Compiling Quantum Circuits using the Palindrome Transform

Details Compiling Quantum Circuits using the Palindrome Transform Compiling Quantum Circuits using the Palindrome Transform

2003-11-03

arxiv.org/abs/quant-ph/0311008v1

Physics

Quantum Physics

17 pages, LaTex

Scientific paper

The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2^n x 2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit and (n-1)-controlled-NOT gates. We first present a general algebraic optimization technique, which we call the Palindrome Transform, that can be used to minimize the number of self-inverting gates in quantum circuits consisting of concatenations of palindromic subcircuits. For a fixed column ordering of two-level decomposition, we then give an numerative algorithm for minimal (n-1)-controlled-NOT circuit construction, which we call the Palindromic Optimization Algorithm. Our work dramatically reduces the number of gates generated by the conventional two-level decomposition method for constructing quantum circuits of (n-1)-controlled single-qubit and (n-1)-controlled-NOT gates.

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