1,637 research outputs found
Asymmetric quantum error correction via code conversion
In many physical systems it is expected that environmental decoherence will
exhibit an asymmetry between dephasing and relaxation that may result in qubits
experiencing discrete phase errors more frequently than discrete bit errors. In
the presence of such an error asymmetry, an appropriately asymmetric quantum
code - that is, a code that can correct more phase errors than bit errors -
will be more efficient than a traditional, symmetric quantum code. Here we
construct fault tolerant circuits to convert between an asymmetric subsystem
code and a symmetric subsystem code. We show that, for a moderate error
asymmetry, the failure rate of a logical circuit can be reduced by using a
combined symmetric asymmetric system and that doing so does not preclude
universality.Comment: 5 pages, 8 figures, presentation revised, figures and references
adde
Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
We provide fast algorithms for simulating many body Fermi systems on a
universal quantum computer. Both first and second quantized descriptions are
considered, and the relative computational complexities are determined in each
case. In order to accommodate fermions using a first quantized Hamiltonian, an
efficient quantum algorithm for anti-symmetrization is given. Finally, a
simulation of the Hubbard model is discussed in detail.Comment: Submitted 11/7/96 to Phys. Rev. Lett. 10 pages, 0 figure
Probabilistic instantaneous quantum computation
The principle of teleportation can be used to perform a quantum computation
even before its quantum input is defined. The basic idea is to perform the
quantum computation at some earlier time with qubits which are part of an
entangled state. At a later time a generalized Bell state measurement is
performed jointly on the then defined actual input qubits and the rest of the
entangled state. This projects the output state onto the correct one with a
certain exponentially small probability. The sufficient conditions are found
under which the scheme is of benefit.Comment: 4 pages, 1 figur
Optical properties of quantum wires: Disorder-scattering in the Lloyd-model
The Lloyd model is extended to the exciton problem in quasi one-dimensional
structures to study the interplay between the Coulomb attraction and disorder
scattering. Within this model the averaging and resummation of the locator
series can be performed analytically. As an application, the optical absorption
in quantum box wires is investigated. Without electron-hole interaction,
fluctuations in the well-width lead to an asymmetric broadening of the
minibands with respect to the lower and upper band-edges.Comment: 7 pages, 6 figure
Two-Bit Gates are Universal for Quantum Computation
A proof is given, which relies on the commutator algebra of the unitary Lie
groups, that quantum gates operating on just two bits at a time are sufficient
to construct a general quantum circuit. The best previous result had shown the
universality of three-bit gates, by analogy to the universality of the Toffoli
three-bit gate of classical reversible computing. Two-bit quantum gates may be
implemented by magnetic resonance operations applied to a pair of electronic or
nuclear spins. A ``gearbox quantum computer'' proposed here, based on the
principles of atomic force microscopy, would permit the operation of such
two-bit gates in a physical system with very long phase breaking (i.e., quantum
phase coherence) times. Simpler versions of the gearbox computer could be used
to do experiments on Einstein-Podolsky-Rosen states and related entangled
quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon
reques
Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers
Quantum computers are important examples of processes whose evolution can be
described in terms of iterations of single step operators or their adjoints.
Based on this, Hamiltonian evolution of processes with associated step
operators is investigated here. The main limitation of this paper is to
processes which evolve quantum ballistically, i.e. motion restricted to a
collection of nonintersecting or distinct paths on an arbitrary basis. The main
goal of this paper is proof of a theorem which gives necessary and sufficient
conditions that T must satisfy so that there exists a Hamiltonian description
of quantum ballistic evolution for the process, namely, that T is a partial
isometry and is orthogonality preserving and stable on some basis. Simple
examples of quantum ballistic evolution for quantum Turing machines with one
and with more than one type of elementary step are discussed. It is seen that
for nondeterministic machines the basis set can be quite complex with much
entanglement present. It is also proved that, given a step operator T for an
arbitrary deterministic quantum Turing machine, it is decidable if T is stable
and orthogonality preserving, and if quantum ballistic evolution is possible.
The proof fails if T is a step operator for a nondeterministic machine. It is
an open question if such a decision procedure exists for nondeterministic
machines. This problem does not occur in classical mechanics.Comment: 37 pages Latexwith 2 postscript figures tar+gzip+uuencoded, to be
published in Phys. Rev.
Entanglement of spin waves among four quantum memories
Quantum networks are composed of quantum nodes that interact coherently by
way of quantum channels and open a broad frontier of scientific opportunities.
For example, a quantum network can serve as a `web' for connecting quantum
processors for computation and communication, as well as a `simulator' for
enabling investigations of quantum critical phenomena arising from interactions
among the nodes mediated by the channels. The physical realization of quantum
networks generically requires dynamical systems capable of generating and
storing entangled states among multiple quantum memories, and of efficiently
transferring stored entanglement into quantum channels for distribution across
the network. While such capabilities have been demonstrated for diverse
bipartite systems (i.e., N=2 quantum systems), entangled states with N > 2 have
heretofore not been achieved for quantum interconnects that coherently `clock'
multipartite entanglement stored in quantum memories to quantum channels. Here,
we demonstrate high-fidelity measurement-induced entanglement stored in four
atomic memories; user-controlled, coherent transfer of atomic entanglement to
four photonic quantum channels; and the characterization of the full
quadripartite entanglement by way of quantum uncertainty relations. Our work
thereby provides an important tool for the distribution of multipartite
entanglement across quantum networks.Comment: 4 figure
Symplectic invariants, entropic measures and correlations of Gaussian states
We present a derivation of the Von Neumann entropy and mutual information of
arbitrary two--mode Gaussian states, based on the explicit determination of the
symplectic eigenvalues of a generic covariance matrix. The key role of the
symplectic invariants in such a determination is pointed out. We show that the
Von Neumann entropy depends on two symplectic invariants, while the purity (or
the linear entropy) is determined by only one invariant, so that the two
quantities provide two different hierarchies of mixed Gaussian states. A
comparison between mutual information and entanglement of formation for
symmetric states is considered, remarking the crucial role of the symplectic
eigenvalues in qualifying and quantifying the correlations present in a generic
state.Comment: 6 pages, no figures, revised version, sections and references added,
to appear in J. Phys.
Implementation of a quantum algorithm to solve Bernstein-Vazirani's parity problem without entanglement on an ensemble quantum computer
Bernstein and Varizani have given the first quantum algorithm to solve parity
problem in which a strong violation of the classical imformation theoritic
bound comes about. In this paper, we refine this algorithm with fewer resource
and implement a two qubits algorithm in a single query on an ensemble quantum
computer for the first time
The Road to Quantum Computational Supremacy
We present an idiosyncratic view of the race for quantum computational
supremacy. Google's approach and IBM challenge are examined. An unexpected
side-effect of the race is the significant progress in designing fast classical
algorithms. Quantum supremacy, if achieved, won't make classical computing
obsolete.Comment: 15 pages, 1 figur
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