1,027 research outputs found
Virtual Quantum Subsystems
The physical resources available to access and manipulate the degrees of
freedom of a quantum system define the set of operationally relevant
observables. The algebraic structure of selects a preferred tensor
product structure i.e., a partition into subsystems. The notion of compoundness
for quantum system is accordingly relativized. Universal control over virtual
subsystems can be achieved by using quantum noncommutative holonomiesComment: Presentation improved, to appear in PRL. 4 Pages, RevTe
Quantum fidelity and quantum phase transitions in matrix product states
Matrix product states, a key ingredient of numerical algorithms widely
employed in the simulation of quantum spin chains, provide an intriguing tool
for quantum phase transition engineering. At critical values of the control
parameters on which their constituent matrices depend, singularities in the
expectation values of certain observables can appear, in spite of the
analyticity of the ground state energy. For this class of generalized quantum
phase transitions we test the validity of the recently introduced fidelity
approach, where the overlap modulus of ground states corresponding to slightly
different parameters is considered. We discuss several examples, successfully
identifying all the present transitions. We also study the finite size scaling
of fidelity derivatives, pointing out its relevance in extracting critical
exponents.Comment: 7 pages, 3 figure
Universal control of quantum subspaces and subsystems
We describe a broad dynamical-algebraic framework for analyzing the quantum
control properties of a set of naturally available interactions. General
conditions under which universal control is achieved over a set of
subspaces/subsystems are found. All known physical examples of universal
control on subspaces/systems are related to the framework developed here.Comment: 4 Pages RevTeX, Some typos fixed, references adde
Computation on a Noiseless Quantum Code and Symmetrization
Let be the state-space of a quantum computer coupled with the
environment by a set of error operators spanning a Lie algebra
Suppose admits a noiseless quantum code i.e., a subspace annihilated by We show that a universal set of
gates over is obtained by any generic pair of -invariant
gates. Such gates - if not available from the outset - can be obtained by
resorting to a symmetrization with respect to the group generated by Any computation can then be performed completely within the coding
decoherence-free subspace.Comment: One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no
figure
Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
Universal quantum computation on decoherence-free subspaces and subsystems
(DFSs) is examined with particular emphasis on using only physically relevant
interactions. A necessary and sufficient condition for the existence of
decoherence-free (noiseless) subsystems in the Markovian regime is derived here
for the first time. A stabilizer formalism for DFSs is then developed which
allows for the explicit understanding of these in their dual role as quantum
error correcting codes. Conditions for the existence of Hamiltonians whose
induced evolution always preserves a DFS are derived within this stabilizer
formalism. Two possible collective decoherence mechanisms arising from
permutation symmetries of the system-bath coupling are examined within this
framework. It is shown that in both cases universal quantum computation which
always preserves the DFS (*natural fault-tolerant computation*) can be
performed using only two-body interactions. This is in marked contrast to
standard error correcting codes, where all known constructions using one or
two-body interactions must leave the codespace during the on-time of the
fault-tolerant gates. A further consequence of our universality construction is
that a single exchange Hamiltonian can be used to perform universal quantum
computation on an encoded space whose asymptotic coding efficiency is unity.
The exchange Hamiltonian, which is naturally present in many quantum systems,
is thus *asymptotically universal*.Comment: 40 pages (body: 30, appendices: 3, figures: 5, references: 2). Fixed
problem with non-printing figures. New references added, minor typos
correcte
Ground-State Entanglement in Interacting Bosonic Graphs
We consider a collection of bosonic modes corresponding to the vertices of a
graph Quantum tunneling can occur only along the edges of
and a local self-interaction term is present. Quantum entanglement of one
vertex with respect the rest of the graph is analyzed in the ground-state of
the system as a function of the tunneling amplitude The topology of
plays a major role in determining the tunneling amplitude
which leads to the maximum ground-state entanglement. Whereas in most of the
cases one finds the intuitively expected result we show that it
there exists a family of graphs for which the optimal value of is pushed
down to a finite value. We also show that, for complete graphs, our bi-partite
entanglement provides useful insights in the analysis of the cross-over between
insulating and superfluid ground statesComment: 5 pages (LaTeX) 5 eps figures include
Bi-partite mode entanglement of bosonic condensates on tunneling graph
We study a set of spatial bosonic modes localized on a graph
The particles are allowed to tunnel from vertex to vertex by hopping along the
edges of We analyze how, in the exact many-body eigenstates of the
system i.e., Bose-Einstein condensates over single-particle eigenfunctions, the
bi-partite quantum entanglement of a lattice vertex with respect to the rest of
the graph depends on the topology of Comment: 3 Pages LaTeX, 2 Figures include
On Protected Realizations of Quantum Information
There are two complementary approaches to realizing quantum information so
that it is protected from a given set of error operators. Both involve encoding
information by means of subsystems. One is initialization-based error
protection, which involves a quantum operation that is applied before error
events occur. The other is operator quantum error correction, which uses a
recovery operation applied after the errors. Together, the two approaches make
it clear how quantum information can be stored at all stages of a process
involving alternating error and quantum operations. In particular, there is
always a subsystem that faithfully represents the desired quantum information.
We give a definition of faithful realization of quantum information and show
that it always involves subsystems. This justifies the "subsystems principle"
for realizing quantum information. In the presence of errors, one can make use
of noiseless, (initialization) protectable, or error-correcting subsystems. We
give an explicit algorithm for finding optimal noiseless subsystems. Finding
optimal protectable or error-correcting subsystems is in general difficult.
Verifying that a subsystem is error-correcting involves only linear algebra. We
discuss the verification problem for protectable subsystems and reduce it to a
simpler version of the problem of finding error-detecting codes.Comment: 17 page
Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment
It is shown that a nonequilibrium environment can be instrumental in
suppressing decoherence between distinct decoherence free subspaces in quantum
registers. The effect is found in the framework of exact coherent-product
solutions for model registers decohering in a bath of degenerate harmonic
modes, through couplings linear in bath coordinates. These solutions represent
a natural nonequilibrium extension of the standard solution for a decoupled
initial register state and a thermal environment. Under appropriate conditions,
the corresponding reduced register distribution can propagate in an unperturbed
manner, even in the presence of entanglement between states belonging to
distinct decoherence free subspaces, and despite persistent bath entanglement.
As a byproduct, we also obtain a refined picture of coherence dynamics under
bang-bang decoherence control. In particular, it is shown that each
radio-frequency pulse in a typical bang-bang cycle induces a revival of
coherence, and that these revivals are exploited in a natural way by the
time-symmetrized version of the bang-bang protocol.Comment: RevTex3, 26 pgs., 2 figs.. This seriously expanded version accepted
by Phys.Rev.A. No fundamentally new content, but rewritten introduction to
problem, self-contained introduction of thermal coherent-product states in
standard operator formalism, examples of zero-temperature decoherence free
Davydov states. Also fixed a typo that propagated into an interpretational
blunder in old Sec.3 [fortunately of no consequence
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