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Time-continuous quantum error correction, necessary to protect quantum information under time-dependent Hamiltonians, relies on weak continuous syndrome measurements. Implementing these measurements requires a continuous coupling among at…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\pi$ over a large set $\S$. This…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
Rydberg atoms provide a highly promising platform for quantum computation, leveraging their strong tunable interactions to encode and manipulate information in the electronic states of individual atoms. Key advantages of Rydberg atoms…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to…
We construct a family of time-independent nearest-neighbor Hamiltonians coupling eight-state systems on a 1D ring that enables universal quantum computation. Hamiltonians in this family can achieve universality either by driving a…
We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
The quantum switch, a process enabling a coherent superposition of different orders of quantum channels, has garnered significant attention due to its ability to enable noiseless communications through noisy channels, such as…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
We perform exact diagonalization and time evolution of the Lechner-Hauke-Zoller (LHZ) annealing architecture [Science Advances 1(9), e1500838 (2015)] for ten physical qubits. Thereby, on a training set consisting of $2400$ problem…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
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 versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
This paper is concerned with the continuous-time quantum walk on Z, Z^d, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on…
Quantum walks are the quantum mechanical analogue of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and…