Quantum
Computers – Implementations |

**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; Plans a commercial 50-qubit computer [@ news sn(17)jun].

@ __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].

@ __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__: Hemaspaandra et
al
qp/99 [speed];
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].

**Approaches** > s.a. quantum computing [specific physical theories].

* __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).

* __Counterfactual computation__:
An approach in which the result of a computation may be learned 'without actually running the computer'.

@ __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 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.

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29 nov 2017