Quantum logic synthesis by symbolic reachability analysis

Abstract

Reversible quantum logic plays an important role in quantum computing. In this paper, we propose an approach to optimally synthesize quantum circuits by symbolic reachability analysis where the primary inputs are purely binary. We present an exact synthesis method with optimal quantum cost and a speedup method with non-optimal quantum cost. Both our methods guarantee the synthesizeability of all reversible circuits. Unlike previous works which use permutative reversible gates, we use a lower level library which includes non-permutative quantum gates. Our approach obtains the minimum cost quantum circuits for Miller's gate, half-adder, and full-adder, which are better than previous results. In addition, we prove the minimum quantum cost (using our elementary quantum gates) for Fredkin, Peres, and Toffoli gates. Our work constitutes the first successful experience of applying satisfiability with formal methods to quantum logic synthesis.

Reversible Arithmetic Logic Gate (ALG) for Quantum Computation

“…These criteria make reversible logic synthesis a more challenging one. Exact synthesis methods, using Boolean satisfiability (SAT) [7], quantified Boolean formula (QBF) [8], dynamic programming [9], symbolic reachability [10], etc., can provide optimal solutions. In recent days, research in the area of reversible logic has been intensified and accelerated by the promising results.…”

Quantum Circuit Simplification Using Templates

“…Typically, certain primitive gates are used as elementary building blocks with an assumed unit cost [4,6,16]. Among these are:…”

Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

“…We applied our minimum cost algorithm to 3 qubit synthesis; the results are shown in the following [2] and G [3] consists of the set of the binary input binary output circuits which are the combinations of 1, 2, 3 Feynman gates respectively. In G [4], there are 60 circuits realized by 4 Feynman gates, the other 24 circuits realized by 3 control gates and 1 Feynman gate.…”

“…In order to use Group Theory, we need to encode the input values. Given our elementary quantum gates, there are four possible values [2] for each qubit: 0, 1, V 0 , and V 1 . We represent quantum states as permutations (of truth table entries), and quantum gates as permutations as well.…”

“…Finding the smallest number of gates to synthesize a reversible circuit does not necessarily result in a quantum implementation with the lowest cost (in terms of quantum gates) [2]. The exact minimal costs for NMR [1] realization of several quantum gates from truly quantum (not permutative) gates such as Pauli Rotations or Controlled-Square-Root-of-Not have been calculated [4].…”