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Phil Gossett

Publications and source records attributed to Phil Gossett.

2 recordsLinked to original sources
arXiv1998

Quantum Carry-Save Arithmetic

This paper shows how to design efficient arithmetic elements out of quantum gates using "carry-save" techniques borrowed from classical computer design. This allows bit-parallel evaluation of all the arithmetic elements required for Shor's algorithm, including modular arithmetic, deferring all carry propagation until the end of the entire computation. This reduces the quantum gate delay from O(N^3) to O(N log N) at a cost of increasing the number of qubits required from O(N) to O(N^2).

quant-ph↗
arXiv1998

NP in BQP with Nonlinearity

If one modifies the laws of Quantum Mechanics to allow nonlinear evolution of quantum states, this paper shows that NP-complete problems would be efficiently solvable in polynomial time with bounded probability (NP in BQP). With that (admittedly very unlikely) assumption, this is demonstrated by describing a polynomially large network of quantum gates that solves the 3SAT problem with bounded probability in polynomial time. As in a previous paper by Abrams and Lloyd (but by a somewhat simpler argument), allowing nonlinearity in the laws of Quantum Mechanics would prove the "weak Church-Turing thesis" to be false. General Relativity is suggested as a possible mechanism to supply the necessary nonlinearity.

quant-ph↗