Synthesizing hybrid quantum circuits without ancilla qudits.
ABSTRACT This paper investigates the synthesis of quantum networks built to realize hybrid switching circuits in the absence of ancilla qudits. We prove that all hybrid reversible circuits can be constructed by hybrid Not and Multiple-Controlled-Not gates. We also prove that any hybrid reversible circuit with only 1 or 2 binary qudits and arbitrary number of other qudits, can be constructed by hybrid Not and Controlled-Not gates. We present two construction-based algorithms to synthesize hybrid reversible circuits without ancilla qudits. The algorithms use hybrid Not and Multiple-Controlled-Not gates or hybrid Not and `1'-Controlled-Not gates, which are exponentially lower than breadth-first search based synthesis algorithms with respect to the input number.
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ABSTRACT: We concretely construct an extension of the controlled-U gate in qudit from some elementary gates. We also construct unitary transformation in two-qudit by means of the extended controlled-U gate and show the universality of it.05/2003;
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ABSTRACT: Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many d-level systems (qudits). Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of theta(d(2n)) gates. This closes the complexity question for all d-level systems (d finite). The optimal asymptotic applies to systems with locality constraints, e.g., nearest neighbor interactions.Physical Review Letters 07/2005; 94(23):230502. · 7.94 Impact Factor
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ABSTRACT: This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiple-valued domain. The authors present an optimal synthesis method to minimize quantum cost and some speedup methods with nonoptimal quantum cost. The methods here are applicable to small reversible functions. Unlike previous works that use permutative reversible gates, a lower level library that includes nonpermutative quantum gates is used here. The proposed approach obtains the minimum cost quantum circuits for Miller gate, half adder, and full adder, which are better than previous results. This cost is minimum for any circuit using the set of quantum gates in this paper, where the control qubit of 2-qubit gates is always basis binary. In addition, the minimum quantum cost in the same manner for Fredkin, Peres, and Toffoli gates is proven. The method can also find the best conversion from an irreversible function to a reversible circuit as a byproduct of the generality of its formulation, thus synthesizing in principle arbitrary multi-output Boolean functions with quantum gate library. This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesisIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 10/2006; · 1.09 Impact Factor