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	Author	Perez, A.
	Title	Asymptotic properties of the Dirac quantum cellular automaton			Type	Journal Article
	Year	2016	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	93	Issue	1	Pages	012328 - 10pp
	Keywords
	Abstract	We show that the Dirac quantum cellular automaton [A. Bisio, G. M. D'Ariano, and A. Tosini, Ann. Phys. (N. Y.) 354, 244 (2015)] shares many properties in common with the discrete-time quantum walk. These similarities can be exploited to study the automaton as a unitary process that takes place at regular time steps on a one-dimensional lattice, in the spirit of general quantum cellular automata. In this way, it becomes an alternative to the quantum walk, with a dispersion relation that can be controlled by a parameter that plays a similar role to the coin angle in the quantum walk. The Dirac Hamiltonian is recovered under a suitable limit. We provide two independent analytical approximations to the long-term probability distribution. It is shown that, starting from localized conditions, the asymptotic value of the entropy of entanglement between internal and motional degrees of freedom overcomes the known limit that is approached by the quantum walk for the same initial conditions and is similar to the ones achieved by highly localized states of the Dirac equation.
	Address	[Perez, A.] Univ Valencia, CSIC, IFIC, Dept Fis Teor, E-46100 Valencia, Spain
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1050-2947	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000368291600005			Approved	no
	Is ISI	yes	International Collaboration	no
	Call Number	IFIC @ pastor @			Serial	2520
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	Author	Gomis, P.; Perez, A.
	Title	Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions			Type	Journal Article
	Year	2016	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	94	Issue	1	Pages	012103 - 11pp
	Keywords
	Abstract	We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the device. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in the presence of decoherence that shows a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the nondiagonal terms with time and use this fact to quantify the amount of decoherence from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model. We analyze a typical experiment and show that, for that setup, the decoherence time is much smaller than the characteristic time scale for the separation of the two beams, implying that they can be described as an incoherent mixture of atoms traveling in the up and down directions with opposite values of the spin projection. Therefore, entanglement is quickly destroyed in the setup we analyzed.
	Address	[Gomis, P.] Univ Valencia, CSIC, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: Pablo.Gomis@uv.es;
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2469-9926	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000378909000003			Approved	no
	Is ISI	yes	International Collaboration	no
	Call Number	IFIC @ pastor @			Serial	2739
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	Author	Bru, L.A.; de Valcarcel, G.J.; Di Molfetta, G.; Perez, A.; Roldan, E.; Silva, F.
	Title	Quantum walk on a cylinder			Type	Journal Article
	Year	2016	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	94	Issue	3	Pages	032328 - 7pp
	Keywords
	Abstract	We consider the two-dimensional alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or “hidden” extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasimomentum in the closed dimension. In the continuous space-time limit, the different components manifest as a set of Dirac equations, with each quasimomentum providing the value of the corresponding mass. We briefly discuss the possible link of these ideas to the simulation of high-energy physical theories that include extra dimensions. Finally, entanglement between the coin and spatial degrees of freedom is studied, showing that the entanglement entropy clearly overcomes the value reached with only one spatial dimension.
	Address	[Bru, Luis A.] Univ Politecn Valencia, ITEAM Res Inst, Opt & Quantum Commun Grp, Camino Vera S-N, E-46022 Valencia, Spain
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2469-9926	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000384060700005			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	2823
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	Author	Marquez-Martin, I.; Di Molfetta, G.; Perez, A.
	Title	Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time			Type	Journal Article
	Year	2017	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	95	Issue	4	Pages	042112 - 5pp
	Keywords
	Abstract	We analyze the properties of a two-and three-dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [Phys. Lett. B 125, 136 (1983)]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker) become localized in one of the dimensions, not from the action of a random noise on the lattice (as in the case of Anderson localization) but from a regular dependence in space. On the other hand, the resulting quantum walk can move freely along the “ordinary” dimensions.
	Address	[Marquez-Martin, I.; Di Molfetta, G.; Perez, A.] Univ Valencia, CSIC, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: giuseppe.dimolfetta@lif.univ-mrs.fr
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2469-9926	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000399931500006			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	3102
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	Author	Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A.
	Title	Dirac equation as a quantum walk over the honeycomb and triangular lattices			Type	Journal Article
	Year	2018	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	97	Issue	6	Pages	062111 - 5pp
	Keywords
	Abstract	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, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in (2 + 1) dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the nonrectangular grids, as in graphene-like materials. The latter, in particular, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.
	Address	[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Aix Marseille Univ, Univ Toulon, LIS, CNRS, Marseille, France, Email: pablo.arrighi@univ-amu.fr;
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2469-9926	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000435076800001			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	3624
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	Author	Marquez-Martin, I.; Arnault, P.; Di Molfetta, G.; Perez, A.
	Title	Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks			Type	Journal Article
	Year	2018	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	98	Issue	3	Pages	032333 - 8pp
	Keywords
	Abstract	Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation and the conserved current satisfies the corresponding conservation equation.
	Address	[Marquez-Martin, Ivan; Arnault, Pablo; Di Molfetta, Giuseppe; Perez, Armando] Univ Valencia, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: ivan.marquez@uv.es;
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2469-9926	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000446163200006			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	3750
Permanent link to this record



	Author	Arnault, P.; Perez, A.; Arrighi, P.; Farrelly, T.
