1,777 research outputs found
An Universal Quantum Network - Quantum CPU
An universal quantum network which can implement a general quantum computing
is proposed. In this sense, it can be called the quantum central processing
unit (QCPU). For a given quantum computing, its realization of QCPU is just its
quantum network. QCPU is standard and easy-assemble because it only has two
kinds of basic elements and two auxiliary elements. QCPU and its realizations
are scalable, that is, they can be connected together, and so they can
construct the whole quantum network to implement the general quantum algorithm
and quantum simulating procedure.Comment: 8 pages, Revised versio
Quantum Computers, Factoring, and Decoherence
In a quantum computer any superposition of inputs evolves unitarily into the
corresponding superposition of outputs. It has been recently demonstrated that
such computers can dramatically speed up the task of finding factors of large
numbers -- a problem of great practical significance because of its
cryptographic applications. Instead of the nearly exponential (, for a number with digits) time required by the fastest classical
algorithm, the quantum algorithm gives factors in a time polynomial in
(). This enormous speed-up is possible in principle because quantum
computation can simultaneously follow all of the paths corresponding to the
distinct classical inputs, obtaining the solution as a result of coherent
quantum interference between the alternatives. Hence, a quantum computer is
sophisticated interference device, and it is essential for its quantum state to
remain coherent in the course of the operation. In this report we investigate
the effect of decoherence on the quantum factorization algorithm and establish
an upper bound on a ``quantum factorizable'' based on the decoherence
suffered per operational step.Comment: 7 pages,LaTex + 2 postcript figures in a uuencoded fil
Towards practical classical processing for the surface code: timing analysis
Topological quantum error correction codes have high thresholds and are well
suited to physical implementation. The minimum weight perfect matching
algorithm can be used to efficiently handle errors in such codes. We perform a
timing analysis of our current implementation of the minimum weight perfect
matching algorithm. Our implementation performs the classical processing
associated with an nxn lattice of qubits realizing a square surface code
storing a single logical qubit of information in a fault-tolerant manner. We
empirically demonstrate that our implementation requires only O(n^2) average
time per round of error correction for code distances ranging from 4 to 512 and
a range of depolarizing error rates. We also describe tests we have performed
to verify that it always obtains a true minimum weight perfect matching.Comment: 13 pages, 13 figures, version accepted for publicatio
Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers
We transfer the concept of linear feed-back shift registers to quantum
circuits. It is shown how to use these quantum linear shift registers for
encoding and decoding cyclic quantum error-correcting codes.Comment: 18 pages, 15 figures, submitted to Proc. R. Soc.
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
Heisenberg chains cannot mirror a state
Faithful exchange of quantum information can in future become a key part of
many computational algorithms. Some Authors suggest to use chains of mutually
coupled spins as channels for quantum communication. One can divide these
proposals into the groups of assisted protocols, which require some additional
action from the users, and natural ones, based on the concept of state
mirroring. We show that mirror is fundamentally not the feature chains of
spins-1/2 coupled by the Heisenberg interaction, but without local magnetic
fields. This fact has certain consequences in terms of the natural state
transfer
Fault-Tolerant Error Correction with Efficient Quantum Codes
We exhibit a simple, systematic procedure for detecting and correcting errors
using any of the recently reported quantum error-correcting codes. The
procedure is shown explicitly for a code in which one qubit is mapped into
five. The quantum networks obtained are fault tolerant, that is, they can
function successfully even if errors occur during the error correction. Our
construction is derived using a recently introduced group-theoretic framework
for unifying all known quantum codes.Comment: 12 pages REVTeX, 1 ps figure included. Minor additions and revision
Optimum Quantum Error Recovery using Semidefinite Programming
Quantum error correction (QEC) is an essential element of physical quantum
information processing systems. Most QEC efforts focus on extending classical
error correction schemes to the quantum regime. The input to a noisy system is
embedded in a coded subspace, and error recovery is performed via an operation
designed to perfectly correct for a set of errors, presumably a large subset of
the physical noise process. In this paper, we examine the choice of recovery
operation. Rather than seeking perfect correction on a subset of errors, we
seek a recovery operation to maximize the entanglement fidelity for a given
input state and noise model. In this way, the recovery operation is optimum for
the given encoding and noise process. This optimization is shown to be
calculable via a semidefinite program (SDP), a well-established form of convex
optimization with efficient algorithms for its solution. The error recovery
operation may also be interpreted as a combining operation following a quantum
spreading channel, thus providing a quantum analogy to the classical diversity
combining operation.Comment: 7 pages, 3 figure
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