Applications of decompositions for synthesis of quantum gates

As a model for quantum computation, quantum circuits have found their wide applications in communications, cryptography and information processing. In order to synthesize arbitrary quantum circuits, we present a new type of gate called quantum multiplex rotation gate, which is implemented by simply elementary gates. A method based on QR decomposition and two optimization rules are proposed to decompose general quantum circuit acting on n-qubits into quantum multiplex rotation gates. In comparison with other synthesis algorithms by QR decomposition, our methods achieve better performance in terms of elementary gate counts, 1.2 × 4n approximately.As a model for quantum computation, quantum circuits have found their wide applications in communications, cryptography and information processing. In order to synthesize arbitrary quantum circuits, we present a new type of gate called quantum multiplex rotation gate, which is implemented by simply elementary gates. A method based on QR decomposition and two optimization rules are proposed to decompose general quantum circuit acting on n-qubits into quantum multiplex rotation gates. In comparison with other synthesis algorithms by QR decomposition, our methods achieve better performance in terms of elementary gate counts, 1.2 × 4n approximately.

IEICE Electronics ExpressJan 1, 20161 citation

Studies on methods for the synthesis of quantum circuits

裕美中島

Jan 1, 20090 citations

Synthesis of Quantum Circuits

Philipp Niemann, Robert Wille

SpringerBriefs in physicsJan 1, 20170 citations

Optimal synthesis of linear reversible circuits

K.N. Patel, Igor L. Markov, J.P. Hayes

In this paper we consider circuit synthesis for $n$ -wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with $O\left(n^2\right)$ gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as $O\left(n^2/\log\, n\right)$ gates.In this paper we consider circuit synthesis for $n$-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with $O\left(n^2\right)$ gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as $O\left(n^2/\log\, n\right)$ gates.

Quantum Information and ComputationMar 1, 200892 citations

Efficient Synthesis of Linear Reversible Circuits

K.N. Patel, Igor L. Markov, John P. Hayes

In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with O(n^2) gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O(n^2/log n) gates. We present an algorithm that is optimal up to a multiplicative constant, as well as Theta(log n) times faster than previous methods. While our results are primarily asymptotic, simulation results show that even for relatively small n our algorithm is faster and yields more efficient circuits than the standard method. Generically our algorithm can be interpreted as a matrix decomposition algorithm, yielding an asymptotically efficient decomposition of a binary matrix into a product of elementary matrices.In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with O(n^2) gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O(n^2/log n) gates. We present an algorithm that is optimal up to a multiplicative constant, as well as Theta(log n) times faster than previous methods. While our results are primarily asymptotic, simulation results show that even for relatively small n our algorithm is faster and yields more efficient circuits than the standard method. Generically our algorithm can be interpreted as a matrix decomposition algorithm, yielding an asymptotically efficient decomposition of a binary matrix into a product of elementary matrices.

arXiv:quant-ph/0302002Feb 3, 200328 citations

Optimal Control and Circuit Synthesis of Quantum Gates

Hyeong-Jin Kim

Jan 1, 20210 citations

In this paper we consider circuit synthesis for

n

-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with

O\left(n^2\right)

gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as

O\left(n^2/\log\, n\right)

gates.