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Quantum Error Correction Via Codes Over GF(4)
TLDR
In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Expand
Quantum error correction via codes over GF(4)
The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. ThisExpand
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 3Expand
Self-Dual Codes
A survey of self-dual codes, written for the Handbook of Coding Theory. Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory.Expand
Algebraic aspects of increasing subsequences
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae forExpand
Quantum nonlocality without entanglement
We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states hasExpand
Nonbinary quantum codes
  • E. Rains
  • Mathematics, Physics
  • IEEE Trans. Inf. Theory
  • 25 March 1997
TLDR
This work considers codes derived from finite symplectic geometry assumed to have additional global symmetries, and gets analogs of quadratic residue codes, including a single-error-correcting code encoding one letter in five, for any alphabet size. Expand
A logarithmic-depth quantum carry-lookahead adder
TLDR
This work reduces the cost of addition dramatically with only a slight increase in the number of required qubits, and can be used within current modularmultiplication circuits to reduce substantially the run-time of Shor's algorithm. Expand
Limiting Distributions for a Polynuclear Growth Model with External Sources
The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by Prähofer and Spohn. Depending on theExpand
Transformations of elliptic hypergeometric integrals
We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BC_n and A_n; as a special case, we recover some integralExpand
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