Related papers: Quantum walks in external gauge fields
We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This…
Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon…
An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced previously. The square of the Hamiltonian turns out to be an…
A simple coined quantum walk in one dimension can be characterized by a $SU(2)$ operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
A particular family of time- and space-dependent discrete-time quantum walks (QWs) is considered in one dimensional physical space. The continuous limit of these walks is defined through a new procedure and computed in full detail. In this…
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…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
Open quantum walks (OQWs) are a new type of quantum walks which are entirely driven by the dissipative interaction with external environments and are formulated as completely positive trace-preserving maps on graphs. A generalized quantum…
One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…
Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is…
In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the…
Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo…
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…