Prospects for quantum enhancement with diabatic quantum annealing

Crosson, Elizabeth; Lidar, Daniel A.

doi:10.1038/s42254-021-00313-6

Cited by 85 publications

(49 citation statements)

References 197 publications

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“…When ĤM and ĤP have discrete spectra, the evolution time T is in O(δ −2 ), where δ is the smallest spectral gap of ĤP for all τ [46]. Therefore, implementing this evolution in a scalable way via analog computation can be challenging [47]. While for AQC involving Hamiltonians with continuous spectra the evolution time cannot be bounded in terms of a well-defined spectral gap, results similar to the conventional adiabatic theorem [48] suggest that the evolution in time T deviates from identity by O(1/T ).…”

Section: Adiabatic Ground-state Preparationmentioning

confidence: 99%

Mixed-Integer Programming Using a Bosonic Quantum Computer

Khosravi¹,

Scherer²,

Ronagh³

2021

Preprint

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We propose a scheme for solving mixed-integer programming problems in which the optimization problem is translated to a ground-state preparation problem on a set of bosonic quantum field modes (qumodes). We perform numerical demonstrations by simulating a circuit-based optical quantum computer with each individual qumode prepared in a Gaussian state. We simulate an adiabatic evolution from an initial mixing Hamiltonian, written in terms of the momentum operators of the qumodes, to a final Hamiltonian which is a polynomial of the position and boson number operators. In these demonstrations, we solve a variety of small non-convex optimization problems in integer programming, continuous non-convex optimization, and mixed-integer programming.

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Section: Adiabatic Ground-state Preparationmentioning

confidence: 99%

Mixed-Integer Programming Using a Bosonic Quantum Computer

Khosravi¹,

Scherer²,

Ronagh³

2021

Preprint

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“…In perhaps the most promising technique currently, diabatic quantum annealing (DQA), a diabatic cascade of Landau-Zener transitions [9], is utilized such that the system can be initialized in the ground state and finalized in the ground state via a shortcut through the excited-state spectrum, leading to prospects of quantum-enabled computational speedups [18,19]. Although this technique poses experimental challenges and hardware requirements, there are notable benefits over AQA besides circumventing the small-gap bottleneck, the most attractive being universality and relative simplicity compared to gate-model implementations [20]. There are already known problems that are suitable for large-scale DQA in the transverse-field Ising model, such as particular instances of perturbed Hamming weight oracle problems, where a diabatic cascade can be formed [9].…”

Section: Introductionmentioning

confidence: 99%

“…Suitable anticrossings are required in DQA, and thus for the protocol to be universally applicable a method of guaranteeing they exist for arbitrary problems is required, among other requirements such as a large spectral separation between the first and second excited states. Furthermore, considering that QMC algorithms generally fail due to so-called sign problems, which are intricately related to the notion of nonstoquasticity of the Hamiltonian being sampled [25][26][27], it is believed that using DQA on problems of a nonstoquastic nature could lead to demonstrable quantum-enabled speedups [20]. Furthermore, it has recently been argued that nonstoquasticity is an essential requirement of an annealing Hamiltonian for demonstrating such speedups [24].…”

Section: Introductionmentioning

confidence: 99%

“…As of yet, there is little work on the experimental implementation of hardware that provides nonstoquastic terms [28], and further the hardware required to implement tuneable nonstoquastic two-local interaction terms [29] is currently under development and is not expected to be available for some time. As such, little is known about how a quantum annealing processor will perform with a diabatic protocol, and it is expected that the environment will play a greater role in determining the feasibility of the method [20].…”

Section: Introductionmentioning

confidence: 99%

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Locally suppressed transverse-field protocol for diabatic quantum annealing

et al. 2021

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Diabatic quantum annealing (DQA) is an alternative algorithm to adiabatic quantum annealing that can be used to circumvent the exponential slowdown caused by small minima in the annealing energy spectrum. We present the locally suppressed transverse-field (LSTF) protocol, a heuristic method for making stoquastic optimization problems compatible with DQA. We show that, provided an optimization problem intrinsically has magnetic frustration due to inhomogeneous local fields, a target qubit in the problem can always be manipulated to create a double minimum in the energy gap between the ground and first excited states during the evolution of the algorithm. Such a double energy minimum can be exploited to induce diabatic transitions to the first excited state and back to the ground state. In addition to its relevance to classical and quantum algorithmic speedups, the LSTF protocol enables DQA proof-of-principle and physics experiments to be performed on existing hardware, provided independent controls exist for the transverse qubit magnetization fields. We discuss the implications on the coherence requirements of the quantum annealing hardware when using the LSTF protocol, considering specifically the cases of relaxation and dephasing. We show that the relaxation rate of a large system can be made to depend only on the target qubit, presenting opportunities for the characterization of the decohering environment in a quantum annealing processor.

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“…Quantum annealing is a quantum metaheuristic originally conceived as a method to obtain the global solution of an optimization problem by using quantum fluctuations to escape from local minima [1][2][3] (see Refs. [4][5][6][7][8] for reviews).…”

Section: Introductionmentioning

confidence: 99%

Breakdown of the weak coupling limit in quantum annealing

Bando,

Yip,

Chen

et al. 2021

Preprint

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Reverse annealing is a variant of quantum annealing, in which the system is prepared in a classical state, reverse-annealed to an inversion point, and then forward-annealed. We report on reverse annealing experiments using the D-Wave 2000Q device, with a focus on the p = 2 p-spin problem, which undergoes a second order quantum phase transition with a gap that closes polynomially in the number of spins. We concentrate on the total and partial success probabilities, the latter being the probabilities of finding each of two degenerate ground states of all spins up or all spins down, the former being their sum. The empirical partial success probabilities exhibit a strong asymmetry between the two degenerate ground states, depending on the initial state of the reverse anneal. To explain these results, we perform open-system simulations using master equations in the limits of weak and strong coupling to the bath. The former, known as the adiabatic master equation (AME), with decoherence in the instantaneous energy eigenbasis, predicts perfect symmetry between the two degenerate ground states, thus failing to agree with the experiment. In contrast, the latter, known as the polaron transformed Redfield equation (PTRE), is in close agreement with experiment. The same is true for a purely classical model known as spin-vector Monte Carlo with transverse-fielddependent updates (SVMC-TF). Thus our results present a strong challenge to the sufficiency of the weak system-bath coupling limit in describing the dynamics of current experimental quantum annealers, at least for annealing on timescales of a µsec or longer.

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Prospects for quantum enhancement with diabatic quantum annealing

Cited by 85 publications

References 197 publications

Mixed-Integer Programming Using a Bosonic Quantum Computer

Mixed-Integer Programming Using a Bosonic Quantum Computer

Locally suppressed transverse-field protocol for diabatic quantum annealing

Breakdown of the weak coupling limit in quantum annealing

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