Quantum simulation of quantum relativistic diffusion via quantum walks

Arnault, Pablo; Macquet, A.; Anglés-Castillo, Andreu; Márquez-Martín, Iván; Pina-Canelles, Vicente; Perez, A.; Molfetta, Giuseppe Di; Arrighi, Pablo

doi:10.1088/1751-8121/ab8245

Cited by 9 publications

(5 citation statements)

References 77 publications

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“…Temporal noise on the coin-operation angle θ [see Eq. ( 9)] will generally cause diffusion to take over the typical ballistic motion of the DQW [34,35], while spatial noise on this coin-operation angle will generally cause Anderson localization [34]. Diffusive behavior also occurs when one performs, along the evolution, measurements on the coin or the spatial degree of freedom of the walker [36].…”

Section: Discussionmentioning

confidence: 99%

Quantum walks in weak electric fields and Bloch oscillations

2020

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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)].

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Section: Discussionmentioning

confidence: 99%

Quantum walks in weak electric fields and Bloch oscillations

2020

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“…Subsequently, the entanglement analysis was extended for other protocols of disorder either in the coin operator 14 , 15 , 21 , 26 – 29 , 29 – 34 or in the step operator 18 , 35 , 36 . Recently, it was brought forth the first model with disorder in the translation operator that displays both the strengthening of entanglement and tunable spreading from slower-than-ballistic to faster-than ballistic 17 and even can be found within a relativistic context 37 . From an experimental perspective, using photonic platforms, it was possible to confirm non-static disorder can favor entanglement 21 .…”

Section: Literature Reviewmentioning

confidence: 99%

Negative correlations can play a positive role in disordered quantum walks

Pires

Queirós

2021

Sci Rep

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We investigate the emerging properties of quantum walks with temporal disorder engineered from a binary Markov chain with tailored correlation, C, and disorder strength, r. We show that when the disorder is weak—$$r \ll 1$$ r ≪ 1 —the introduction of negative correlation leads to a counter-intuitive higher production of spin-lattice entanglement entropy, $$S_e$$ S e , than the setting with positive correlation, that is $$S_e(-|C|)>S_e(|C|)$$ S e ( - | C | ) > S e ( | C | ) . These results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.

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“…Such models can simulate dynamics of various physical systems, e.g. [15][16][17][18][19][20][21][22][23][24], and are known to be capable of universal quantum computation [25][26][27][28], and as a consequence, of universal quantum simulation [29]. Moreover, they were already implemented on many experimental platforms [30].…”

Section: Introductionmentioning

confidence: 99%

Complementarity in quantum walks

Grudka

Kurzyński

Polak

et al. 2023

J. Phys. A: Math. Theor.

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The eigenbases of two quantum observables, $\{|a_i\rangle\}_{i=1}^D$ and $\{|b_j\rangle\}_{j=1}^D$, form Mutually Unbiassed Bases (MUB) if $|\langle a_i |b_j \rangle| = 1/\sqrt{D}$ for all $i$ and $j$. In realistic situations MUB are hard to obtain and one looks for Approximate MUB (AMUB), in which case the corresponding eigenbases obey $|\langle a_i |b_j \rangle| \leq c/\sqrt{D}$, where $c$ is some positive constant independent of $D$. In majority of cases observables corresponding to MUB and AMUB do not have clear physical interpretation. Here we study discrete-time quantum walks on $d$-cycles with a position and coin-dependent phase-shift. Such a model simulates a dynamics of a quantum particle moving on a ring with an artificial gauge field. In our case the amplitude of the phase-shift is governed by a single discrete parameter $q$. We solve the model analytically and observe that for prime $d$ the eigenvectors of two quantum walk evolution operators form AMUB. Namely, if $d$ is prime the corresponding eigenvectors of the evolution operators, that act in the $D$-dimensional Hilbert space ($D=2d$), obey $|\langle v_q|v'_{q'} \rangle| \leq \sqrt{2}/\sqrt{D}$ for $q\neq q'$ and for all $|v_q\rangle$ and $|v'_{q'}\rangle$. Finally, we show that the analogous AMUB relation still holds in the continuous version of this model, which corresponds to a one-dimensional Dirac particle.

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Quantum simulation of quantum relativistic diffusion via quantum walks

Cited by 9 publications

References 77 publications

Quantum walks in weak electric fields and Bloch oscillations

Quantum walks in weak electric fields and Bloch oscillations

Negative correlations can play a positive role in disordered quantum walks

Complementarity in quantum walks

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