191,094 research outputs found
Structured Error Recovery for Codeword-Stabilized Quantum Codes
Codeword stabilized (CWS) codes are, in general, non-additive quantum codes
that can correct errors by an exhaustive search of different error patterns,
similar to the way that we decode classical non-linear codes. For an n-qubit
quantum code correcting errors on up to t qubits, this brute-force approach
consecutively tests different errors of weight t or less, and employs a
separate n-qubit measurement in each test. In this paper, we suggest an error
grouping technique that allows to simultaneously test large groups of errors in
a single measurement. This structured error recovery technique exponentially
reduces the number of measurements by about 3^t times. While it still leaves
exponentially many measurements for a generic CWS code, the technique is
equivalent to syndrome-based recovery for the special case of additive CWS
codes.Comment: 13 pages, 9 eps figure
Clustered Error Correction of Codeword-Stabilized Quantum Codes
Codeword stabilized (CWS) codes are a general class of quantum codes that
includes stabilizer codes and many families of non-additive codes with good
parameters. For such a non-additive code correcting all t-qubit errors, we
propose an algorithm that employs a single measurement to test all errors
located on a given set of t qubits. Compared with exhaustive error screening,
this reduces the total number of measurements required for error recovery by a
factor of about 3^t.Comment: 4 pages, 2 figures, revtex4; number of editorial changes in v
Toward an architecture for quantum programming
It is becoming increasingly clear that, if a useful device for quantum
computation will ever be built, it will be embodied by a classical computing
machine with control over a truly quantum subsystem, this apparatus performing
a mixture of classical and quantum computation.
This paper investigates a possible approach to the problem of programming
such machines: a template high level quantum language is presented which
complements a generic general purpose classical language with a set of quantum
primitives. The underlying scheme involves a run-time environment which
calculates the byte-code for the quantum operations and pipes it to a quantum
device controller or to a simulator.
This language can compactly express existing quantum algorithms and reduce
them to sequences of elementary operations; it also easily lends itself to
automatic, hardware independent, circuit simplification. A publicly available
preliminary implementation of the proposed ideas has been realized using the
C++ language.Comment: 23 pages, 5 figures, A4paper. Final version accepted by EJPD ("swap"
replaced by "invert" for Qops). Preliminary implementation available at:
http://sra.itc.it/people/serafini/quantum-computing/qlang.htm
Codeword stabilized quantum codes: algorithm and structure
The codeword stabilized ("CWS") quantum codes formalism presents a unifying
approach to both additive and nonadditive quantum error-correcting codes
(arXiv:0708.1021). This formalism reduces the problem of constructing such
quantum codes to finding a binary classical code correcting an error pattern
induced by a graph state. Finding such a classical code can be very difficult.
Here, we consider an algorithm which maps the search for CWS codes to a problem
of identifying maximum cliques in a graph. While solving this problem is in
general very hard, we prove three structure theorems which reduce the search
space, specifying certain admissible and optimal ((n,K,d)) additive codes. In
particular, we find there does not exist any ((7,3,3)) CWS code though the
linear programming bound does not rule it out. The complexity of the CWS search
algorithm is compared with the contrasting method introduced by Aggarwal and
Calderbank (arXiv:cs/0610159).Comment: 11 pages, 1 figur
Efficient Code for Relativistic Quantum Summoning
Summoning retrieves quantum information, prepared somewhere in spacetime, at
another specified point in spacetime, but this task is limited by the quantum
no-cloning principle and the speed-of-light bound. We develop a thorough
mathematical framework for summoning quantum information in a relativistic
system and formulate a quantum summoning protocol for any valid configuration
of causal diamonds in spacetime. For single-qubit summoning, we present a
protocol based on a Calderbank-Shor-Steane code that decreases the space
complexity for encoding by a factor of two compared to the previous best result
and reduces the gate complexity from scaling as the cube to the square of the
number of causal diamonds. Our protocol includes decoding whose gate complexity
scales linearly with the number of causal diamonds. Our thorough framework for
quantum summoning enables full specification of the protocol, including spatial
and temporal implementation and costs, which enables quantum summoning to be a
well posed protocol for relativistic quantum communication purposes.Comment: 15 pages, 7 figure
- …