26,292 research outputs found
Universality and programmability of quantum computers
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of
universal physical simulation procedure. Much of the writing about quantum
logic circuits and quantum Turing machines has shown how these machines can
simulate an arbitrary unitary transformation on a finite number of qubits. The
problem of universality has been addressed most famously in a paper by Deutsch,
and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum
logic circuit model, developed by Feynman and Deutsch, has been more prominent
in the research literature than Deutsch's quantum Turing machines. Quantum
Turing machines form a class closely related to deterministic and probabilistic
Turing machines and one might hope to find a universal machine in this class. A
universal machine is the basis of a notion of programmability. The extent to
which universality has in fact been established by the pioneers in the field is
examined and this key notion in theoretical computer science is scrutinised in
quantum computing by distinguishing various connotations and concomitant
results and problems.Comment: 17 pages, expands on arXiv:0705.3077v1 [quant-ph
Fast simulation of a quantum phase transition in an ion-trap realisable unitary map
We demonstrate a method of exploring the quantum critical point of the Ising
universality class using unitary maps that have recently been demonstrated in
ion trap quantum gates. We reverse the idea with which Feynman conceived
quantum computing, and ask whether a realisable simulation corresponds to a
physical system. We proceed to show that a specific simulation (a unitary map)
is physically equivalent to a Hamiltonian that belongs to the same universality
class as the transverse Ising Hamiltonian. We present experimental signatures,
and numerical simulation for these in the six-qubit case.Comment: 12 pages, 6 figure
Driven Markovian Quantum Criticality
We identify a new universality class in one-dimensional driven open quantum
systems with a dark state. Salient features are the persistence of both the
microscopic non-equilibrium conditions as well as the quantum coherence of
dynamics close to criticality. This provides a non-equilibrium analogue of
quantum criticality, and is sharply distinct from more generic driven systems,
where both effective thermalization as well as asymptotic decoherence ensue,
paralleling classical dynamical criticality. We quantify universality by
computing the full set of independent critical exponents within a functional
renormalization group approach.Comment: 5+3 pages, 2 figures; published version with improved presentation of
result
Two-Bit Gates are Universal for Quantum Computation
A proof is given, which relies on the commutator algebra of the unitary Lie
groups, that quantum gates operating on just two bits at a time are sufficient
to construct a general quantum circuit. The best previous result had shown the
universality of three-bit gates, by analogy to the universality of the Toffoli
three-bit gate of classical reversible computing. Two-bit quantum gates may be
implemented by magnetic resonance operations applied to a pair of electronic or
nuclear spins. A ``gearbox quantum computer'' proposed here, based on the
principles of atomic force microscopy, would permit the operation of such
two-bit gates in a physical system with very long phase breaking (i.e., quantum
phase coherence) times. Simpler versions of the gearbox computer could be used
to do experiments on Einstein-Podolsky-Rosen states and related entangled
quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon
reques
Hypergeometric analytic continuation of the strong-coupling perturbation series for the 2d Bose-Hubbard model
We develop a scheme for analytic continuation of the strong-coupling
perturbation series of the pure Bose-Hubbard model beyond the Mott
insulator-to-superfluid transition at zero temperature, based on hypergeometric
functions and their generalizations. We then apply this scheme for computing
the critical exponent of the order parameter of this quantum phase transition
for the two-dimensional case, which falls into the universality class of the
three-dimensional model. This leads to anontrivial test of the
universality hypothesis.Comment: 5 figure
A Linear-Optical Proof that the Permanent is #P-Hard
One of the crown jewels of complexity theory is Valiant's 1979 theorem that
computing the permanent of an n*n matrix is #P-hard. Here we show that, by
using the model of linear-optical quantum computing---and in particular, a
universality theorem due to Knill, Laflamme, and Milburn---one can give a
different and arguably more intuitive proof of this theorem.Comment: 12 pages, 2 figures, to appear in Proceedings of the Royal Society A.
doi: 10.1098/rspa.2011.023
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