3,566 research outputs found
Controlling qubit transitions during non-adiabatic rapid passage through quantum interference
In adiabatic rapid passage, the Bloch vector of a qubit is inverted by slowly
inverting an external field to which it is coupled, and along which it is
initially aligned. In non-adiabatic twisted rapid passage, the external field
is allowed to twist around its initial direction with azimuthal angle \phi(t)
at the same time that it is non-adiabatically inverted. For polynomial twist,
\phi(t) \sim Bt^{n}. We show that for n \ge 3, multiple qubit resonances can
occur during a single inversion of the external field, producing strong
interference effects in the qubit transition probability. The character of the
interference is controllable through variation of the twist strength B.
Constructive and destructive interference are possible, greatly enhancing or
suppressing qubit transitions. Experimental confirmation of these controllable
interference effects has already occurred. Application of this interference
mechanism to the construction of fast fault-tolerant quantum CNOT and NOT gates
is discussed.Comment: 8 pages, 7 figures, 2 tables; submitted to J. Mod. Op
Traversable Wormholes and Black Hole Complementarity
Black hole complementarity is incompatible with the existence of traversable
wormholes. In fact, traversable wormholes cause problems for any theory where
information comes out in the Hawking radiation.Comment: 4 pages, CALT-68-193
A quantum analog of Huffman coding
We analyze a generalization of Huffman coding to the quantum case. In
particular, we notice various difficulties in using instantaneous codes for
quantum communication. Nevertheless, for the storage of quantum information, we
have succeeded in constructing a Huffman-coding inspired quantum scheme. The
number of computational steps in the encoding and decoding processes of N
quantum signals can be made to be of polylogarithmic depth by a massively
parallel implementation of a quantum gate array. This is to be compared with
the O (N^3) computational steps required in the sequential implementation by
Cleve and DiVincenzo of the well-known quantum noiseless block coding scheme of
Schumacher. We also show that O(N^2(log N)^a) computational steps are needed
for the communication of quantum information using another Huffman-coding
inspired scheme where the sender must disentangle her encoding device before
the receiver can perform any measurements on his signals.Comment: Revised version, 7 pages, two-column, RevTex. Presented at 1998 IEEE
International Symposium on Information Theor
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
Efficient discrete-time simulations of continuous-time quantum query algorithms
The continuous-time query model is a variant of the discrete query model in
which queries can be interleaved with known operations (called "driving
operations") continuously in time. Interesting algorithms have been discovered
in this model, such as an algorithm for evaluating nand trees more efficiently
than any classical algorithm. Subsequent work has shown that there also exists
an efficient algorithm for nand trees in the discrete query model; however,
there is no efficient conversion known for continuous-time query algorithms for
arbitrary problems.
We show that any quantum algorithm in the continuous-time query model whose
total query time is T can be simulated by a quantum algorithm in the discrete
query model that makes O[T log(T) / log(log(T))] queries. This is the first
upper bound that is independent of the driving operations (i.e., it holds even
if the norm of the driving Hamiltonian is very large). A corollary is that any
lower bound of T queries for a problem in the discrete-time query model
immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in
the continuous-time query model.Comment: 12 pages, 6 fig
A monomial matrix formalism to describe quantum many-body states
We propose a framework to describe and simulate a class of many-body quantum
states. We do so by considering joint eigenspaces of sets of monomial unitary
matrices, called here "M-spaces"; a unitary matrix is monomial if precisely one
entry per row and column is nonzero. We show that M-spaces encompass various
important state families, such as all Pauli stabilizer states and codes, the
AKLT model, Kitaev's (abelian and non-abelian) anyon models, group coset
states, W states and the locally maximally entanglable states. We furthermore
show how basic properties of M-spaces can transparently be understood by
manipulating their monomial stabilizer groups. In particular we derive a
unified procedure to construct an eigenbasis of any M-space, yielding an
explicit formula for each of the eigenstates. We also discuss the computational
complexity of M-spaces and show that basic problems, such as estimating local
expectation values, are NP-hard. Finally we prove that a large subclass of
M-spaces---containing in particular most of the aforementioned examples---can
be simulated efficiently classically with a unified method.Comment: 11 pages + appendice
Quantum Teleportation is a Universal Computational Primitive
We present a method to create a variety of interesting gates by teleporting
quantum bits through special entangled states. This allows, for instance, the
construction of a quantum computer based on just single qubit operations, Bell
measurements, and GHZ states. We also present straightforward constructions of
a wide variety of fault-tolerant quantum gates.Comment: 6 pages, REVTeX, 6 epsf figure
Passive decoy state quantum key distribution: Closing the gap to perfect sources
We propose a quantum key distribution scheme which closely matches the
performance of a perfect single photon source. It nearly attains the physical
upper bound in terms of key generation rate and maximally achievable distance.
Our scheme relies on a practical setup based on a parametric downconversion
source and present-day, non-ideal photon-number detection. Arbitrary
experimental imperfections which lead to bit errors are included. We select
decoy states by classical post-processing. This allows to improve the effective
signal statistics and achievable distance.Comment: 4 pages, 3 figures. State preparation correcte
Methodology for quantum logic gate constructions
We present a general method to construct fault-tolerant quantum logic gates
with a simple primitive, which is an analog of quantum teleportation. The
technique extends previous results based on traditional quantum teleportation
(Gottesman and Chuang, Nature {\bf 402}, 390, 1999) and leads to
straightforward and systematic construction of many fault-tolerant encoded
operations, including the and Toffoli gates. The technique can also be
applied to the construction of remote quantum operations that cannot be
directly performed.Comment: 17 pages, mypsfig2, revtex. Revised with a different title, a new
appendix for clarifying fault-tolerant preparation of quantum states, and
various minor change
Efficient classical simulation of slightly entangled quantum computations
We present a scheme to efficiently simulate, with a classical computer, the
dynamics of multipartite quantum systems on which the amount of entanglement
(or of correlations in the case of mixed-state dynamics) is conveniently
restricted. The evolution of a pure state of n qubits can be simulated by using
computational resources that grow linearly in n and exponentially in the
entanglement. We show that a pure-state quantum computation can only yield an
exponential speed-up with respect to classical computations if the entanglement
increases with the size n of the computation, and gives a lower bound on the
required growth.Comment: 4 pages. Major changes. Significantly improved simulation schem
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