Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs

Wu, Tong; Izaac, Josh; Li, Zi Xi; Wang, Kai; Chen, Zhaozhong; Zhu, Shining; Wang, J. B.; Ma, Xiaosong

doi:10.1103/physrevlett.125.240501

Cited by 22 publications

(13 citation statements)

References 51 publications

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“…That means, to realize the CTQW algorithm, the resources we need in our classical circuit scheme have the same complexity to that of those quantum schemes as described in Refs. [ 13 , 40 ].…”

Section: Discussionmentioning

confidence: 99%

Electric-Circuit Realization of Fast Quantum Search

et al. 2021

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Quantum search algorithm, which can search an unsorted database quadratically faster than any known classical algorithms, has become one of the most impressive showcases of quantum computation. It has been implemented using various quantum schemes. Here, we demonstrate both theoretically and experimentally that such a fast search algorithm can also be realized using classical electric circuits. The classical circuit networks to perform such a fast search have been designed. It has been shown that the evolution of electric signals in the circuit networks is analogies of quantum particles randomly walking on graphs described by quantum theory. The searching efficiencies in our designed classical circuits are the same to the quantum schemes. Because classical circuit networks possess good scalability and stability, the present scheme is expected to avoid some problems faced by the quantum schemes. Thus, our findings are advantageous for information processing in the era of big data.

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Section: Discussionmentioning

confidence: 99%

Electric-Circuit Realization of Fast Quantum Search

et al. 2021

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“…The interference of two 16-dimensional quantum states was observed in an experimental quantum-enhanced stochastic simulation [33]. The PT-symmetric quantum walk was experimentally realized on directed graphs with genuine photonic Fock states [34]. These experiments might provide a new classical insight to quantum mechanics.…”

Section: Introductionmentioning

confidence: 93%

Extending Quantum Probability from Real Axis to Complex Plane

Yang

Han

2021

Entropy

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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability Ψ2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.

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“…The interference of two 16dimensional quantum states was observed in an experimental quantumenhanced stochastic simulation [33]. The PT-symmetric quantum walk was experimentally realized on directed graphs with genuine photonic Fock states [34]. These experiments might provide a new classical insight to quantum mechanics.…”

Section: Introductionmentioning

confidence: 93%

Extending Quantum Probability from Real Axis to Complex Plane

Yang¹,

Han²

2020

Preprint

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Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

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Experimental Parity-Time Symmetric Quantum Walks for Centrality Ranking on Directed Graphs

Cited by 22 publications

References 51 publications

Electric-Circuit Realization of Fast Quantum Search

Electric-Circuit Realization of Fast Quantum Search

Extending Quantum Probability from Real Axis to Complex Plane

Extending Quantum Probability from Real Axis to Complex Plane

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