1,759 research outputs found
Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians
We present two universal models of quantum computation with a
time-independent, frustration-free Hamiltonian. The first construction uses
3-local (qubit) projectors, and the second one requires only 2-local
qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea and
use a railroad-switch type clock register. The resources required to simulate a
quantum circuit with L gates in this model are O(L) small-dimensional quantum
systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L)
local, constant norm, projector terms, the possibility to prepare computational
basis product states, a running time O(L log^2 L), and the possibility to
measure a few qubits in the computational basis. Our models also give a
simplified proof of the universality of 3-local Adiabatic Quantum Computation.Comment: Added references to work by de Falco et al., and realized that
Feynman's '85 paper already contained the idea of a switch in i
IS THERE A CLASSICAL ANALOG OF A QUANTUM TIME-TRANSLATION MACHINE?
In a recent article [D. Suter, Phys. Rev. {\bf A 51}, 45 (1995)] Suter has
claimed to present an optical implementation of the quantum time-translation
machine which ``shows all the features that the general concept predicts and
also allows, besides the quantum mechanical, a classical description.'' It is
argued that the experiment proposed and performed by Suter does not have the
features of the quantum time-translation machine and that the latter has no
classical analog.Comment: 7 pages, LaTe
Variance Control in Weak Value Measurement Pointers
The variance of an arbitrary pointer observable is considered for the general
case that a complex weak value is measured using a complex valued pointer
state. For the typical cases where the pointer observable is either its
position or momentum, the associated expressions for the pointer's variance
after the measurement contain a term proportional to the product of the weak
value's imaginary part with the rate of change of the third central moment of
position relative to the initial pointer state just prior to the time of the
measurement interaction when position is the observable - or with the initial
pointer state's third central moment of momentum when momentum is the
observable. These terms provide a means for controlling pointer position and
momentum variance and identify control conditions which - when satisfied - can
yield variances that are smaller after the measurement than they were before
the measurement. Measurement sensitivities which are useful for estimating weak
value measurement accuracies are also briefly discussed.Comment: submitted to Phys Rev
Fault-tolerant quantum computation with long-range correlated noise
We prove a new version of the quantum accuracy threshold theorem that applies
to non-Markovian noise with algebraically decaying spatial correlations. We
consider noise in a quantum computer arising from a perturbation that acts
collectively on pairs of qubits and on the environment, and we show that an
arbitrarily long quantum computation can be executed with high reliability in D
spatial dimensions, if the perturbation is sufficiently weak and decays with
the distance r between the qubits faster than 1/r^D.Comment: 4 page
Finite automata for caching in matrix product algorithms
A diagram is introduced for visualizing matrix product states which makes
transparent a connection between matrix product factorizations of states and
operators, and complex weighted finite state automata. It is then shown how one
can proceed in the opposite direction: writing an automaton that ``generates''
an operator gives one an immediate matrix product factorization of it. Matrix
product factorizations have the advantage of reducing the cost of computing
expectation values by facilitating caching of intermediate calculations. Thus
our connection to complex weighted finite state automata yields insight into
what allows for efficient caching in matrix product algorithms. Finally, these
techniques are generalized to the case of multiple dimensions.Comment: 18 pages, 19 figures, LaTeX; numerous improvements have been made to
the manuscript in response to referee feedbac
Nonlocal Aspects of a Quantum Wave
Various aspects of nonlocality of a quantum wave are discussed. In
particular, the question of the possibility of extracting information about the
relative phase in a quantum wave is analyzed. It is argued that there is a
profound difference in the nonlocal properties of the quantum wave between
fermion and boson particles. The phase of the boson quantum state can be found
from correlations between results of measurements in separate regions. These
correlations are identical to the Einstein-Podolsky-Rosen (EPR) correlations
between two entangled systems. An ensemble of results of measurements performed
on fermion quantum waves does not exhibit the EPR correlations and the relative
phase of fermion quantum waves cannot be found from these results. The
existence of a physical variable (the relative phase) which cannot be measured
locally is the nonlocality aspect of the quantum wave of a fermion.Comment: 12 page
Sequential weak measurement
The notion of weak measurement provides a formalism for extracting
information from a quantum system in the limit of vanishing disturbance to its
state. Here we extend this formalism to the measurement of sequences of
observables. When these observables do not commute, we may obtain information
about joint properties of a quantum system that would be forbidden in the usual
strong measurement scenario. As an application, we provide a physically
compelling characterisation of the notion of counterfactual quantum
computation
PR-box correlations have no classical limit
One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture
that two axioms, namely relativistic causality ("no superluminal signalling")
and nonlocality, so nearly contradict each other that a unique theory - quantum
mechanics - reconciles them. But superquantum (or "PR-box") correlations imply
that quantum mechanics is not the most nonlocal theory (in the sense of
nonlocal correlations) consistent with relativistic causality. Let us consider
supplementing these two axioms with a minimal third axiom: there exists a
classical limit in which macroscopic observables commute. That is, just as
quantum mechanics has a classical limit, so must any generalization of quantum
mechanics. In this classical limit, PR-box correlations violate relativistic
causality. Generalized to all stronger-than-quantum bipartite correlations,
this result is a derivation of Tsirelson's bound without assuming quantum
mechanics.Comment: for a video of this talk at the Aharonov-80 Conference in 2012 at
Chapman University, see quantum.chapman.edu/talk-10, published in Quantum
Theory: A Two-Time Success Story (Yakir Aharonov Festschrift), eds. D. C.
Struppa and J. M. Tollaksen (New York: Springer), 2013, pp. 205-21
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