Related papers: Decoherence enhances performance of quantum walks …
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
Advancements in Noisy Intermediate-Scale Quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific, well-defined computational tasks. In this work, we explore and control quantum…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing…
We have studied how decoherence affects a quantum walk on the line. As expected, it is highly sensitive, consisting as it does of an extremely delocalized particle. We obtain an expression for the rate at which the standard deviation falls…
We study quantum advantage in one-step rendezvous games on simple graphs analytically, numerically, and using noisy intermediate-scale quantum (NISQ) processors. Our protocols realise the recently discovered [arXiv:2207.14404] optimal…
Many symmetry protected or symmetry enriched phases of quantum matter have the property that every ground state in a given such phase endows measurement based quantum computation with the same computational power. Such phases are called…
We present a method for characterizing the performance of noisy quantum processors using discrete time crystals. Deviations from ideal persistent oscillatory behavior give rise to numerical scores by which relative quantum processor…
We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…
An examination of the concept of using classical degrees of freedom to drive the evolution of quantum computers is given. Specifically, when externally generated, coherent states of the electromagnetic field are used to drive transitions…
In systems considered for quantum computing, i.e., for control of quantum dynamics with the goal of processing information coherently, decoherence and deviation from pure quantum states, are the main obstacles to fault-tolerant error…
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…