2,250 research outputs found
Toward fault-tolerant quantum computation without concatenation
It has been known that quantum error correction via concatenated codes can be
done with exponentially small failure rate if the error rate for physical
qubits is below a certain accuracy threshold. Other, unconcatenated codes with
their own attractive features-improved accuracy threshold, local
operations-have also been studied. By iteratively distilling a certain
two-qubit entangled state it is shown how to perform an encoded Toffoli gate,
important for universal computation, on CSS codes that are either
unconcatenated or, for a range of very large block sizes, singly concatenated.Comment: 12 pages, 2 figures, replaced: new stuff on error models, numerical
example for concatenation criteri
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
Fusion rules and vortices in superconductors
The "half-quantum" vortices () and quasiparticles () in a
two-dimensional superconductor obey the Ising-like fusion rules
, , and . We explain how the physical fusion of vortex-antivortex pairs allows
us to use these rules to read out the information encoded in the topologically
protected space of degenerate ground states. We comment on the potential
applicability of this fact to quantum computation.
Modified 11/30/05 to reflect manuscript as accepted for publication. Includes
corrected last section.Comment: 23 pages, REVTEX
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
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
Tools for Quantum Algorithms
We present efficient implementations of a number of operations for quantum
computers. These include controlled phase adjustments of the amplitudes in a
superposition, permutations, approximations of transformations and
generalizations of the phase adjustments to block matrix transformations. These
operations generalize those used in proposed quantum search algorithms.Comment: LATEX, 15 pages, Minor changes: one author's e-mail and one reference
numbe
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
Nonnegative subtheories and quasiprobability representations of qubits
Negativity in a quasiprobability representation is typically interpreted as
an indication of nonclassical behavior. However, this does not preclude states
that are non-negative from exhibiting phenomena typically associated with
quantum mechanics - the single qubit stabilizer states have non-negative Wigner
functions and yet play a fundamental role in many quantum information tasks. We
seek to determine what other sets of quantum states and measurements for a
qubit can be non-negative in a quasiprobability representation, and to identify
nontrivial unitary groups that permute the states in such a set. These sets of
states and measurements are analogous to the single qubit stabilizer states. We
show that no quasiprobability representation of a qubit can be non-negative for
more than four bases and that the non-negative bases in any quasiprobability
representation must satisfy certain symmetry constraints. We provide an
exhaustive list of the sets of single qubit bases that are non-negative in some
quasiprobability representation and are also permuted by a nontrivial unitary
group. This list includes two families of three bases that both include the
single qubit stabilizer states as a special case and a family of four bases
whose symmetry group is the Pauli group. For higher dimensions, we prove that
there can be no more than 2^{d^2} states in non-negative bases of a
d-dimensional Hilbert space in any quasiprobability representation.
Furthermore, these bases must satisfy certain symmetry constraints,
corresponding to requiring the bases to be sufficiently complementary to each
other.Comment: 17 pages, 8 figures, comments very welcome; v2 published version.
Note that the statement and proof of Theorem III.2 in the published version
are incorrect (an erratum has been submitted), and this arXiv version (v2)
presents the corrected theorem and proof. The conclusions of the paper are
unaffected by this correctio
Generalized parity measurements
Measurements play an important role in quantum computing (QC), by either
providing the nonlinearity required for two-qubit gates (linear optics QC), or
by implementing a quantum algorithm using single-qubit measurements on a highly
entangled initial state (cluster state QC). Parity measurements can be used as
building blocks for preparing arbitrary stabilizer states, and, together with
1-qubit gates are universal for quantum computing. Here we generalize parity
gates by using a higher dimensional (qudit) ancilla. This enables us to go
beyond the stabilizer/graph state formalism and prepare other types of
multi-particle entangled states. The generalized parity module introduced here
can prepare in one-shot, heralded by the outcome of the ancilla, a large class
of entangled states, including GHZ_n, W_n, Dicke states D_{n,k}, and, more
generally, certain sums of Dicke states, like G_n states used in secret
sharing. For W_n states it provides an exponential gain compared to linear
optics based methods.Comment: 7 pages, 1 fig; updated to the published versio
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
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