Although much work has been devoted to multivalued quantum logic synthesis, the question of whether multivalued quantum circuits are more efficient than conventional binary quantum circuits is still open. This article is devoted to the optimization of generic multivalued quantum circuits. Multivalued quantum Shannon decompositions are improved so that the circuits obtained are asymptotically optimal for all dimensionality $d$ . The syntheses of uniformly multifold controlled ${R}_{y}$ rotations are also optimized to make the circuits further simplified. Moreover, the theoretical lower bound of complexity for multivalued quantum circuits is investigated, and a quantity known as the efficiency index is proposed to evaluate the efficiency of the synthesis of various quantum circuits. The algorithm for qudit circuits given here is an efficient synthesis routine which produces improved results for all dimensionality $d$ , whether the number of qudits $n$ is small or large. The two facts, the leading factor of the lower bound of complexity for qudit circuits is small by a factor of $d\ensuremath{-}1$ in comparison to that for qubit circuits and the asymptotic efficiency index is increased with an increase of dimensionality $d$ , reveal the potential advantage of qudit circuits over generic qubit circuits. Generic $n$ -qudit circuits with $d\ensuremath{\ge}5$ and generic two-ququart circuits synthesized by the algorithm given here are practical circuits which are more efficient than the most efficient qubit circuits.Although much work has been devoted to multivalued quantum logic synthesis, the question of whether multivalued quantum circuits are more efficient than conventional binary quantum circuits is still open. This article is devoted to the optimization of generic multivalued quantum circuits. Multivalued quantum Shannon decompositions are improved so that the circuits obtained are asymptotically optimal for all dimensionality $d$. The syntheses of uniformly multifold controlled ${R}_{y}$ rotations are also optimized to make the circuits further simplified. Moreover, the theoretical lower bound of complexity for multivalued quantum circuits is investigated, and a quantity known as the efficiency index is proposed to evaluate the efficiency of the synthesis of various quantum circuits. The algorithm for qudit circuits given here is an efficient synthesis routine which produces improved results for all dimensionality $d$, whether the number of qudits $n$ is small or large. The two facts, the leading factor of the lower bound of complexity for qudit circuits is small by a factor of $d\ensuremath{-}1$ in comparison to that for qubit circuits and the asymptotic efficiency index is increased with an increase of dimensionality $d$, reveal the potential advantage of qudit circuits over generic qubit circuits. Generic $n$-qudit circuits with $d\ensuremath{\ge}5$ and generic two-ququart circuits synthesized by the algorithm given here are practical circuits which are more efficient than the most efficient qubit circuits.

arXiv:1506.04394Physical Review ADec 9, 201524 citations

A Review on Quantum Circuits: Qubits, Qudits, Reversible Logic Circuits and its Applications

Nilay Awasthi

Quantum Computing has already stepped into the world and is also fostering research in many domains. The efficiency and reliability of Quantum efficiency is limited by the Hardware implementation resources existing now. Various domains of qubit implementation have been explored, for coming down to the conclusion, that which is the best implementation of the qubit. Further, the concept of qudits is also been initiated in the research industry and is been explored. In this paper, we explore the various domains of different qubit implementation, shed light on qudits and present the designing of reversible gate which are used for making reversible circuits.Quantum Computing has already stepped into the world and is also fostering research in many domains. The efficiency and reliability of Quantum efficiency is limited by the Hardware implementation resources existing now. Various domains of qubit implementation have been explored, for coming down to the conclusion, that which is the best implementation of the qubit. Further, the concept of qudits is also been initiated in the research industry and is been explored. In this paper, we explore the various domains of different qubit implementation, shed light on qudits and present the designing of reversible gate which are used for making reversible circuits.

Jan 1, 20200 citations

Basic circuits for quantum computation

Gunajit Kalita

Advances in computersAug 5, 20250 citations

Synthesis of multivalued quantum logic circuits by elementary gates

Yao-Min Di, Hai‐Rui Wei

We propose the generalized controlled $X$ (gcx) gate as the two-qudit elementary gate, and based on Cartan decomposition, we also give the one-qudit elementary gates. Then we discuss the physical implementation of these elementary gates and show that it is feasible with current technology. With these elementary gates many important qudit quantum gates can be synthesized conveniently. We provide efficient methods for the synthesis of various kinds of controlled qudit gates and greatly simplify the synthesis of existing generic multi-valued quantum circuits. Moreover, we generalize the quantum Shannon decomposition (QSD), the most powerful technique for the synthesis of generic qubit circuits, to the qudit case. A comparison of ququart ( $d=4$ ) circuits and qubit circuits reveals that using ququart circuits may have an advantage over the qubit circuits in the synthesis of quantum circuits.We propose the generalized controlled $X$ (gcx) gate as the two-qudit elementary gate, and based on Cartan decomposition, we also give the one-qudit elementary gates. Then we discuss the physical implementation of these elementary gates and show that it is feasible with current technology. With these elementary gates many important qudit quantum gates can be synthesized conveniently. We provide efficient methods for the synthesis of various kinds of controlled qudit gates and greatly simplify the synthesis of existing generic multi-valued quantum circuits. Moreover, we generalize the quantum Shannon decomposition (QSD), the most powerful technique for the synthesis of generic qubit circuits, to the qudit case. A comparison of ququart ($d=4$) circuits and qubit circuits reveals that using ququart circuits may have an advantage over the qubit circuits in the synthesis of quantum circuits.

arXiv:1302.0056Physical Review AJan 22, 201373 citations

Quantum circuits for cryptanalysis

Brittanney Amento

Jan 1, 20160 citations

d

. The syntheses of uniformly multifold controlled

{R}_{y}

rotations are also optimized to make the circuits further simplified. Moreover, the theoretical lower bound of complexity for multivalued quantum circuits is investigated, and a quantity known as the efficiency index is proposed to evaluate the efficiency of the synthesis of various quantum circuits. The algorithm for qudit circuits given here is an efficient synthesis routine which produces improved results for all dimensionality

d

, whether the number of qudits

n

is small or large. The two facts, the leading factor of the lower bound of complexity for qudit circuits is small by a factor of $d\ensuremath{-}1$ in comparison to that for qubit circuits and the asymptotic efficiency index is increased with an increase of dimensionality

d

, reveal the potential advantage of qudit circuits over generic qubit circuits. Generic

n

-qudit circuits with $d\ensuremath{\ge}5$ and generic two-ququart circuits synthesized by the algorithm given here are practical circuits which are more efficient than the most efficient qubit circuits.

We propose the generalized controlled

X

(gcx) gate as the two-qudit elementary gate, and based on Cartan decomposition, we also give the one-qudit elementary gates. Then we discuss the physical implementation of these elementary gates and show that it is feasible with current technology. With these elementary gates many important qudit quantum gates can be synthesized conveniently. We provide efficient methods for the synthesis of various kinds of controlled qudit gates and greatly simplify the synthesis of existing generic multi-valued quantum circuits. Moreover, we generalize the quantum Shannon decomposition (QSD), the most powerful technique for the synthesis of generic qubit circuits, to the qudit case. A comparison of ququart (

d=4

) circuits and qubit circuits reveals that using ququart circuits may have an advantage over the qubit circuits in the synthesis of quantum circuits.