72 citations · 610 across the 64 of their papers we have counts for
39 papers · 1 filter
Connes Distance in Discrete-Time Quantum Walks
Rayan Trabelsi, A. F. Reyes-Lega, Pablo Arrighi
We study the geometric spread of discrete-time quantum walks using Connes' distance formula. We introduce its discrete analogue by adapting the continuous spectral metric to the la…
Dirac quantum walk on tetrahedra
Ugo Nzongani, Nathanaël Eon, Iván Márquez-Martín +3
Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs ar…
A relativistic discrete spacetime formulation of 3+1 QED
Nathanaël Eon, Giuseppe Di Molfetta, Giuseppe Magnifico +1
This work provides a relativistic, digital quantum simulation scheme for both and dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation o…
Generalised tensors and traces
Pablo Arrighi, Amélia Durbec, Matt Wilson
Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations b…
Quantum networks theory
Pablo Arrighi, Amélia Durbec, Matt Wilson
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so t…
Addressable quantum gates
Pablo Arrighi, Christopher Cedzich, Marin Costes +2
We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipul…
A discrete relativistic spacetime formalism for 1+1-QED with continuum limits
Kevissen Sellapillay, Pablo Arrighi, Giuseppe Di Molfetta
We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles…
Quantum simulation of quantum relativistic diffusion via quantum walks
Pablo Arnault, Adrian Macquet, Andreu Anglés-Castillo +6
Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a…
The Grover search as a naturally occurring phenomenon
Mathieu Roget, Stéphane Guillet, Pablo Arrighi +1
We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical…
A quantum walk with both a continuous-time and a continuous-spacetime limit
Giuseppe Di Molfetta, Pablo Arrighi
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum m…
An overview of Quantum Cellular Automata
Pablo Arrighi
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global…
A quantum cellular automaton for one-dimensional QED
Pablo Arrighi, Cédric Bény, Terry Farrelly
We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally inva…
From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
Pablo Arrighi, Giuseppe Di Molfetta, Iván Márquez-Martín +1
A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QW admit, as their continuum limit, a well…
Discrete-time quantum walks as fermions of lattice gauge theory
Pablo Arnault, Armando Pérez, Pablo Arrighi +1
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time…
The Dirac equation as a quantum walk over the honeycomb and triangular lattices
Pablo Arrighi, Giuseppe Di Molfetta, Iván Márquez-Martín +1
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, l…
Quantum walking in curved spacetime: discrete metric
Pablo Arrighi, Giuseppe Di Molfetta, Stefano Facchini
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuu…
Quantum walking in curved spacetime: dimensions, and beyond
Pablo Arrighi, Stefano Facchini
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, l…
Quantum walking in curved spacetime
Pablo Arrighi, Stefano Facchini, Marcelo Forets
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar…
Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
Pablo Arrighi, Stefano Facchini, Marcelo Forets
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diag…
Decoupled Quantum Walks, models of the Klein-Gordon and wave equations
Pablo Arrighi, Stefano Facchini
Decoupling a vectorial PDE consists in solving the system for each component, thereby obtaining scalar PDEs that prescribe the evolution of each component independently. We present…
The Dirac equation as a quantum walk: higher dimensions, observational convergence
Pablo Arrighi, Marcelo Forets, Vincent Nesme
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a latt…
The physical Church-Turing thesis and the principles of quantum theory
Pablo Arrighi, Gilles Dowek
Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet several works have shown how quantum theory as it stands could breach the…
Partitioned quantum cellular automata are intrinsically universal
Pablo Arrighi, Jonathan Grattage
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions.…
A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
Pablo Arrighi, Jonathan Grattage
We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimension…