Evolutionary approach to quantum symbolic logic synthesis

Abstract

In this paper we present an evolutionary approach to the quantum symbolic logic synthesis that was introduced in [1]. We use a Genetic Algorithm to synthesize quantum circuits from examples, allowing to synthesize functions that are both completely and incompletely specified. The symbolic synthesis is implemented in the GA so as to verify our approach. The Occam Razor principle, fundamental to inductive learning as well as to logic synthesis, is satisfied in this approach by seeking circuits of reduced complexity. The GA is tested on a set of benchmark functions representing single output quantum circuits as well as multiple entangled-qubit state generators.

A review of procedures to evolve quantum algorithms

“…The specific encoding used in this GA lends itself to be computed in parallel, thus it should be more efficiently implementable given quantum technologies. Between Lukac, Perkowski and others [56,72,74] there has also been promising research conducted into using GAs to evolve efficient implementations of basic quantum (and reversible) gates.…”

Evolutionary quantum logic synthesis of Boolean reversible logic circuits embedded in ternary quantum space using structural restrictions

“…The GA that was used for the experiments is an extension of our previous work [22,23]. It designs Boolean quantum circuits embedded in multi-valued quantum space by only evaluating the Boolean input-output either by measuring for the two observables bases |0 and |1 or by comparing the coefficients of the circuit matrix with the target circuit matrix.…”

“…For clarity we discuss only the most relevant features of the evolutionary search. For a complete description of the used GA the reader should consult [19,20,22,23].…”

“…Thus the design of a slightly larger quantum circuits will contain hundreds of the control pulses. From our previous experience with evolutionary quantum logic synthesis (EQLS), circuits with so many gates are difficult to synthesize because during the evolutionary process the building blocks are too large [19,20,22]. Thus, evolutionary synthesis should be not done on the level of control pulses.…”

“…On one hand the Genetic Programming has been widely used to synthesize quantum circuits and logic functions [17,28,29,39,41,42]. On the other hand GA based methods have been applied to various quantum circuits as well [19,22,23,25,44]. In general the focus of these approaches is either on a particular function (Reversible, quantum-permutative) or a general approach is used to see how well the evolutionary approach deals with this difficult problem.…”