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We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and…

Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…

Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize…

In this paper, reversible circuits consisting of NOT, CNOT and 2-CNOT gates are studied. Several asymptotically optimal by the order of magnitude synthesis methods are described. Some circuit's complexity reduction approaches are…

We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the…

This paper presents a heuristic cost minimization approach to synthesizing linear reversible circuits. Two bidirectional linear reversible circuit synthesis methods are introduced, the Alternating Elimination with Cost Minimization method…

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We…

Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…

Reversible logic has applications in various research areas including signal processing, cryptography and quantum computation. In this paper, direct NCT-based synthesis of a given $k$-cycle in a cycle-based synthesis scenario is examined.…

From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…

We propose the theory of Cayley graphs as a framework to analyse gate counts and quantum costs resulting from reversible circuit synthesis. Several methods have been proposed in the reversible logic synthesis literature by considering…

The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits…

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…

Current proposals for quantum compilers require the synthesis and optimization of linear reversible circuits and among them CNOT circuits. Since these circuits represent a significant part of the cost of running an entire quantum circuit,…

The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a…

Recently, reversible circuit synthesis has been intensively studied. One of the problems that has not been solved for a long time was exact minimization of gate count (GC) in 4-bit circuits. Finally, last year a tool of practical usage for…

The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic operations on quantum data, e.g., reversible arithmetic circuits. In physical implementations, however, TOFFOLI gates are decomposed into six CNOT gates…

What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an…

We study the problem of CNOT-optimal quantum circuit synthesis over gate sets consisting of CNOT and Z-basis rotations of arbitrary angles. We show that the circuit-polynomial correspondence relates such circuits to Fourier expansions of…

Reversible logic has applications in various research areas including low-power design and quantum computation. In this paper, a rule-based optimization approach for reversible circuits is proposed which uses both negative and positive…