Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation, and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian generator of CTQWs, which are the complex phases along the loops of the underlying graph, was acknowledged for its interest in optimizing or suppressing transport on specific topologies. We argue that the quantum-classical distance, a figure of merit which was introduced to capture the difference in dynamics between a CTQW and its classical, stochastic counterpart, guides the optimization of parameters of the Hamiltonian to achieve better quantum transport on cycle graphs and spatial search for the quantum speed limit without an oracle on complete graphs, the latter also implying fast uniform mixing. We compare the variations of this quantity with the 1-norm of coherence and the inverse participation ratio, showing that the quantum-classical distance is linked to both, but in a topology-dependent relation, which is key to spot the most interesting quantum evolution in each case.

Quantum-classical distance as a tool to design optimal chiral quantum walks / M. Frigerio, C. Benedetti, S. Olivares, M.G.A. Paris. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - 105:3(2022 Mar 11), pp. 032425.032425-1-032425.032425-15. [10.1103/physreva.105.032425]

Quantum-classical distance as a tool to design optimal chiral quantum walks

M. Frigerio
Primo
;
C. Benedetti
Secondo
;
S. Olivares
Penultimo
;
M.G.A. Paris
Ultimo
2022

Abstract

Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation, and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian generator of CTQWs, which are the complex phases along the loops of the underlying graph, was acknowledged for its interest in optimizing or suppressing transport on specific topologies. We argue that the quantum-classical distance, a figure of merit which was introduced to capture the difference in dynamics between a CTQW and its classical, stochastic counterpart, guides the optimization of parameters of the Hamiltonian to achieve better quantum transport on cycle graphs and spatial search for the quantum speed limit without an oracle on complete graphs, the latter also implying fast uniform mixing. We compare the variations of this quantity with the 1-norm of coherence and the inverse participation ratio, showing that the quantum-classical distance is linked to both, but in a topology-dependent relation, which is key to spot the most interesting quantum evolution in each case.
chiral quantum walk; quantum advantage; complex Hamiltonian;
Settore FIS/03 - Fisica della Materia
11-mar-2022
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.032425
Article (author)
File in questo prodotto:
File Dimensione Formato  
PhysRevA.105.032425-min.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 17.5 MB
Formato Adobe PDF
17.5 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
2106.11685.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 5.85 MB
Formato Adobe PDF
5.85 MB Adobe PDF Visualizza/Apri
PhysRevA.105.032425-light.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 6.21 MB
Formato Adobe PDF
6.21 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/916562
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 8
social impact