Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R42: Quantum Annealing: Theory |
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Sponsoring Units: DQI Chair: Maxim Vavilov, University of Wisconsin - Madison Room: BCEC 210A |
Thursday, March 7, 2019 8:00AM - 8:12AM |
R42.00001: Adaptive quantum annealing based on weak measurements to suppress the errors due to Landau-Zener transitions Yongchao Tang, Antonio Martinez, Song Zhang, Juan Atalaya, Birgitta K Whaley, Adrian Lupascu Quantum annealing is undermined by Landau-Zener transitions from the ground to the first excited state around small energy gaps. This kind of error can be suppressed by slowing down quantum annealing near the minimum gap. We study the relationship between the minimum gap and potential observables that can be used to gain information on the minimum gap using weak measurements. The measurement of energy curvature is promising as a measure of the location of the minimum gap. We apply master equations for the quantum annealing monitored by weak measurements to study the impacts of noise. The simulations show that Landau-Zener type errors can be suppressed by making the rate of quantum annealing dependent on monitoring with weak measurements. |
Thursday, March 7, 2019 8:12AM - 8:24AM |
R42.00002: Feedback control of a monitored system evolving adiabatically Ka Wa Yip, Daniel A Lidar Time evolution of a system evolving adiabatically while coupled weakly to a thermal bath can be described by a quantum adiabatic master equation in Lindblad form. In quantum annealing it is desirable is to maintain the state as the ground state of the time-dependent Hamiltonian. This is difficult due to diabatic or thermal transitions. We devised a quantum feedback control method to reverse the effect of thermal excitation. Under specific continuous measurement schemes, quantum trajectories of the measurement records can be obtained and feedbacks conditioned on these records can be applied to increase the ground state population. We derived the feedback master equation for markovian feedback (feedback delay $\tau \rightarrow 0$) and further gave the timescale condition for feedback Markovianity. However, realistic feedbacks are non-markovian and subjected to non-negligible feedback delay, detector efficiency and restrictions of the form of the feedback Hamiltonian. We studied the effectiveness of feedback control under such limitations and explored how the optimized feedback delay time depends on the annealing schedule. |
Thursday, March 7, 2019 8:24AM - 8:36AM |
R42.00003: Many-body quantum systems provide a mechanism for robust and efficient quantum search Kostyantyn Kechedzhi, Vadim Smelyanskiy, Lara Faoro, Sergio Boixo, Hartmut Neven, Lev B Ioffe, Boris Altshuler Searching low energy subspace of a classical spin glass is computationally hard due to ladscape of deep local minima separated by barriers. Applying a transverse field gives rise to tunneling between the quantum states defined within individual spin-glass minima. The number of transitions from a state grows exponentially with the number d of spin flips during the transition. This growth can compensate the decrease of the matrix elements with d leading to a transition from many-body localized to non-ergodic extended phase, where eigenstaes are sparse superpositions of spin configurations corresponding to local minima within a narrow energy belt. We demonstrate a remarkable structure in the low energy eigenspectrum: it is partitioned into the alternating sequence of bands of two qualitatively different types, x- and z-, which retain characteristics of transverse field eigenstates and classical spin glass, respectively. We demonstrate this novel intermittency in a "wide band" impurity model with a bi-modal classical density of states with a delta-peak at zero energy containing most states and the second peak containing an exponentially smaller number of states lying at low energy. This non-ergodic structure of the eignespectrum provides a mechanism for efficient quantum search. |
Thursday, March 7, 2019 8:36AM - 8:48AM |
R42.00004: Control of Phase Transitions in Wajnflasz–Pick model Yuya Seki, Shu Tanaka, Shiro Kawabata We construct a quantum Wajnflasz–Pick model, and investigate a nature of quantum phase transitions of the model. Quantum phase transition phenomena have drawn attention in the field of quantum computing as well as condensed matter physics, since the phenomena are closely related to the performance of quantum annealing (QA) and quantum adiabatic computation (QAC). Adding a driver Hamiltonian that causes spin flip and state transitions within upper and lower states to the Hamiltonian of classical Wajnflasz–Pick model, we construct the quantum model where phase transitions are controllable. Numerical analysis showed that the model undergoes first-order phase transitions whereas a corresponding spin-1/2 model does not undergo first-order phase transitions. In particular, we observed an anomalous phenomenon that the system undergoes first-order phase transitions twice under certain conditions. The results indicate that the performance of QA and QAC can be affected by the choice of the number of upper and lower states and the parameter in the driver Hamiltonian. |
