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Wilkinson, Kieran N.; Estarellas, Marta P.; Spiller, Timothy P.; D’Amico, Irene

doi:10.26421/qic18.3-4

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…This has motivated the study of quantum walks with an environmental interaction, as is described by QSWs. The QSW framework has been investigated in the context of relaxing property [27][28][29] and propagation speed [30,31], showing advantages for speed-up in learning algorithms [32], and enhancement of excitation transport [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Quantum state discrimination on reconfigurable noise-robust quantum networks

Pozza

Caruso

2020

Phys. Rev. Research

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A fundamental problem in quantum information processing is the discrimination among a set of quantum states of a system. In this paper, we address this problem on an open quantum system described by a graph, whose evolution is defined by a quantum stochastic walk. In particular, the structure of the graph mimics those of neural networks, with the quantum states to discriminate encoded on input nodes and with the discrimination obtained on the output nodes. We optimize the parameters of the network to obtain the highest probability of correct discrimination. Numerical simulations show that after a transient time the probability of correct decision approaches the theoretical optimal quantum limit. These results are confirmed analytically for small graphs. Finally, we analyze the robustness and reconfigurability of the network for different set of quantum states and show that this architecture can pave the way to experimental realizations of our protocol as well as novel quantum generalizations of deep learning.

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Section: Introductionmentioning

confidence: 99%

Quantum state discrimination on reconfigurable noise-robust quantum networks

Pozza

Caruso

2020

Phys. Rev. Research

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“…For example, Einstein-Podolsky-Rosen (EPR) pairs, which may be considered as qubit pairs in the form of a Bell state, furnish one of the simplest illustrations of maximum entanglement at the bipartite level. The demonstration that such EPR pairs can be rapidly and robustly generated with spin chains [9] has also provided additional impetus for their study.…”

Section: Introductionmentioning

confidence: 99%

Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems

M.¹,

Rundle²,

Samson³

et al. 2022

Preprint

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We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-1 2 one-dimensional spin-chain models, viz., the Ising and anisotropic XY models in a transverse field, and the XXZ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system's singlesite, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in witnessing and characterizing first-, second-and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method's ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function's utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be intuitively analyzed.

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Beyond the Swap Test: Optimal Estimation of Quantum State Overlap

et al. 2020

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We study the estimation of the overlap between two Haar-random pure quantum states in a finite-dimensional Hilbert space, given M and N copies of them. We compute the statistics of the optimal measurement, which is a projection onto permutation-invariant subspaces, and provide lower bounds for the mean square error for both local and Bayesian estimation. In the former case, the bound is asymptotically saturable by a maximum likelihood estimator, whereas in the latter we give a simple exact formula for the optimal value. Furthermore, we introduce two LOCC strategies, relying on the estimation of one or both the states, and show that, although they are suboptimal, they outperform the commonly-used swap test. In particular, the swap test is extremely inefficient for small values of the overlap, which become exponentially more likely as the dimension increases. Finally, we show that the optimal measurement is less invasive than the swap test and study the robustness to depolarizing noise for qubit states.

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Cited by 3 publications

References 27 publications

Quantum state discrimination on reconfigurable noise-robust quantum networks

Quantum state discrimination on reconfigurable noise-robust quantum networks

Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems

Beyond the Swap Test: Optimal Estimation of Quantum State Overlap

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