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The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
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…
Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on…
We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that it…
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two…
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…
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…
Reversible sequential circuits are going to be the significant memory blocks for the forthcoming computing devices for their ultra low power consumption. Therefore design of various types of latches has been considered a major objective for…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
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…
Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. Multivalued quantum systems have also been used in the framework of quantum cryptography, and the concept of a…
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…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
Synthesis of reversible logic circuits has gained great atten- tion during the last decade. Various synthesis techniques have been pro- posed, some generate optimal solutions (in gate count) and are termed as exact, while others are…
In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer…
Current noisy intermediate-scale quantum (NISQ) devices can only execute small circuits with shallow depth, as they are still constrained by the presence of noise: quantum gates have error rates and quantum states are fragile due to…
We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic…
Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As…