Thursday, March 7, 2019 8:48AM - 9:00AM |
R42.00005: Energy gap scaling of quantum annealing based on Wajnflasz--Pick model Shohei Watabe, Yuya Seki, Shiro Kawabata The conventional quantum annealer, transverse field Ising model, is known to suffer from the energy gap shrinkage for the scalable system, which may not provide the solution of the optimization problem within the realistic time scale. An idea for possibly overcoming this problem proposed by Seki, Tanaka, and Kawabata is to employ the Wajnflasz-Pick model, i.e., a qudit. By analyzing the order of the phase transition within the mean-field approach with the uniform interaction, they have found that the performance of quantum annealing is controlled by the number of upper and lower states of the spin. In this study, in order to confirm their claim, we revisit the energy gap of the finite size Wajnflasz--Pick model with all-to-all random interaction. |
Thursday, March 7, 2019 9:00AM - 9:12AM |
R42.00006: Assessing the Quantum in Quantum Annealing Wade DeGottardi, David Ferguson, Sergey Novikov, Huo Chen, Daniel A Lidar Annealing is a general purpose computational strategy which endeavors to harness fluctuations to solve sampling problems. A drawback of this approach is that it is difficult to program an annealer to sample from a user specified distribution. Quantum annealing (QA) utilizes quantum effects to drive fluctuations and thus can potentially sample from specific distributions with an algorithmic speedup. A crucial element of understanding QA is to clearly delineate fluctuations that arise from quantum effects from those that arise from non-quantum effects such as thermal fluctuations. Our approach to this problem utilizes the theory of quantum distributions on phase space and focuses on the specific non-linear dynamics that arise in Josephson junction circuits. By comparing quantum and classical dynamics, we are able to pinpoint the role that quantum effects play. |
Thursday, March 7, 2019 9:12AM - 9:24AM |
R42.00007: Adiabatic quantum computation with effective Hamiltonians Hayato Goto, Taro Kanao Adiabatic quantum computation (AQC) with Kerr-nonlinear parametric oscillators, or KPOs for short, has been proposed [1-3], which is called bifurcation-based AQC [1]. The Hamiltonian used there is an effective one in a rotating frame and in the rotating-wave approximation. This is a notable difference between this approach and standard AQC using real Hamiltonians. Based on this difference, here we propose a method to improve the performance of bifurcation-based AQC, which is not applicable to standard AQC using real Hamiltonians. |
Thursday, March 7, 2019 9:24AM - 9:36AM |
R42.00008: Parameter setting for quantum annealing Andrea Di Gioacchino, Salvatore Mandra, Eleanor Rieffel Solving a combinatorial optimization problem with the current generation of adiabatic quantum devices, as the D-Wave 2000Q, requires to express the cost function of the optimization problem in the QUBO form, which in many cases includes penalty terms to enforce hard constraints. |
Thursday, March 7, 2019 9:36AM - 9:48AM |
R42.00009: Predicting the behavior of analog quantum annealers with statistical learning Andrey Lokhov, Yaroslav Kharkov, Carleton Coffrin, Marc Vuffray Quantum annealers have a potential to provide a breakthrough in hard optimization and machine learning problems. Emerging physical implementations of quantum annealers are extremely sophisticated from the engineering point of view, and prediction of their performance remains a challenging problem. Here, we uncover the probabilistic relation between input and output of quantum annealers using the novel rigorous statistical learning tools. Extensive analysis of the output data allows us to check whether it satisfies the desired features assumed in the initial design of the device, to learn the machine's global response function, and to detect the echo of the chip architecture. In particular, our tests on D-Wave 2X and 2000Q quantum annealers revealed the presence of multi-body interactions and spurious next-nearest neighbor couplings between qubits as compared to the hardware-implemented topology of the chip. These results show how state-of-the-art statistical learning algorithms can quantify the performance of physical quantum annealers, suggest a path towards mitigating the effects of persistent biases inevitably present in every analog device, and guide the design of new hardware architectures. |
Thursday, March 7, 2019 9:48AM - 10:00AM |
R42.00010: Quantum annealing and thermalization: insights from integrability Fuxiang Li, Nikolai Sinitsyn, Vladimir Y Chernyak We solve a model that has basic features that {are desired for quantum annealing computations: entanglement in the ground state,} controllable annealing speed, ground state energy separated by a gap during the whole evolution, and programmable computational problem that is encoded by parameters of the Ising part of the spin Hamiltonian. Our solution enables exact nonperturbative characterization of final nonadiabatic excitations, including scaling of their number with the annealing rate and the system size. |
