Integrated Quantum-Walk Structure and NAND Tree on a Photonic Chip

Wang, Yao; Ziwei, Cui; Lü, Yanwu; Zhang, Xiao‐Ming; Gao, Jun; Chang, Yi‐Jun; Yung, Man‐Hong; Jin, Xian

doi:10.1103/physrevlett.125.160502

Cited by 7 publications

(5 citation statements)

References 31 publications

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“…(1). Indeed, for the site |r , the transition amplitude of the time evolution governed by H PST at time t (0 ≤ t ≤ π 2 ) is given by [21],…”

Section: Continuous-time Quantum Walks and Quantum Slidementioning

confidence: 99%

“…Besides, with t = π 4 and N large enough in H PST , a Gaussian wave packet with momentum distributed around − π 2 can be obtained on the pre-engineered chain via the binomial-Gaussian approximation, achieving the quantum slide scheme [21]. The basic construction of FIG.…”

Section: Continuous-time Quantum Walks and Quantum Slidementioning

confidence: 99%

“…As far as we know, few studies in CTQW have discussed the issue of preparing an initial wave packet that possesses a proper momentum. On the other hand, a recent work [21] proposed a method to realize Gaussian wave packets of − π 2 momentum by adopting a "quantum slide" used for solving the NAND tree problem and is experimentally verified. Unfortunately, the momentum of the wave packets formed in the slide is fixed to − π 2 , which limits its application to other problems.…”

Section: Introductionmentioning

confidence: 98%

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Quantum Computing by Quantum Walk on Quantum Slide

Wang¹,

Cheng²,

Cui³

et al. 2022

Preprint

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Continuous-time quantum walk is one of the alternative approaches to quantum computation, where a universal set of quantum gates can be achieved by scattering a quantum walker on some specially-designed structures embedded in a sparse graph [Childs, Phys. Rev. Lett. 2009]. Recent advances in femtosecond laser-inscribed optical waveguides represent a promising physical platform for realizing this quantum-walk model of quantum computation. However, the major challenge is the problem of preparing a plane-wave initial state. Previously, the idea of quantum slide has been proposed and experimentally realized for demonstrating the working principle of NAND tree [Wang et al. Phy. Rev. Lett. 2020]. Here we show how quantum slide can be further applied to realize universal quantum computation, bypassing the plane-wave requirement. Specifically, we apply an external field to the perfect-state-transfer chain, which can generate a moving Gaussian wave packet with an arbitrary momentum. When the phase is properly tuned, the universal gate set in Childs' proposal can be realized in our scheme. Furthermore, we show that the gate fidelities increase with the length of the slide, and can reach unity asymptotically.

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“…(1). Indeed, for the site |r , the transition amplitude of the time evolution governed by H PST at time t (0 ≤ t ≤ π 2 ) is given by [21],…”

Section: Continuous-time Quantum Walks and Quantum Slidementioning

confidence: 99%

Section: Continuous-time Quantum Walks and Quantum Slidementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Quantum Computing by Quantum Walk on Quantum Slide

Wang¹,

Cheng²,

Cui³

et al. 2022

Preprint

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show abstract

“…实验结果证明了量子加速击中效应, 并且最佳命中时间和网络深度之间成线性关系. Shi等 [72] 与非逻辑树问题(NAND tree)也是一类具有量子加速优势的问题, 其结构如图8所示. Wang等 [73] 通过结合量子滑梯以及与非树, 在集成光子芯片上实现了量子与非逻辑.…”

Section: × 49unclassified

Research progress of integrated optical quantum computing

Zhou¹,

Wang²,

Weng³

et al. 2022

Acta Phys. Sin.

Self Cite

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Quantum computing, based on the inherent superposition and entanglement properties of quantum states, can break through the limits of classical computing power. However, under the current technical conditions, the number of qubits that can be manipulated is still limited. In addition, the preparation of high-precision quantum gates and additional quantum error correction systems acquires more auxiliary bits and extra cost much. Therefore, the realization of a universal fault-tolerant quantum computer seems to be a long-term goal. The development of analog quantum computing is a transition path which can be used to simulate many-body physics problem. Quantum walks, as the quantum counterpart of classical random walks, is a research hotspot in analog quantum computing. Due to the unique quantum superposition characteristics, quantum walks exhibit the ballistic transport properties of outward diffusion, so quantum walks provide acceleration in computing power for various algorithms. Based on quantum walks, different computing models are derived to deal with practical physical problems in different fields, such as Biology, Physics, Economics and Computer Science. A large number of technical routes are devoted to realizing quantum walk experiments, including optical fiber networks, superconducting systems, nuclear magnetic resonance systems and trapped ion atom systems. Among these routes, photons are considered as the reliable information carriers in quantum walk experiments due to their controllability, long coherence time and fast speed. Therefore, in this review, we focus on different quantum walk theories and experimental implementations in optical versions, such as traditional optical platforms, optical fiber platforms and Integrated Optical Quantum Platform. In recent years, relying on the rapid development of integrated optical quantum platforms, the quantum walks experiments have moved towards the stage of integration and miniaturization, and at the same time, the experimental scale and the number of qubits have gradually increased. To this end, we summarize the technological progress of integrated optical quantum computing, including various integrated optical quantum experimental platforms and their applications. Secondly, we specifically discuss the quantum walk experiments and practical applications based on integrated optical quantum platforms. Finally, we briefly describe other quantum algorithms and corresponding experimental implementations. These quantum computing schemes provide computational speedups for specific physical problems. In the future, with the further development of integrated optical quantum technology, along with the increase in the number of controllable qubits and the realization of the supporting quantum error correction system, a larger-scale many-body physical system can be constructed to further expand these algorithms and move towards the field of optical quantum computing to a new stage.

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“…Photonic implementations are among the most promising approaches in this regard, using either bulk optics or integrated photonic chips. Previously implemented photonic quantum random walks include walks on a 1D linear graph [16][17][18], on a circle [19,20], and in two-dimensional, cycle-free (tree) graphs [21][22][23][24][25], using either continuous time or discrete time steps. Quantum walks with more than one walking particle have also been implemented using photonics in a way that mimics bosonic or fermionic particle behaviors [26].…”

Section: Introductionmentioning

confidence: 99%

Quantum random walks in coupled photonic ring resonators

Adão¹,

Caño‐García²,

Nieder³

et al. 2022

Preprint

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Quantum random walks use interference for faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze quantum random walks implemented by coherent light propagation in series-coupled photonic ring resonators. We propose a family of graphs modeling these devices and compare quantum and classical random walks on these structures, calculating steady-state and time-dependent solutions. We obtain conditions for quantum advantage in this setting and show how to recover classical random walks by averaging over quantum phases. Preliminary device feasibility tests are carried out via simulations and experimental results using polymeric directional couplers.

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Integrated Quantum-Walk Structure and NAND Tree on a Photonic Chip

Cited by 7 publications

References 31 publications

Quantum Computing by Quantum Walk on Quantum Slide

Quantum Computing by Quantum Walk on Quantum Slide

Research progress of integrated optical quantum computing

Quantum random walks in coupled photonic ring resonators

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