1,369 research outputs found
Quantum Error Correction and Orthogonal Geometry
A group theoretic framework is introduced that simplifies the description of
known quantum error-correcting codes and greatly facilitates the construction
of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1
error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors,
and 1 to 29 qubits correcting 5 errors.Comment: RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have
changed the statement of Theorem 2 to correct it -- we now get worse rates
than we previously claimed for our quantum codes. Minor changes have been
made to the rest of the pape
Quantum Error Correction via Codes over GF(4)
The problem of finding quantum error-correcting codes is transformed into the
problem of finding additive codes over the field GF(4) which are
self-orthogonal with respect to a certain trace inner product. Many new codes
and new bounds are presented, as well as a table of upper and lower bounds on
such codes of length up to 30 qubits.Comment: Latex, 46 pages. To appear in IEEE Transactions on Information
Theory. Replaced Sept. 24, 1996, to correct a number of minor errors.
Replaced Sept. 10, 1997. The second section has been completely rewritten,
and should hopefully be much clearer. We have also added a new section
discussing the developments of the past year. Finally, we again corrected a
number of minor error
Pisces IV submersible observations in the epicentral region of the 1929 Grand Banks earthquake
The PISCES IVsubmersible was used to investigate the upper continental slope around 44 ON, 56 W, near the epicentre of the 1929 Grand Banks earthquake. Four dives in water depths of 800-2000 m were undertaken to observe speci3c features identijied with the SeaMARC I sidescan system in 1983. Two dives were made in the head of Eastern Valley where pebbly mudstones ofprobable Pleistocene age were recognized outcropping on the seafloor. Constructional features of cobbles and boulders, derived by exhumation and reworking of the pebbly mudstone, were also observed. These include gravel/sand bedforms (transverse waves) on the valley floor. Slope failure features in semiconsolidated mudstone were recognized on two dives onto the St. Pierre slope. Exposures in these mudstones are rapidly eroded by intense burrowing by benthic organisms
Resources Required for Topological Quantum Factoring
We consider a hypothetical topological quantum computer where the qubits are
comprised of either Ising or Fibonacci anyons. For each case, we calculate the
time and number of qubits (space) necessary to execute the most computationally
expensive step of Shor's algorithm, modular exponentiation. For Ising anyons,
we apply Bravyi's distillation method [S. Bravyi, Phys. Rev. A 73, 042313
(2006)] which combines topological and non-topological operations to allow for
universal quantum computation. With reasonable restrictions on the physical
parameters we find that factoring a 128 bit number requires approximately 10^3
Fibonacci anyons versus at least 3 x 10^9 Ising anyons. Other distillation
algorithms could reduce the resources for Ising anyons substantially.Comment: 4+epsilon pages, 4 figure
Magnetic qubits as hardware for quantum computers
We propose two potential realisations for quantum bits based on nanometre
scale magnetic particles of large spin S and high anisotropy molecular
clusters. In case (1) the bit-value basis states |0> and |1> are the ground and
first excited spin states Sz = S and S-1, separated by an energy gap given by
the ferromagnetic resonance (FMR) frequency. In case (2), when there is
significant tunnelling through the anisotropy barrier, the qubit states
correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the
two-fold degenerate ground state Sz = +- S. In each case the temperature of
operation must be low compared to the energy gap, \Delta, between the states
|0> and |1>. The gap \Delta in case (2) can be controlled with an external
magnetic field perpendicular to the easy axis of the molecular cluster. The
states of different molecular clusters and magnetic particles may be entangled
by connecting them by superconducting lines with Josephson switches, leading to
the potential for quantum computing hardware.Comment: 17 pages, 3 figure
Experimental demonstration of Shor's algorithm with quantum entanglement
Shor's powerful quantum algorithm for factoring represents a major challenge
in quantum computation and its full realization will have a large impact on
modern cryptography. Here we implement a compiled version of Shor's algorithm
in a photonic system using single photons and employing the non-linearity
induced by measurement. For the first time we demonstrate the core processes,
coherent control, and resultant entangled states that are required in a
full-scale implementation of Shor's algorithm. Demonstration of these processes
is a necessary step on the path towards a full implementation of Shor's
algorithm and scalable quantum computing. Our results highlight that the
performance of a quantum algorithm is not the same as performance of the
underlying quantum circuit, and stress the importance of developing techniques
for characterising quantum algorithms.Comment: 4 pages, 5 figures + half-page additional online materia
One-Way Quantum Computing in the Optical Frequency Comb
One-way quantum computing allows any quantum algorithm to be implemented
easily using just measurements. The difficult part is creating the universal
resource, a cluster state, on which the measurements are made. We propose a
radically new approach: a scalable method that uses a single, multimode optical
parametric oscillator (OPO). The method is very efficient and generates a
continuous-variable cluster state, universal for quantum computation, with
quantum information encoded in the quadratures of the optical frequency comb of
the OPO.Comment: v2: changed author order; 4 pages, 3 figures; supplemental movie
available at http://faculty.virginia.edu/quantum/torus.mo
Controllable exchange coupling between two singlet-triplet qubits
We study controllable exchange coupling between two singlet-triplet qubits.
We start from the original second quantized Hamiltonian of a quadruple quantum
dot system and obtain the effective spin-spin interaction between the two
qubits using the projection operator method. Under a strong uniform external
magnetic field and an inhomogeneous local micro-magnetic field, the effective
interqubit coupling is of the Ising type, and the coupling strength can be
expressed in terms of quantum dot parameters. Finally, we discuss how to
generate various two-qubit operations using this controllable coupling, such as
entanglement generation, and controlled-NOT gate.Comment: 9 pages, 3 figure
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