49 research outputs found
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
Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors
The exchange interaction between identical qubits in a quantum information
processor gives rise to unitary two-qubit errors. It is shown here that
decoherence free subspaces (DFSs) for collective decoherence undergo Pauli
errors under exchange, which however do not take the decoherence free states
outside of the DFS. In order to protect DFSs against these errors it is
sufficient to employ a recently proposed concatenated DFS-quantum error
correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett.
{\bf 82}, 4556 (1999)].Comment: 7 pages, no figures. Discussion in section V.A. significantly
expanded. Several small changes. Two authors adde
Empirical Determination of Bang-Bang Operations
Strong and fast "bang-bang" (BB) pulses have been recently proposed as a
means for reducing decoherence in a quantum system. So far theoretical analysis
of the BB technique relied on model Hamiltonians. Here we introduce a method
for empirically determining the set of required BB pulses, that relies on
quantum process tomography. In this manner an experimenter may tailor his or
her BB pulses to the quantum system at hand, without having to assume a model
Hamiltonian.Comment: 14 pages, 2 eps figures, ReVTeX4 two-colum
Encoded Recoupling and Decoupling: An Alternative to Quantum Error Correcting Codes, Applied to Trapped Ion Quantum Computation
A recently developed theory for eliminating decoherence and design
constraints in quantum computers, ``encoded recoupling and decoupling'', is
shown to be fully compatible with a promising proposal for an architecture
enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature
417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates
are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions
at a time. The encoding offers continuous protection against collective
dephasing. Decoupling pulses, that are also implemented using the SM scheme
directly to the encoded qubits, are capable of further reducing various other
sources of qubit decoherence, such as due to differential dephasing and due to
decohered vibrational modes. The feasibility of using the relatively slow SM
pulses in a decoupling scheme quenching the latter source of decoherence
follows from the observed 1/f spectrum of the vibrational bath.Comment: 12 pages, no figure
Greenberger-Horne-Zeilinger-like proof of Bell's theorem involving observers who do not share a reference frame
Vaidman described how a team of three players, each of them isolated in a
remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to
always win a game which would be impossible to always win without quantum
resources. However, Vaidman's method requires all three players to share a
common reference frame; it does not work if the adversary is allowed to
disorientate one player. Here we show how to always win the game, even if the
players do not share any reference frame. The introduced method uses a 12-qubit
state which is invariant under any transformation
(where , where is a
unitary operation on a single qubit) and requires only single-qubit
measurements. A number of further applications of this 12-qubit state are
described.Comment: REVTeX4, 6 pages, 1 figur
Correlated Errors in Quantum Error Corrections
We show that errors are not generated correlatedly provided that quantum bits
do not directly interact with (or couple to) each other. Generally, this
no-qubits-interaction condition is assumed except for the case where two-qubit
gate operation is being performed. In particular, the no-qubits-interaction
condition is satisfied in the collective decoherence models. Thus, errors are
not correlated in the collective decoherence. Consequently, we can say that
current quantum error correcting codes which correct single-qubit-errors will
work in most cases including the collective decoherence.Comment: no correction, 3 pages, RevTe
One-dimensional quantum walk with unitary noise
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise
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
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
Entanglement required in achieving entanglement-assisted channel capacities
Entanglement shared between the two ends of a quantum communication channel
has been shown to be a useful resource in increasing both the quantum and
classical capacities for these channels. The entanglement-assisted capacities
were derived assuming an unlimited amount of shared entanglement per channel
use. In this paper, bounds are derived on the minimum amount of entanglement
required per use of a channel, in order to asymptotically achieve the capacity.
This is achieved by introducing a class of entanglement-assisted quantum codes.
Codes for classes of qubit channels are shown to achieve the quantum
entanglement-assisted channel capacity when an amount of shared entanglement
per channel given by, E = 1 - Q_E, is provided. It is also shown that for very
noisy channels, as the capacities become small, the amount of required
entanglement converges for the classical and quantum capacities.Comment: 9 pages, 2 figures, RevTex