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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 (down) 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
Permanent link to this record
 
 
Author Angles-Castillo, A.; Perez, A.
Title A quantum walk simulation of extra dimensions with warped geometry Type Journal Article
Year 2022 Publication (down) Scientific Reports Abbreviated Journal Sci Rep
Volume 12 Issue 1 Pages 1926 - 12pp
Keywords
Abstract We investigate the properties of a quantum walk which can simulate the behavior of a spin 1/2 particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup constitutes a 1+ 1 dimensional version of the Randall-Sundrum model, which plays an important role in high energy physics. In the continuum spacetime limit, the quantum walk reproduces the Dirac equation corresponding to the model, which allows to anticipate some of the properties that can be reproduced by the quantum walk. In particular, we observe that the probability distribution becomes, at large time steps, concentrated near the “low energy” brane, and can be approximated as the lowest eigenstate of the continuum Hamiltonian that is compatible with the symmetries of the model. In this way, we obtain a localization effect whose strength is controlled by a warp coefficient. In other words, here localization arises from the geometry of the model, at variance with the usual effect that is originated from random irregularities, as in Anderson localization. In summary, we establish an interesting correspondence between a high energy physics model and localization in quantum walks.
Address [Angles-Castillo, Andreu] Univ Valencia, CSIC, Dept Fis Teor, Valencia 46100, Spain, Email: andreu.angles@ific.uv.es
Corporate Author Thesis
Publisher Nature Portfolio 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:000751472600024 Approved no
Is ISI yes International Collaboration no
Call Number IFIC @ pastor @ Serial 5107
Permanent link to this record
 
 
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 (down) 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 Perez, A.
Title Information encoding of a qubit into a multilevel environment Type Journal Article
Year 2010 Publication (down) Physical Review A Abbreviated Journal Phys. Rev. A
Volume 81 Issue 5 Pages 052326 - 6pp
Keywords
Abstract I consider the interaction of a small quantum system (a qubit) with a structured environment consisting of many levels. The qubit will experience a decoherence process, which implies that part of its initial information will be encoded into correlations between system and environment. I investigate how this information is distributed on a given subset of levels as a function of its size, using the mutual information between both entities, in the spirit of the partial-information plots studied by Zurek and co-workers. In this case we can observe some differences, which arise from the fact that I am partitioning just one quantum system and not a collection of them. However, some similar features, like redundancy (in the sense that a given amount of information is shared by many subsets), which increases with the size of the environment, are also found here.
Address [Perez, A.] Univ Valencia, CSIC, Dept Fis Teor, E-46100 Burjassot, 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 ISI:000278140000064 Approved no
Is ISI yes International Collaboration no
Call Number IFIC @ elepoucu @ Serial 445
Permanent link to this record
 
 
Author Hinarejos, M.; Di Franco, C.; Romanelli, A.; Perez, A.
Title Chirality asymptotic behavior and non-Markovianity in quantum walks on a line Type Journal Article
Year 2014 Publication (down) Physical Review A Abbreviated Journal Phys. Rev. A
Volume 89 Issue 5 Pages 052330 - 7pp
Keywords
Abstract We investigate the time evolution of the chirality reduced density matrix for a discrete-time quantum walk on a one-dimensional lattice. The matrix is obtained by tracing out the spatial degree of freedom. We analyze the standard case, without decoherence, and the situation in which decoherence appears in the form of broken links in the lattice. By examining the trace distance for possible pairs of initial states as a function of time, we conclude that the evolution of the reduced density matrix is non-Markovian, in the sense defined by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)]. As the level of noise increases, the dynamics approaches a Markovian process. The highest non-Markovianity corresponds to the case without decoherence. The reduced density matrix tends always to a well-defined limit that we calculate, but only in the decoherence-free case is this limit nontrivial.
Address [Hinarejos, Margarida; Perez, Armando] Univ Valencia, CSIC, Dept Fis Teor, E-46100 Burjassot, 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:000336751300003 Approved no
Is ISI yes International Collaboration yes
Call Number IFIC @ pastor @ Serial 1807
Permanent link to this record
 
 
Author Perez, A.
Title Asymptotic properties of the Dirac quantum cellular automaton Type Journal Article
Year 2016 Publication (down) 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
Permanent link to this record
 
 
Author Gomis, P.; Perez, A.
Title Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions Type Journal Article
Year 2016 Publication (down) 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
Permanent link to this record
 
 
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 (down) 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
Permanent link to this record
 
 
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 (down) 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
Permanent link to this record
 
 
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 (down) 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
Permanent link to this record