Noisy quantum walks of two indistinguishable interacting particles

Siloi, Ilaria; Benedetti, Claudia; Jacoboni, Carlo; Piilo, Jyrki; Maniscalco, Sabrina; Paris, Matteo G. A.; Bordone, Paolo

doi:10.1103/physreva.95.022106

Cited by 30 publications

(26 citation statements)

References 59 publications

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“…Our choice for the noise is motivated by its relevance in systems of interest for quantum information processing [17][18][19][20][21], and by the fact that RTN is at the root of the 1/ f noise affecting superconducting qubits [22]. In recent years some works have addressed the properties of CTQWs on the one-dimensional lattice subject to random telegraph noise [23][24][25][26], also in the presence of spatial correlations [27]. In this paper we analyze the effects of RTN on spatial search on graphs with generic topology.…”

Section: Introductionmentioning

confidence: 99%

Quantum spatial search on graphs subject to dynamical noise

et al. 2018

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We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order N, also proving that noiseless spatial search shows optimal quantum speedup in the latter, in the computational limit N 1. The noise is modeled by independent sources of random telegraph noise (RTN), dynamically perturbing the links of the graph. We observe two different behaviors depending on the switching rate of RTN: fast noise only slightly degrades performance, whereas slow noise is more detrimental and, in general, lowers the success probability. In particular, we still find a quadratic speed-up for the average running time of the algorithm, while for the star graph with external target node we observe a transition to classical scaling. We also address how the effects of noise depend on the order of the graphs, and discuss the role of the graph topology. Overall, our results suggest that realizations of quantum spatial search are possible with current technology, and also indicate the star graph as the perfect candidate for the implementation by noisy quantum walks, owing to its simple topology and nearly optimal performance also for just few nodes.

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Section: Introductionmentioning

confidence: 99%

Quantum spatial search on graphs subject to dynamical noise

et al. 2018

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“…as explained in the following. Indeed, the isotropy requirement implies that A k=0 commutes with the representation of the isotropy group L, whence we can classify the QW by requiring identity (9) and then multiplying the QW operator A on the left by (I ⊗V ), with V unitary commuting with the representation of L. In the case that the representation is irreducible, then by Schur lemma we have only V = I s . From now on we will restrict to s = 2, which corresponds to the simplest nontrivial QW in the case of G Abelian.…”

Section: Quantum Walks On Cayley Graphs Of Z Dmentioning

confidence: 99%

“…Recently the possibility of implementing actual quantum simulations of quantum fields [2][3][4][5] has been accompanied by novel approaches to foundations of the theory [6][7][8][9], including its derivation from informational principles [1,10] and the recovery of its Lorentz covariance [11]. This has provided a progress in the research based on the idea originally proposed by Feynman [12] of recovering physics as pure quantum information processing.…”

Section: Introductionmentioning

confidence: 99%

Isotropic quantum walks on lattices and the Weyl equation

2017

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We present a thorough classification of the isotropic quantum walks on lattices of dimension d = 1, 2, 3 with a coin system of dimension s = 2. For d = 3 there exist two isotropic walks, namely the Weyl quantum walks presented in Ref.[1], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.

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“…The study of quantum random walks in noisy environments have played a fundamental role in understanding non-trivial quantum phenomena observed in an interdisciplinary framework of studies ranging from biology [1,2], chemistry [3], materials science [4] and electronics [5], to photonics [6][7][8][9] and ultracold matter [10,11]. For many years, most of the research efforts had been focused on the propagation of single particles [12]; however, a great interest in describing the dynamics of correlated particles in noisy systems has recently arisen [13][14][15][16], mainly because it has been recognized that many-particle quantum correlations can be preserved in noisy networks by properly controlling the initial state of the particles, their statistics, indistinguishability or their type of interaction [17,18].…”

Section: Introductionmentioning

confidence: 99%

Two-particle quantum correlations in stochastically-coupled networks

et al. 2019

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Quantum walks in dynamically-disordered networks have become an invaluable tool for understanding the physics of open quantum systems. Although much work has been carried out considering networks affected by diagonal disorder, it is of fundamental importance to study the effects of fluctuating couplings. This is particularly relevant in materials science models, where the interaction forces may change depending on the species of the atoms being linked. In this work, we make use of stochastic calculus to derive a master equation for the dynamics of one and two non-interacting correlated particles in tight-binding networks affected by off-diagonal dynamical disorder. We show that the presence of noise in the couplings of a quantum network creates a pure-dephasing-like process that destroys all coherences in the single-particle Hilbert subspace. Moreover, we show that when two or more correlated particles propagate in the network, coherences accounting for particle indistinguishability are robust against the impact of off-diagonal noise, thus showing that it is possible, in principle, to find specific conditions for which many indistinguishable particles can traverse stochastically-coupled networks without losing their ability to interfere.

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Noisy quantum walks of two indistinguishable interacting particles

Cited by 30 publications

References 59 publications

Quantum spatial search on graphs subject to dynamical noise

Quantum spatial search on graphs subject to dynamical noise

Isotropic quantum walks on lattices and the Weyl equation

Two-particle quantum correlations in stochastically-coupled networks

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