Floquet-engineered quantum walks

Abstract

The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required. It is, however, generally difficult to control the behavior of quantum walks due to stochastic processes. Here we unveil the walking mechanism based on its particle-wave duality and then present tailoring quantum walks using the walking mechanism (Floquet oscillations) under designed time-dependent coins, to manipulate the desired state on demand, as in universal quantum computation primitives. Our results open the path towards control of quantum walks.

Steering of Quantum Walks through Coherent Control of High-dimensional Bi-photon Quantum Frequency Combs with Tunable State Entropies

“…In this work, we demonstrate a novel pumping and filtering scheme 32 in PPLN waveguide-based QFC to maneuver its entropy, by tailoring its joint spectral intensity (JSI). Further, gaining control over the direction of quantum walk (QW), although very critical to QIP and quantum information transport 33 , has been indeed difficult 34,35 , and often impossible due to its inherent stochastic nature. Unidirectional one and twodimensional QW from separable two-particle states have been shown theoretically 36 .…”

“…However, no control over the directions of the demonstrated QWs 52 could be achieved, which were initiated from the maximally entangled states. Recently, Floquet engineered discrete-and continuous-time QWs and their control have been reported numerically by using time-dependent coins 34 , and by tweaking the node-coupling coefficients 35 . The role of space-dependent coins 53 , and initial conditions 54 on QWs are also studied extensively.…”

Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift

“…In this vein, QWs have been investigated on a large scale which has resulted in the exploration of various types of walks. This includes QWs with decoherence [49][50][51][52][53], QWs with time-dependent coin [54][55][56][57][58], QWs with position dependent coin [59,60], and QWs with different types of phase defects [61][62][63].…”

“…In this paper we engineer QW protocols (one standard QW protocol and one split-step protocol) which imprint a time and spin-dependent phase shift (TSDPS) to the wave function of a quantum particle undergoing a QW on a one-dimensional (1D) lattice. We get inspiration from the previous works [55][56][57][58][61][62][63][64] where a desired time evolution of a QW is achieved either by manipulating the coin parameter by making it time or position dependent, or by introducing different types of spatial phase defects into the wavefunction of the quantum particle. Our engineered QWs share common features, e.g., complete revivals and partial revivals in the probability distribution of QWs which are investigated in [55,56,58,63].…”

“…We get inspiration from the previous works [55][56][57][58][61][62][63][64] where a desired time evolution of a QW is achieved either by manipulating the coin parameter by making it time or position dependent, or by introducing different types of spatial phase defects into the wavefunction of the quantum particle. Our engineered QWs share common features, e.g., complete revivals and partial revivals in the probability distribution of QWs which are investigated in [55,56,58,63]. We use the phase factor (φ) as a control knob to control and manipulate the evolution of a QW.…”