Feedback‐Assisted Quantum Search by Continuous‐Time Quantum Walks

Abstract

The quantum search of a target node on a cycle graph by means of a quantum walk assisted by continuous measurement and feedback are addressed. Unlike previous spatial search approaches, where the oracle is described as a projector on the target state, a dynamical oracle implemented through a feedback Hamiltonian is considered. The idea is based on continuously monitoring the position of the quantum walker on the graph and then applying a unitary feedback operation based on the information obtained from measurement. The feedback changes the couplings between the nodes and it is optimized at each time via a numerical procedure. The stochastic trajectories describing the evolution for graphs of dimensions up to N = 15 are numerically simulated, and the performance of the protocol is quantified via the average fidelity between the state of the walker and the target node. Different constraints on the control strategy are discussed. For unbounded controls, the protocol is able to quickly localize the walker on the target node. How the performance is lowered by posing an upper bound on the control couplings is then discussed. Finally, it is shown how a digital feedback protocol seems in general as efficient as the continuous bounded one.

Programmable high-dimensional Hamiltonian in a photonic waveguide array

“…Waveguide arrays 1 are a powerful platform for the optical simulation of condensed matter physics effects ranging from Bloch oscillations 2 to enhanced coherent transport via controllable decoherence 3 , adiabatic passage 4 , 5 , Anderson localization 6 , and many more 7 . Quantum walks in waveguide arrays 8 , 9 have been proposed for simulating particle statistics 10 , 11 , boson sampling 12 , 13 , quantum state transfer 14 , 15 , quantum state generation 16 , 17 , quantum search 18 , 19 , optical transformation 20 and could implement 1 and 2-qubit gates 21 , 22 with the potential of implementing universal unitaries 23 . Waveguide arrays have been used to model topological band structures 24 , 25 and their interplay through non-Hermiticities generated by mode-selective gain and loss 26 .…”

Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning

“…In the class of parametrized Hamiltonians, an exceptionally diffused and useful example is that of quantum walks (QWs). QWs are a universal and versatile tool that can be harnessed to perform a plethora of tasks ranging from energy transport [42][43][44] to quantum algorithms, [45][46][47][48][49][50][51] quantum computation, [52][53][54] and quantum communication. 55 In particular, continuous-time quantum walks (CTQWs) are the quantum analog of classical random walks [56][57][58][59] that describe the continuous evolution of a quantum particle over a set of discrete positions.…”

Identifying network topologies via quantum walk distributions

“…In order to achieve such scalability, a perspective is that of extending these results to incorporated machine learning techniques. By relying solely on measured probabilities, our technique provides a simple but yet effective strategy for the routine characterization of networks, and as such constitutes an enabling step towards most developing quantum technologies based on complex networks [46][47][48][49][50][51], as well as a tool for exploring new involved simulation regimes which have non-trivial mapping between the experimental control and the CTQW parameters [52][53][54].…”