Electric-Circuit Realization of Fast Quantum Search

Pan, Naiqiao; Chen, Tian; Sun, Houjun; Zhang, Xiangdong

doi:10.34133/2021/9793071

Cited by 26 publications

(18 citation statements)

References 48 publications

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“…Meanwhile, the presented model is general, and can be applicable to other physical systems like photonic [45,46], acoustic [47,48], polaritonic [49] and mechanical systems [50]. Considering the rapid developments of this discipline [51][52][53][54][55][56], we believe that our work will stimulate considerable attention in a broad range of scientific and engineering communities.…”

Section: Discussionmentioning

confidence: 89%

Majorana-like end states in one-dimensional dimerized Kitaev topolectrical circuit

et al. 2022

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Majorana zero modes (MZMs) have attracted tremendous attention in condensed matter and materials physics communities due to the implications in topological quantum computation. One-dimensional (1D) dimerized Kitaev chain is a prototype model for MZMs, but its realization remains a challenge in material systems. Here, we develop a distinctive approach to achieve Majorana-like end states (MESs) by implementing practical dimerized Kitaev topolectrical circuits. Specifically, two arrays of inductors are arranged to simulate particles and antiparticles, while intra- and inter-array capacitive connections are used to model hopping and superconducting pairing. Three topological phases can be achieved by tuning the capacitance, i.e. the trivial phase, Su-Schrieffer-Heeger topological phase and Kitaev phase, with distinct field strength distributions in real space. Majorana splitting is observed around a domain wall in the circuit, and we propose an efficient experimental observable-edge distance-to characterize the process as premonition of topological phase transition. Remarkably, dynamics of the Gaussian wave packet in time domain provide an excellent signal to detect MESs in experiments, as only MESs allow nonlocal propagation in circuit network. Our results not only manifest the superiorities of topolectrical circuits for exotic topological states, but also pave the way for possible applications in electrical engineering and signal processing.

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Section: Discussionmentioning

confidence: 89%

Majorana-like end states in one-dimensional dimerized Kitaev topolectrical circuit

et al. 2022

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“…[1][2][3][4][5][6][7] Quantum walk (QW) on graphs plays an important role in the field of quantum algorithms. [8][9][10][11][12][13][14][15][16][17][18][19][20][21] Fast hitting, [5,6] which refers to a particle starting from the entrance node on a graph and trying to hit the exit node quickly, is one of the properties of QWs on graphs that quantum algorithms can take advantage of to demonstrate remarkable quantum speedup. Theoretical researches have shown that the fast hitting problem on unbalanced tree, which needs exponential time in classical algorithm, can be implemented within polynomial time based on QW algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] It has been proved that a fast search algorithm can be simulated using classical circuit. [16] But it is still a conundrum whether the unbalanced tree can be constructed directly using classical electric circuits to prove the quantum fast hitting with exponential speedup. Since the classical circuit technology is relatively mature, if such a way can be simulated, it is expected to have important impact on quantum speedup in classically intractable complex problems.…”

Section: Introductionmentioning

confidence: 99%

Electric‐Circuit Simulation of Quantum Fast Hitting with Exponential Speedup

et al. 2022

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The ultimate goal of developing quantum algorithms and constructing quantum computers is to achieve faster information processing than using current classical computers. Quantum walks are powerful kernels in quantum computing protocols and possess strong capabilities in speeding up various simulation and optimization tasks. One striking example is provided by quantum walkers evolving on unbalanced trees, which demonstrate faster hitting performances than classical random walk. However, direct experimental construction of unbalanced trees to prove quantum advantage with exponential speedup remains a great challenge due to the highly complex arrangements of the structure. This study attempts to simulate quantum algorithm by classical circuit. Inspired by the quantum algorithm, the classical circuit networks are designed and fabricated with unbalanced tree structures. It is then demonstrated, both theoretically and experimentally, that the quantum algorithm for the fast hitting problem can be simulated in the structure. It is shown that the hitting efficiency of electric signals in the circuit networks with unbalanced tree structures is exponentially faster than the corresponding cases of classical random walks. Because classical circuit networks possess good scalability and stability, the results open up a scalable new path toward quantum speedup in complex problems.

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“…In this work, we experimentally explore the QSSM by designing circuit networks. Recently, based on the similarity between circuit Laplacian and lattice Hamiltonian, simulating various physical phenomena with electric circuits has attracted lots of interest [21][22][23][24][25][26][27][28][29][30][31][32][33]. Compared with other classical platforms, circuit networks possess remarkable advantages of being versatile and reconfigurable.…”

Section: Introductionmentioning

confidence: 99%

Topolectrical circuit realization of quadrupolar surface semimetals

2022

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Recent studies have shown that there are two types of topological quadrupolar semimetals. One is the quadrupolar bulk semimetal, which is a conventional semimetal with gapless nodes in the bulk spectrum. The other type is named the quadrupolar surface semimetal, possessing a gapped bulk but gapless nodes on the surface spectrum. There have been many experiments on the implementation of quadrupolar bulk semimetals. However, the quadrupolar surface semimetal has never been realized. Here we report on the experimental realization of the quadrupolar surface semimetal in the circuit system. To highlight the properties of the quadrupolar surface semimetal, we also prepare a quadrupolar bulk semimetal in the circuit as a contrast. It has been demonstrated that the quadrupolar surface semimetal has a bulk band gap, but two gapless nodes appear on the surfaces. Also, the electrons not only concentrate on the hinges but also on the corresponding surfaces. Our studies provide novel ways to control electrical signals and may have potential applications in the field of intergraded circuit design.

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Electric-Circuit Realization of Fast Quantum Search

Cited by 26 publications

References 48 publications

Majorana-like end states in one-dimensional dimerized Kitaev topolectrical circuit

Majorana-like end states in one-dimensional dimerized Kitaev topolectrical circuit

Electric‐Circuit Simulation of Quantum Fast Hitting with Exponential Speedup

Topolectrical circuit realization of quadrupolar surface semimetals

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