282 research outputs found
Could Grover's quantum algorithm help in searching an actual database?
I investigate whether it would technologically and economically make sense to
build database search engines based on Grover's quantum search algorithm. The
answer is not fully conclusive but in my judgement rather negative.Comment: 7 pages, LaTe
Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into
an oscillator such that the qubit is protected against small shifts
(translations) in phase space. The idea underlying this encoding is that error
processes of low rate can be expanded into small shift errors. The qubit space
is defined as an eigenspace of two mutually commuting displacement operators
and which act as large shifts/translations in phase space. We
propose and analyze the approximate creation of these qubit states by coupling
the oscillator to a sequence of ancilla qubits. This preparation of the states
uses the idea of phase estimation where the phase of the displacement operator,
say , is approximately determined. We consider several possible forms of
phase estimation. We analyze the performance of repeated and adapative phase
estimation as the simplest and experimentally most viable schemes given a
realistic upper-limit on the number of photons in the oscillator. We propose a
detailed physical implementation of this protocol using the dispersive coupling
between a transmon ancilla qubit and a cavity mode in circuit-QED. We provide
an estimate that in a current experimental set-up one can prepare a good code
state from a squeezed vacuum state using rounds of adapative phase
estimation, lasting in total about sec., with (heralded) chance
of success.Comment: 24 pages, 15 figures. Some minor improvements to text and figures.
Some of the numerical data has been replaced by more accurate simulations.
The improved simulation shows that the code performs better than originally
anticipate
Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
We demonstrate the existence of general constraints on distributed quantum
correlations, which impose a trade-off on bipartite and multipartite
entanglement at once. For all N-mode Gaussian states under permutation
invariance, we establish exactly a monogamy inequality, stronger than the
traditional one, that by recursion defines a proper measure of genuine
N-partite entanglement. Strong monogamy holds as well for subsystems of
arbitrary size, and the emerging multipartite entanglement measure is found to
be scale invariant. We unveil its operational connection with the optimal
fidelity of continuous variable teleportation networks.Comment: 4 pages, 2 figures. Final version, published in PR
Simulating quantum computation by contracting tensor networks
The treewidth of a graph is a useful combinatorial measure of how close the
graph is to a tree. We prove that a quantum circuit with gates whose
underlying graph has treewidth can be simulated deterministically in
time, which, in particular, is polynomial in if
. Among many implications, we show efficient simulations for
log-depth circuits whose gates apply to nearby qubits only, a natural
constraint satisfied by most physical implementations. We also show that
one-way quantum computation of Raussendorf and Briegel (Physical Review
Letters, 86:5188--5191, 2001), a universal quantum computation scheme with
promising physical implementations, can be efficiently simulated by a
randomized algorithm if its quantum resource is derived from a small-treewidth
graph.Comment: 7 figure
Dispersive Qubit Measurement by Interferometry with Parametric Amplifiers
We perform a detailed analysis of how an amplified interferometer can be used
to enhance the quality of a dispersive qubit measurement, such as one performed
on a superconducting transmon qubit, using homodyne detection on an amplified
microwave signal. Our modeling makes a realistic assessment of what is possible
in current circuit-QED experiments; in particular, we take into account the
frequency-dependence of the qubit-induced phase shift for short microwaves
pulses. We compare the possible signal-to-noise ratios obtainable with
(single-mode) SU(1,1) interferometers with the current coherent measurement and
find a considerable reduction in measurement error probability in an
experimentally-accessible range of parameters
Detecting entanglement using a double quantum dot turnstile
We propose a scheme based on using the singlet ground state of an electron
spin pair in a double quantum dot nanostructure as a suitable set-up for
detecting entanglement between electron spins via the measurement of an optimal
entanglement witness. Using time-dependent gate voltages and magnetic fields
the entangled spins are separated and coherently rotated in the quantum dots
and subsequently detected at spin-polarized quantum point contacts. We analyze
the coherent time evolution of the entangled pair and show that by counting
coincidences in the four exits an entanglement test can be done. This set-up is
close to present-day experimental possibilities and can be used to produce
pairs of entangled electrons ``on demand''.Comment: 5 pages, 2 figures - published versio
Simulating quantum operations with mixed environments
We study the physical resources required to implement general quantum
operations, and provide new bounds on the minimum possible size which an
environment must be in order to perform certain quantum operations. We prove
that contrary to a previous conjecture, not all quantum operations on a
single-qubit can be implemented with a single-qubit environment, even if that
environment is initially prepared in a mixed state. We show that a mixed
single-qutrit environment is sufficient to implement a special class of
operations, the generalized depolarizing channels.Comment: 4 pages Revtex + 1 fig, pictures at
http://stout.physics.ucla.edu/~smolin/tetrahedron .Several small correction
Classical simulation of quantum many-body systems with a tree tensor network
We show how to efficiently simulate a quantum many-body system with tree
structure when its entanglement is bounded for any bipartite split along an
edge of the tree. This is achieved by expanding the {\em time-evolving block
decimation} simulation algorithm for time evolution from a one dimensional
lattice to a tree graph, while replacing a {\em matrix product state} with a
{\em tree tensor network}. As an application, we show that any one-way quantum
computation on a tree graph can be efficiently simulated with a classical
computer.Comment: 4 pages,7 figure
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