image: Figure | The structure of the ring resonator and the 1D DTQW in the synthetic frequency dimension. a, Illustration of the structure of the ring resonator. b, One-dimensional synthetic spin lattice in the frequency dimension. c, Schematic of 1D DTQW in the synthetic frequency dimension. The area of each circle represents the magnitude of the polarization-dependent amplitude of the walker.
Credit: Luqi Yuan et al.
Photonic systems offer great platforms for performing quantum walks. Adding long-range couplings between photonic lattice sites gives the direct way in algorithmically speeding up the efficiency of quantum walk in photonic lattices, which is essential for realizing quantum computing with desired quantum-gate functionality in integrated photonics. However, such long-range connectivity is added as an addition in many experiment, where nearby hopping is dominating.
In a new paper published in Light: Science & Applications, a team of scientists, led by Professor Luqi Yuan from State Key Laboratory of Photonics and Communications, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China and co-workers have proposed a new scheme for 1D DTQW systems including translation operators with coherent multiple long-range connectivity in the synthetic frequency lattice. They suggest to use strong modulations of an electro-optic modulator (EOM) in a ring resonator to break the weak coupling limit and show multiple long-range couplings can transport the quantum walker largely separated apart, following the topological band in a coherent way and with the faster diffusion speed.
“The coherent multiple long-range couplings in the 1D DTQW in the frequency dimension come from the strong modulations of the EOM. When under the weak modulation limit, there is only nearest neighbor couplings between two adjacent sites in the photonic lattice. However, as the modulation strength grows to break the limit, the connections between any two lattice points simultaneously appear in a coherent way, and the wavefunction of the walker can spread to every site in only one time step. This is the so-called coherent multiple long-range couplings in the 1D DTQW in the frequency dimension.” These scientists summarized the principle of their work.
“To achieve these coherent multiple long-range couplings, we use the concept of synthetic frequency dimension where discrete frequency modes of light can be used to construct lattice models. In our proposal, we use one ring resonator to construct the 1D photonic lattice, where equal-spaced frequency modes serve as the lattice points. By periodically changing the polarizations of the light and doing polarization-dependent strong modulation on the light field via a polarization rotator, a polarization splitter, two EOMs, and a polarization combiner inside the ring resonator, we can achieve the 1D DTQW in the frequency dimension with the coherent multiple long-range couplings.” These scientists expressed their proposal.
“The coherent multiple long-range translations in this quantum walk system can induce the topological band, which no longer significantly improves the diffusion speed of the walker, but also provides a way for implementing quantum gate operations in one time step. We can use this proposal to implement the X, Y, Z gates, Hadamard gate, phase-shift gate, and CNOT gate, which is beneficial for achieving the universal quantum computing.” These scientists added.
“Our proposal combines fields of topological photonics and quantum computing. It is based on a geometrically simple but experimental feasible single ring system under dynamic modulation, which recently has been applied to integrated-photonic configurations. This strategy may be further extended to the multi-qubit and multi-photon cases by using two ring resonators and nonlinear process, respectively, showing the strong scalability of our proposal. A new perspective for possibly solving the speed limitation problem of quantum algorithms in photonic chips is then provided in our work, which may appeal to the general public from photonics and quantum information.” The scientists forecasted.
Article Title
Quantum walk with coherent multiple translations induces fast quantum gate operations