Synthesis of quantum logic circuits

Abstract

The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community [18,28,7,27,17]. We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two.The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of difficult gates (quantum controlled-NOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearest-neighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.

Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons

“…Our decomposition ofÛ thus requires only 6 CNOT's, far less than the estimated upper bound given in Ref. [24]. We believe that, although we cannot claim for optimality and further improvements may be in order, the decomposition we propose could well be seen as rather efficient.…”

“…There is no need to synthesize a full six-qubit unitary operation, which represents a remarkable simplification in design due, in part, to our choice for information encoding. When the class of allowed gates is restricted to single-and two-qubit ones, any three-qubit unitary operation can be implemented with at most 20 CNOT gates and arbitrary single-qubit rotations [24]. In what (b) (a) Fig.…”

Hierarchical Synthesis of Quantum and Reversible Architectures

“…Commonly used quantum gates are the one qubit X , Y , Z gates, the Hadamard gate H the S and T gates and the two qubits CNOT gate. An n-qubits quantum gate U can be decomposed [3,6,27,32] (or approximated with arbitrary accuracy) into a sequence of elementary gates acting on different qubits each instant of time.…”

“…Thus, reversible circuit methodologies can be used and then library transformation can be applied to convert from the reversible library to a quantum library. When the specifications are in the form of a unitary matrix U of dimension 2 n × 2 n for a circuit consisting of n qubits then decomposition methods can be applied [3,6,27,32]. In such methods the unitary U is decomposed in a sequence of one-qubit and two qubit gates where the specific gates depend on the library.…”

Faithful teleportation via multi-particle quantum states in a network with many agents

“…Since up to now the high-dimensional unitary operation seems not easy to implement, its only problematic part is the unitary transformation. However, since it occupies an important position in the research of quantum information and quantum computation, efforts have been devoted to developing some potential schemes and both experimental and theoretical studies have been conducted [22][23][24][25][26][27][28].…”