Experimental demonstration of a quantum annealing algorithm for the traveling salesman problem in a nuclear-magnetic-resonance quantum simulator

Chen, Hongwei; Kong, Xinggong; Chong, Bo; Gan, Qintao; Zhou, Xin; Peng, Xinhua; Du, Jiangfeng

doi:10.1103/physreva.83.032314

Cited by 38 publications

(29 citation statements)

References 27 publications

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“…Therefore, the spin lock technique can overcome the limitation of the CSFQ to be used for the QA. In the NMR, the spin-lock based QA has been discussed and demonstrated [31,32]. While DC magnetic fields are applied along x axis in the conventional QA, the AC driving fields along x axis are applied in the spin lock-based QA.…”

Section: Introductionmentioning

confidence: 99%

“…This means that, the performance of the spin-lock based QA can be degraded if the Rabi frequency of the driving is comparable with the qubit frequency. Since the qubit frequency (an order of GHz) is just a few orders of magnitude larger than the other typical frequencies (an order of MHz) [31], a careful assessment of the error accumulation due to the violation of the RWA is necessary to evaluate the practicality of the spin-lock based QA with the CSFQs. It is worth mentioning that, in our previous study at the SSDM [33], we implement a numerical simulation along this direction with a fixed number of the qubits.…”

Section: Introductionmentioning

confidence: 99%

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Quantum annealing with capacitive-shunted flux qubits

Matsuzaki

Hakoshima

Seki

et al. 2020

Jpn. J. Appl. Phys.

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Quantum annealing (QA) provides us with a way to solve combinatorial optimization problems. In the previous demonstration of the QA, a superconducting flux qubit (FQ) was used. However, the flux qubits in these demonstrations have a short coherence time such as tens of nano seconds. For the purpose to utilize quantum properties, it is necessary to use another qubit with a better coherence time. Here, we propose to use a capacitive-shunted flux qubit (CSFQ) for the implementation of the QA. The CSFQ has a few order of magnitude better coherence time than the FQ used in the QA. We theoretically show that, although it is difficult to perform the conventional QA with the CSFQ due to the form and strength of the interaction between the CSFQs, a spin-lock based QA can be implemented with the CSFQ even with the current technology. Our results pave the way for the realization of the practical QA that exploits quantum advantage with long-lived qubits. * matsuzaki.yuichiro@aist.go.jp † hakoshima-hideaki@aist.go.jp arXiv:2001.09844v2 [quant-ph]

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum annealing with capacitive-shunted flux qubits

Matsuzaki

Hakoshima

Seki

et al. 2020

Jpn. J. Appl. Phys.

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“…Papers [1,12,15] use a heuristic algorithm that may not find an optimal result. Papers [4,14] demonstrate their efforts on small TSPs with 4 and 6 cities, respectively.…”

Section: Literature Relating the Traveling Salesman Problem To Quantumentioning

confidence: 99%

“…Chen and his coauthors [4] use the notation and formulation of [12] for a quantum solution to a 4-city TSP on a nuclear magnetic resonance quantum simulator.…”

Section: Literature Relating the Traveling Salesman Problem To Quantumentioning

confidence: 99%

Small Traveling Salesman Problems

Warren¹

2017

JAAM

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Abstract. This paper illustrates fundamental principles about small traveling salesman problems (TSPs) which are a current application for quantum annealing computers. The 2048 qubit, quantum annealing computer manufactured by D-Wave Systems is estimated to be able to solve all TSPs on 8 cities, which advances a recent 4-city result on a quantum simulator. Additionally, the D-Wave quantum computer is expected to find all optimal tours for each TSP. To prepare for this, we show the expected quantum output for 5,000 randomly generated TSPs on 6, 8 and 10 cities. The examples in the TSPLIB have 14 or more cities. These are too large for the current quantum annealing processors. We have included an annotated bibliography about solving the TSP on a quantum computer. Keywords:Traveling salesman, optimal tour, combinatorial analysis, discrete optimization, quantum annealing AMS Classification Codes: 68R05, 81P68, 90C27 IntroductionRecently first steps have been taken to solve the traveling salesman problem (TSP) using the computational advantages promised by quantum algorithms [13]. As with any emerging effort, the initial steps have been limited and focused on a small number of cities that fit on the hardware. The major contributions of this paper are for 6, 8 and 10 city TSPs. We present empirical evidence based on 15,000 random samples, 5,000 for each number of cities. The majority of evidence indicates that the number of optimal tours and the length of an optimal tour increase together. All of the data shows that as the number of cities increases, the number of optimal tours increases. In all cases, the distances between cities are random integers in the interval [1,21].Outside the quantum world, the traveling salesman problem continues to be a hot topic that attracts wide interest. The problem is easy to explain and has several diverse applications [9,18], as well as theoretical studies [2,20]. There are many fascinating ways to solve it, usually approximately. Given a set of cities and the directed distances between each pair of cities, the TSP asks for a shortest route that visits each city exactly once and returns to the starting city. There are excellent, non-quantum TSP surveys [5,7,10].Quantum computing, particularly quantum annealing [3], is a new paradigm for discrete optimization that could use TSP benchmarks for the hardware. Quantum computing opens the possibility of large speedup with high probability of optimal answers, but requires new techniques for solving the TSP [11,19].The paper is organized as follows: Section 2 has references for other reports that use quantum computing algorithms for solving the TSP. Section 3 contains the results from a study of the expected output for TSPs from current quantum annealing computers. The output is envisioned to be all optimal tours, since these are obtained on a quantum annealing simulator. We have classified this output for 6, 8 and 10-city TSPs which is the estimated size that can be solved currently. The last section points to future quantum work for the TS...

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“…In this context, the adiabatic theorem of quantum mechanics [4] has been consolidated as a valuable tool, allowing for QSE protocols designed to a wide range of applications, such as state transfer [5], dynamics of quantum critical phenomena [6], and quantum computation [7][8][9]. Moreover, adiabatic QSE has been experimentally realized through a number of techniques, such as nuclear magnetic resonance (NMR) [10][11][12], superconducting qubits [13], trapped ions [14,15], and optical lattices [16]. On general grounds, adiabatic QSE is obtained through a slowly varying time-dependent Hamiltonian H(t), which drives an instantaneous eigenstate |n(0) of the initial Hamiltonian H(0) to the corresponding instantaneous eigenstate |n(T ad ) of the final Hamiltonian H(T ad ).…”

Section: Introductionmentioning

confidence: 99%

Nonadiabatic quantum state engineering driven by fast quench dynamics

et al. 2014

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There are a number of tasks in quantum information science that exploit non-transitional adiabatic dynamics. Such a dynamics is bounded by the adiabatic theorem, which naturally imposes a speed limit in the evolution of quantum systems. Here, we investigate an approach for quantum state engineering exploiting a shortcut to the adiabatic evolution, which is based on rapid quenches in a continuous-time Hamiltonian evolution. In particular, this procedure is able to provide state preparation faster than the adiabatic brachistochrone. Remarkably, the evolution time in this approach is shown to be ultimately limited by its "thermodynamical cost," provided in terms of the average work rate (average power) of the quench process. We illustrate this result in a scenario that can be experimentally implemented in a nuclear magnetic resonance setup.

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Experimental demonstration of a quantum annealing algorithm for the traveling salesman problem in a nuclear-magnetic-resonance quantum simulator

Cited by 38 publications

References 27 publications

Quantum annealing with capacitive-shunted flux qubits

Quantum annealing with capacitive-shunted flux qubits

Small Traveling Salesman Problems

Nonadiabatic quantum state engineering driven by fast quench dynamics

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