1,541 research outputs found
Quantum information processing via a lossy bus
We describe a method to perform two qubit measurements and logic operations
on pairs of qubits which each interact with a harmonic oscillator degree of
freedom (the \emph{bus}), but do not directly interact with one another. Our
scheme uses only weak interactions between the qubit and the bus, homodyne
measurements, and single qubit operations. In contrast to earlier schemes, the
technique presented here is extremely robust to photon loss in the bus mode,
and can function with high fidelity even when the rate of photon loss is
comparable to the strength of the qubit-bus coupling.Comment: Added more discussion on effects of noise. Typos correcte
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
The quantum query complexity of Boolean matrix multiplication is typically
studied as a function of the matrix dimension, n, as well as the number of 1s
in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values
of \ell. This is an improvement over previous algorithms for all values of
\ell. On the other hand, we show that for any \eps < 1 and any \ell <= \eps
n^2, there is an \Omega(n\sqrt{\ell}) lower bound for this problem, showing
that our algorithm is essentially tight.
We first reduce Boolean matrix multiplication to several instances of graph
collision. We then provide an algorithm that takes advantage of the fact that
the underlying graph in all of our instances is very dense to find all graph
collisions efficiently
Nonlocal resources in the presence of Superselection Rules
Superselection rules severely alter the possible operations that can be
implemented on a distributed quantum system. Whereas the restriction to local
operations imposed by a bipartite setting gives rise to the notion of
entanglement as a nonlocal resource, the superselection rule associated with
particle number conservation leads to a new resource, the \emph{superselection
induced variance} of local particle number. We show that, in the case of pure
quantum states, one can quantify the nonlocal properties by only two additive
measures, and that all states with the same measures can be asymptotically
interconverted into each other by local operations and classical communication.
Furthermore we discuss how superselection rules affect the concepts of
majorization, teleportation and mixed state entanglement.Comment: 4 page
Magic state distillation with low overhead
We propose a new family of error detecting stabilizer codes with an encoding
rate 1/3 that permit a transversal implementation of the pi/8-rotation on
all logical qubits. The new codes are used to construct protocols for
distilling high-quality `magic' states by Clifford group gates and Pauli
measurements. The distillation overhead has a poly-logarithmic scaling as a
function of the output accuracy, where the degree of the polynomial is
. To construct the desired family of codes, we introduce
the notion of a triorthogonal matrix --- a binary matrix in which any pair and
any triple of rows have even overlap. Any triorthogonal matrix gives rise to a
stabilizer code with a transversal -gate on all logical qubits, possibly
augmented by Clifford gates. A powerful numerical method for generating
triorthogonal matrices is proposed. Our techniques lead to a two-fold overhead
reduction for distilling magic states with output accuracy compared
with the best previously known protocol.Comment: 11 pages, 3 figure
Clifford Gates by Code Deformation
Topological subsystem color codes add to the advantages of topological codes
an important feature: error tracking only involves measuring 2-local operators
in a two dimensional setting. Unfortunately, known methods to compute with them
were highly unpractical. We give a mechanism to implement all Clifford gates by
code deformation in a planar setting. In particular, we use twist braiding and
express its effects in terms of certain colored Majorana operators.Comment: Extended version with more detail
Quantum divisibility test and its application in mesoscopic physics
We present a quantum algorithm to transform the cardinality of a set of
charged particles flowing along a quantum wire into a binary number. The setup
performing this task (for at most N particles) involves log_2 N quantum bits
serving as counters and a sequential read out. Applications include a
divisibility check to experimentally test the size of a finite train of
particles in a quantum wire with a one-shot measurement and a scheme allowing
to entangle multi-particle wave functions and generating Bell states,
Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder
interferometer.Comment: 9 pages, 5 figure
Discrete Wigner functions and quantum computational speedup
In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of
discrete Wigner functions W to represent quantum states in a finite Hilbert
space dimension d. I characterize a set C_d of states having non-negative W
simultaneously in all definitions of W in this class. For d<6 I show C_d is the
convex hull of stabilizer states. This supports the conjecture that negativity
of W is necessary for exponential speedup in pure-state quantum computation.Comment: 7 pages, 2 figures, RevTeX. v2: clarified discussion on dynamics,
added refs., published versio
Contextuality in Measurement-based Quantum Computation
We show, under natural assumptions for qubit systems, that measurement-based
quantum computations (MBQCs) which compute a non-linear Boolean function with
high probability are contextual. The class of contextual MBQCs includes an
example which is of practical interest and has a super-polynomial speedup over
the best known classical algorithm, namely the quantum algorithm that solves
the Discrete Log problem.Comment: Version 3: probabilistic version of Theorem 1 adde
Using continuous measurement to protect a universal set of quantum gates within a perturbed decoherence-free subspace
We consider a universal set of quantum gates encoded within a perturbed
decoherence-free subspace of four physical qubits. Using second-order
perturbation theory and a measuring device modeled by an infinite set of
harmonic oscillators, simply coupled to the system, we show that continuous
observation of the coupling agent induces inhibition of the decoherence due to
spurious perturbations. We thus advance the idea of protecting or even creating
a decoherence-free subspace for processing quantum information.Comment: 7 pages, 1 figure. To be published in Journal of Physics A:
Mathematical and Genera
Relaxation to equilibrium driven via indirect control in Markovian dynamics
We characterize to what extent it is possible to modify the stationary states
of a quantum dynamical semigroup, that describes the irreversible evolution of
a two-level system, by means of an auxiliary two-level system. We consider
systems that can be initially entangled or uncorrelated. We find that the
indirect control of the stationary states is possible, even if there are not
initial correlations, under suitable conditions on the dynamical parameters
characterizing the evolution of the joint system.Comment: revtex4, 7 page
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