# Quantum walk with coherent multiple translations induces fast quantum gate operations

## TL;DR

This paper introduces a new quantum walk method using coherent multiple translations to enable fast quantum gate operations in a topological band.

## Contribution

The novel use of coherent multiple translations in a modulated ring enables fast single and two-qubit quantum gate operations in one time step.

## Key findings

- Coherent multiple translations in a modulated ring support discrete-time quantum walks with topological bands.
- Single-qubit state preparation and CNOT gates are achieved in a single time step.
- The method could lead to efficient quantum operations on photonic chips.

## Abstract

Quantum walks with one-dimensional translational symmetry are important for quantum algorithms, where the speed-up of the diffusion speed can be reached if long-range couplings are added. Our work studies a scheme of a ring under the strong resonant modulation that can support a discrete-time quantum walk including coherent multiple long-range translations in a natural way along the synthetic frequency dimension. These multiple translation paths are added in a coherent way, which makes the walker evolve under the topological band. Therein, not only the fast diffusion speed is expected, but more importantly, we find that single quantum gate operations can be performed in the quasi-momentum space. In particular, we show the arbitrary single-qubit state preparation and an example of CNOT two-qubit gate with only one time step, dramatically increasing quantum algorithms. Our study uses the modulated ring to provide fast quantum gate operations based on coherent multiple path quantum walk, which may provide unique designs for efficient quantum operations on photonic chips.

The strong modulation introduces coherent-multiple-transition into discrete time quantum walks in the frequency space, inducing topological band and fast quantum gate operations.