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arXiv:2001.09844 · Japanese Journal of Applied Physics

Quantum annealing with capacitive-shunted flux qubits

Yuichiro Matsuzaki, Hideaki Hakoshima, Yuya Seki, Shiro Kawabata

Published Nov 26, 2019• 14 citations
arXivHTMLPDF

Abstract

Abstract 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 FQs 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.

DOI
10.7567/1347-4065/ab5b30

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Abstract 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 FQs 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.
Abstract Quantum annealers require accurate control and optimized operation schemes to reduce noise levels, in order to eventually demonstrate a computational advantage over classical algorithms. We study a high coherence four-junction capacitively shunted flux qubit (CSFQ), using dispersive measurements to extract system parameters and model the device. Josephson junction asymmetry inherent to the device causes a deleterious nonlinear cross-talk when annealing the qubit. We implement a nonlinear annealing path to correct the asymmetry in situ, resulting in a substantial increase in the probability of the qubit being in the correct state given an applied flux bias. We also confirm the multi-level structure of our CSFQ circuit model by annealing it through small spectral gaps and observing quantum signatures of energy level crossings. Our results demonstrate an anneal-path correction scheme designed and implemented to improve control accuracy for high-coherence and high-control quantum annealers, which leads to an enhancement of success probability in annealing protocols.
Quantum annealing is a method to solve optimization problems that leverages quantum tunneling in a coupled qubit system. We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent quantum annealing applications. We find that for high qubit frequencies, thermal noise in the bias line makes a significant contribution to the relaxation, arising from the design choice to experimentally explore both fast annealing and high-frequency control. The measured dephasing rate is primarily due to intrinsic low-frequency flux noise in the two qubit loops, with additional contribution from the low-frequency noise of control electronics used for fast annealing. Our results characterize decoherence in a realistic setup for quantum annealing and are relevant for ongoing efforts toward building superconducting quantum annealers with increased coherence. Quantum annealers hold promise of outperforming classical computers in solving hard optimization problems, but one main challenge is understanding the role of noise in quantum annealing. Here, the authors characterize the relevant noise sources in a tunable flux qubit, a building block for quantum annealers, and provide a benchmark for future work on highly-coherent quantum annealers.
While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.
We proposed and theoretically investigated the self-shunted superconducting flux qubits (SSFQs) with relatively large Josephson junctions with the diameter over1  μm\text{1}\; \mu \text{m}1μm. Because of the large self-capacitance of several 10 fF in the junctions, the large shunt capacitor with dimensions of several 100$ \mu \text{m}oftheconventionalcapacitivelyshuntedfluxquantumbits(qubits)canbeeliminated,resultinginsignificantreductionofthefootprint.WesystematicallycalculatedtheSSFQperformances,suchastheanharmonicity,andinvestigatedtheirdependencesonthecircuitparameters.Asaresult,itwasshownthattheSSFQshavethelargeanharmonicityof400–2000MHzforthereasonableparameters,suchasthelargejunctionareaofaround1of the conventional capacitively shunted flux quantum bits (qubits) can be eliminated, resulting in significant reduction of the footprint. We systematically calculated the SSFQ performances, such as the anharmonicity, and investigated their dependences on the circuit parameters. As a result, it was shown that the SSFQs have the large anharmonicity of 400–2000 MHz for the reasonable parameters, such as the large junction area of around 1oftheconventionalcapacitivelyshuntedfluxquantumbits(qubits)canbeeliminated,resultinginsignificantreductionofthefootprint.WesystematicallycalculatedtheSSFQperformances,suchastheanharmonicity,andinvestigatedtheirdependencesonthecircuitparameters.Asaresult,itwasshownthattheSSFQshavethelargeanharmonicityof400–2000MHzforthereasonableparameters,suchasthelargejunctionareaofaround1 \mu \text{m}^{2}andthesmallcriticalcurrentdensityofaround10and the small critical current density of around 10andthesmallcriticalcurrentdensityofaround10\text{A/cm}^{2}$. Furthermore, we derived and estimated the relative relaxation time of the SSFQs due to the charge and flux noises. As a result, we found that the high anharmonicity over 800 MHz could be achieved without degrading the relaxation time from that of the high-coherence flux qubits. The SSFQs offer the new choice of the highly scalable qubits, which achieve both the small footprint and high anharmonicity.
Superconducting quantum computers are rapidly reaching scales where bottlenecks to scaling arise from the practical aspects of the fabrication process. To improve quantum computer performance, implementation technology that guarantees the scalability of the number of qubits is essential. Increasing the degrees of freedom in routing by 2.5-dimensional implementation is important for realizing circuit scalability. We report an implementation technology to overcome the scaling bottlenecks using a reliable connection qubit with a demonstration of quantum annealing. The method comprises interconnection based on quantum annealing using a superconducting flux qubit, precise coupling status control, and flip-chip bonding. We perform experiments and simulations with a proof-of-concept demonstration of qubit coupling via interconnection using a flux qubit. The coupling status is strictly controllable by quantum annealing. A low-temperature flip-chip bonding technology is introduced for the 2.5-dimensional interconnection. The superconducting flux qubit, formed across two different chips via bumps, is demonstrated for the first time to show a state transition like that in a conventional qubit. The quantum annealing flux qubit and flip-chip bonding enable new interconnections between qubits. A perspective on the possibility of applying this technology to the connection between gate-type qubits is described.
We report the experimental realization of a 3D capacitively shunt superconducting flux qubit with long coherence times. At the optimal flux bias point, the qubit demonstrates energy relaxation times in the range of 60–90 μs and a Hahn-echo coherence time of about 80 μs, which can be further improved by dynamical decoupling. Qubit energy relaxation can be attributed to quasiparticle tunneling and unwanted two-level-system defects, while qubit dephasing is caused by flux noise away from the optimal point. Our results show that 3D c-shunt flux qubits demonstrate improved performance over other types of flux qubits, which is advantageous for applications such as quantum magnetometry and spin sensing.