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• W2759980128 abstract "To extend the continuous-time quantum walk (CTQW) to simulate $P$ distinguishable particles on a graph $G$ composed of $N$ vertices, the Hamiltonian of the system is expanded to act on an ${N}^{P}$-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph $G$ via a single-particle CTQW propagating on the Cartesian graph product ${G}^{ensuremath{square}P}$. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated ${N}^{P}$ state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure ${G}^{ensuremath{square}P}$ in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing ``redundant'' and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed $N$." @default.
• W2759980128 created "2017-10-06" @default.
• W2759980128 creator A5002250366 @default.
• W2759980128 creator A5040713757 @default.
• W2759980128 date "2017-09-22" @default.
• W2759980128 modified "2023-10-18" @default.
• W2759980128 title "Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions" @default.
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• W2759980128 doi "https://doi.org/10.1103/physreve.96.032136" @default.
• W2759980128 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/29346966" @default.
• W2759980128 hasPublicationYear "2017" @default.
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