Thursday, March 7, 2019 10:00AM - 10:12AM |
R42.00011: The computational complexity of optical quantum annealers and Ising machines Raphael Pooser, Ryan Bennnk Quantum annealers hold promise as optimization platforms for quantum machine learning applications and as layered neural networks. Recently, Optical Ising Machines (OIM) have been presented as a straight forward method to achieve this computational model. Relying on optical nonlinearities inside resonators, these devces are a network of coupled optical parametric oscillators (OPOs), a mature and practical technology in the field of continuous-variable quantum computing (CVQC). Despite the use of a key ingredient of CVQC (the second order nonlinearity which facilitates entanglement), the computational model of OIMs remains an open question. Here, we present a study of three different computational models based on physics of increasing complexity. We outline a fully classical nonlinear system of coupled oscillators, a semiclassical model of OPOs in the truncated Wigner representation, and a fully quantum treatment in the positive P representation. We present benchmarks of each model and outline their relative capability to capture the relevant physics responsible for practical computation in OIMs. Using these benchmarks, based on known quadratic optimization problems, we determine the computational complexity of these devices. |
Thursday, March 7, 2019 10:12AM - 10:24AM |
R42.00012: The power of pausing: advancing understanding of thermalization in experimental quantum annealers Jeffrey Marshall, Davide Venturelli, Itay Hen, Eleanor Rieffel We investigate annealing schedules involving an intermediate pause, on the current generation of quantum annealing hardware: the D-Wave 2000Q. We show that a pause mid-way through the anneal can cause a dramatic change in the output distribution, and we provide evidence suggesting thermalization is occurring during such a pause. We demonstrate that upon pausing the system in a narrow region shortly after the minimum gap, the probability of successfully finding the ground state of the problem Hamiltonian can be increased by several orders of magnitude. We relate this effect to relaxation, after excitations occurring in the region near to the minimum gap. For a set of problems of size 500 qubits we demonstrate that the distribution returned from the annealer very closely matches a classical Boltzmann distribution of the problem Hamiltonian, albeit one with a noticeably higher temperature than that of the device. |
Thursday, March 7, 2019 10:24AM - 10:36AM |
R42.00013: Understanding the Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization Tameem Albash The viability of non-stoquastic catalyst Hamiltonians to deliver consistent quantum speedups in quantum adiabatic optimization remains an open question. Several studies (Crosson et al. (2014), Hormozi et al. (2017)) on random Ising problems have shown that stoquastic catalysts typically outperform non-stoquastic ones. A stark counterexample to this is the exponential speedup of non-stoquastic catalysts over stoquastic ones for infinite-range ferromagnetic p-spin models with p > 3 (Seki & Nishimori (2012)). We provide details on how the non-stoquastic catalyst provides an advantage in these models. We use this insight to then construct a geometrically local 2-body example that exhibits a similar exponential advantage for a non-stoquastic catalyst over a stoquastic one, up to the maximum system size we are able to study. |
Thursday, March 7, 2019 10:36AM - 10:48AM |
R42.00014: Gap-independent cooling and hybrid quantum-classical annealing (HQCA) Lukas S Theis, Peter Schuhmacher, Michael Marthaler, Frank K Wilhelm We present an efficient gap-independent cooling scheme for a quantum annealer that |
Thursday, March 7, 2019 10:48AM - 11:00AM |
R42.00015: Enhancing quantum adiabaticity in adiabatic quantum computers with multiple local minima Lin Tian The adiabatic criterion is a key requirement for the successful implementation of adiabatic quantum computing. However, in interacting many-body systems, the energy gap often decreases quickly with the number of qubits, which results in the violation of the adiabatic criterion and diabatic transition to the excited states. In a recent work [1], we presented an approach to enhance quantum adiabaticity that does not require the spectral knowledge of the adiabatic quantum computers or the construction of unphysical many-body interactions. In this talk, we show that this approach can be applied to adiabatic quantum computers with multiple local minima in the energy separation between the ground and the excited states. We demonstrate this approach with numerical simulation. [1] L. Tian, arXiv:1802.02285. |
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