)-a1610 [the IBM quantum computer];
Boixo et al a1608 [characterizing quantum supremacy];
Svozil a1911,
Alicki a2001 [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 a1612 [the ProjectQ open source software];
Kalai a1908-in [argument against feasibility];
Leymann et al a2003-proc [in the cloud].

**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].

@ __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];
> 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].

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