Related papers: Feedback-assisted quantum search by continuous-tim…
An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers,…
Topological quantum sensing leverages unique topological features to suppress noise and improve the precision of parameter estimation, emerging as a promising tool in both fundamental research and practical application. In this Letter, we…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
So far, only the results on 3 qubit spaces (both on superconducting and ion-trap realisations of quantum processors) have beaten the classical unstructured search in the expected number of oracle calls using optimal protocols in both…
We present a formulation of measurement-based feedback control of a single quantum particle in one spatial dimension. An arbitrary linear combination of the position and momentum of the particle is continuously monitored, and feedback…
Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS…
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
Attention-based neural networks such as transformers have revolutionized various fields such as natural language processing, genomics, and vision. Here, we demonstrate the use of transformers for quantum feedback control through both a…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers…
The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering. Today, the increasing demand for applied quantum technologies requires to adapt this level of control to…