Linear Quantum Circuits Research Articles

A method for synthesis and optimization for linear nearest neighbor quantum circuits by parallel processing

In order to realize the linear nearest neighbor{(LNN)} of the quantum circuits and reduce the quantum cost of linear reversible quantum circuits, a method for synthesizing and optimizing linear reversible quantum circuits based on matrix multiplication of the structure of the quantum circuit is proposed. This method shows the matrix representation of linear quantum circuits by multiplying matrices of different parts of the whole circuit. The LNN realization by adding the SWAP gates is proposed and the equivalence of two ways of adding the SWAP gates is proved. The elimination rules of the SWAP gates between two overlapped adjacent quantum gates in different cases are proposed, which reduce the quantum cost of quantum circuits after realizing the LNN architecture. We propose an algorithm based on parallel processing in order to effectively reduce the time consumption for large-scale quantum circuits. Experiments show that the quantum cost can be improved by 34.31\% on average and the speed-up ratio of the GPU-based algorithm can reach 4 times compared with the CPU-based algorithm. The average time optimization ratio of the benchmark large-scale circuits in RevLib processed by the parallel algorithm is {95.57\%} comparing with the serial algorithm.

Network realization of triplet-type quantum stochastic systems

This paper focuses on a problem of network synthesis for a class of quantum stochastic systems. The systems under consideration are of triplet-type form and stem from linear quantum optics and linear quantum circuits. A new quantum network realization approach is proposed by generalizing the scattering operator from the scalar form to a unitary matrix in network components. It shows that the triplet-type quantum stochastic system can be approximated by a quantum network which consists of some one-degree-of-freedom generalized open-quantum harmonic oscillators (1DGQHOs) via series, concatenation and feedback connections.

Experimentally simulating quantum walks with self-collimated light.

In self-collimated photonic crystal, periodically arranged air holes of sub-wavelength scale provide flattened equi-frequency curves perpendicular to the ΓM direction, which allow light or photons propagating in a quasi-uniform medium without diffraction. Here we for the first time experimentally simulate four-step single-photon discrete time quantum walks with classical light in such a photonic crystal chip fabricated on silicon-on-insulator. Similarities between theoretical expectations and experimental results are higher than 0.98. The functional area is compact and can be extended to construct more complicated linear quantum circuits.

Network Synthesis of Linear Dynamical Quantum Stochastic Systems

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and nonlinear quantum optical elements. An example is also provided to illustrate the theory.