	Title	Discrete-time quantum walks as fermions of lattice gauge theory			Type	Journal Article
	Year	2019	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	99	Issue	3	Pages	032110 - 16pp
	Keywords
	Abstract	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 dynamics is thus not only manifestly unitary, but also ultralocal, i.e., the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go results stating that no nontrivial scalar quantum cellular automaton can be translationally invariant [D. A. Meyer, J. Stat. Phys. 85, 551 (1996); Phys. Lett. A 223, 337 (1996)]. All results are presented in a single-particle framework and for a (1+1)-dimensional space-time.
	Address	[Arnault, Pablo; Perez, Armando] Univ Valencia, Dept Fis Teor, Dr Moliner 50, E-46100 Burjassot, Spain, Email: pablo.arnault@ific.uv.es
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2469-9926	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000461896700002			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	3950
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	Author	Arnault, P.; Pepper, B.; Perez, A.
	Title	Quantum walks in weak electric fields and Bloch oscillations			Type	Journal Article
	Year	2020	Publication	Physical Review A	Abbreviated Journal	Phys. Rev. A
	Volume	101	Issue	6	Pages	062324 - 12pp
	Keywords
	Abstract	Bloch oscillations appear when an electric field is superimposed on a quantum particle that evolves on a lattice with a tight-binding Hamiltonian (TBH), i.e., evolves via what we call an electric TBH; this phenomenon will be referred to as TBH Bloch oscillations. A similar phenomenon is known to show up in so-called electric discrete-time quantum walks (DQWs) [C. Cedzich et al., Phys. Rev. Lett. 111, 160601 (2013);] this phenomenon will be referred to as DQW Bloch oscillations. This similarity is particularly salient when the electric field of the DQW is weak. For a wide, i.e., spatially extended, initial condition, one numerically observes semiclassical oscillations, i.e., oscillations of a localized particle, for both the electric TBH and the electric DQW. More precisely, the numerical simulations strongly suggest that the semiclassical DQW Bloch oscillations correspond to two counterpropagating semiclassical TBH Bloch oscillations. In this work it is shown that, under certain assumptions, the solution of the electric DQW for a weak electric field and a wide initial condition is well approximated by the superposition of two continuous-time expressions, which are counterpropagating solutions of an electric TBH whose hopping amplitude is the cosine of the arbitrary coin-operator mixing angle. In contrast, if one wishes the continuous-time approximation to hold for spatially localized initial conditions, one needs at least the DQW to be lazy, as suggested by numerical simulations and by the fact that this has been proven in the case of a vanishing electric field [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)].
	Address	[Arnault, Pablo; Pepper, Benjamin; Perez, A.] Univ Valencia, CSIC, Dept Fis Teor, Cerrer Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ific.uv.es;
	Corporate Author				Thesis
	Publisher	Amer Physical Soc	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1050-2947	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000541400900002			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	4431
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	Author	Nzongani, U.; Zylberman, J.; Doncecchi, C.E.; Perez, A.; Debbasch, F.; Arnault, P.
	Title	Quantum circuits for discrete-time quantum walks with position-dependent coin operator			Type	Journal Article
	Year	2023	Publication	Quantum Information Processing	Abbreviated Journal	Quantum Inf. Process.
	Volume	22	Issue	7	Pages	270 - 46pp
	Keywords	Quantum walks; Quantum circuits; Quantum simulation
	Abstract	The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode 2(n) position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. Themain idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent 2 x 2-block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error epsilon (in terms of the spectral norm), the depth and size of which scale as O(1/epsilon). A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position).
	Address	[Nzongani, Ugo; Doncecchi, Carlo-Elia; Arnault, Pablo] Univ Paris Saclay, CNRS, INRIA, Lab Methodes Formelles,ENS Paris Saclay, F-91190 Gif Sur Yvette, France, Email: ugo.nzongani@universite-paris-saclay.fr;
	Corporate Author				Thesis
	Publisher	Springer	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1570-0755	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:001022408900002			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	5587
Permanent link to this record



	Author	Arrighi, P.; Di Molfetta, G.; Marquez-Martin, I.; Perez, A.
	Title	From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks			Type	Journal Article
	Year	2019	Publication	Scientific Reports	Abbreviated Journal	Sci Rep
	Volume	9	Issue		Pages	10904 - 10pp
	Keywords
	Abstract	A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. In a previous paper, we showed that QWs over the honeycomb and triangular lattices can be used to simulate the Dirac equation. We apply a spacetime coordinate transformation upon the lattice of this QW, and show that it is equivalent to introducing spacetime-dependent local unitaries-whilst keeping the lattice fixed. By exploiting this duality between changes in geometry, and changes in local unitaries, we show that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)-dimensional curved spacetime. Interestingly, the duality crucially relies on the non linear-independence of the three preferred directions of the honeycomb and triangular lattices: The same construction would fail for the square lattice. At the practical level, this result opens the possibility to simulate field theories on curved manifolds, via the quantum walk on different kinds of lattices.
	Address	[Arrighi, Pablo; Di Molfetta, Giuseppe; Marquez-Martin, Ivan] Univ Toulon & Var, Aix Marseille Univ, CNRS, LIS, Marseille, France, Email: pablo.arrighi@univ-amu.fr;
	Corporate Author				Thesis
	Publisher	Nature Publishing Group	Place of Publication		Editor
	Language	English	Summary Language		Original Title
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2045-2322	ISBN		Medium
	Area		Expedition		Conference
	Notes	WOS:000477701800007			Approved	no
	Is ISI	yes	International Collaboration	yes
	Call Number	IFIC @ pastor @			Serial	4081
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