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arXiv:2410.05955

Reducing errors and gate operations in digitized quantum annealing with local counterdiabatic driving

Takuya Hatomura

Published Oct 8, 2024• 0 citations
arXivHTMLPDF

Abstract

Local counterdiabatic driving is a method of improving the performance of adiabatic control and digital implementation of quantum annealing with local counterdiabatic driving has been discussed. In this paper, we propose a decomposition formula which enables us to reduce digitization errors and the number of gate operations in digitized quantum annealing with local counterdiabatic driving.

DOI
10.48550/arxiv.2410.05955

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Local counterdiabatic driving is a method of improving the performance of adiabatic control and digital implementation of quantum annealing with local counterdiabatic driving has been discussed. In this paper, we propose a decomposition formula which enables us to reduce digitization errors and the number of gate operations in digitized quantum annealing with local counterdiabatic driving.
Abstract We study errors caused by digitization of shortcuts to adiabaticity by counterdiabatic driving. We find possibility of error scaling O ( M − 2 ) with the number of time slices M, whereas worse error scaling O ( M − 1 ) is predicted in the conventional theory of the first-order Suzuki-Trotter decomposition. We point out this possibility by considering a state-dependent error bound and confirm emergence of this error scaling O ( M − 2 ) by numerical simulation. Moreover, we numerically show that intermediate error scaling can be observed in digitization of approximate counterdiabatic driving. These results reveal usefulness of digitized counterdiabatic driving from the viewpoints of both cost and performance.
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcuts to adiabaticity aim to retain the adiabatic condition upon speed-up. We outline a new method which combines the two methodologies and takes advantage of the strengths of each. The new technique improves upon approximate local counterdiabatic driving with the addition of time-dependent control fields. We refer to this new method as counterdiabatic optimised local driving (COLD) and we show that it can result in a substantial improvement when applied to annealing protocols, state preparation schemes, entanglement generation and population transfer on a lattice. We also demonstrate a new approach to the optimisation of control fields which does not require access to the wavefunction or the computation of system dynamics. COLD can be enhanced with existing advanced optimal control methods and we explore this using the chopped randomised basis method and gradient ascent pulse engineering.
We present counterdiabatic reverse annealing, a quantum annealing protocol that extends the range of application of reverse annealing to the previously inaccessible short-time domain. This is achieved by exploiting approximate counterdiabatic driving expanded in low-order nested commutators. In this work, we offer a comparative study of the performance of this technique to that of unassisted reverse annealing in terms of metrics such as the ground-state fidelity and the time to solution. We provide a quantitative measure of the energetic cost of counterdiabatic reverse annealing and show that significant improvements are possible even using local counterdiabatic potentials, paving the way toward the experimental implementation in near-term quantum devices.
Local counterdiabatic driving (CD) provides a feasible approach for realizing approximate adiabatic or reversible processes like quantum state preparation using only local controls and without demanding excessively long protocol times. However, in many instances getting high accuracy of such CD protocols requires engineering very complicated new controls or pulse sequences. In this work, we describe a systematic method for altering the adiabatic path by adding extra local controls along which performance of local CD protocols is enhanced, both close to and far from the adiabatic limit. We also identify an iterative procedure to improve the performance of local counterdiabatic driving further without any knowledge of the quantum wave function. We then show that these methods provides dramatic improvement in the preparation of nontrivial Greenberger-Horne-Zeilinger ground states of several different spin systems with both short-range and long-range interactions.
In this paper, the issue of reducing the time-to-solution in adiabatic quantum computation is addressed. The authors apply a variational principle to derive approximations of the counterdiabatic driving operator as a shortcut to adiabaticity. Two different ansatzes are discussed for the ferromagnetic ppp-spin model and its generalizations, including short-range interactions and random couplings. Numerical simulations show good performances, almost independently of the system size, up to hundreds of qubits
Counterdiabatic driving realizes parameter displacement of an energy eigenstate of a given parametrized Hamiltonian using the adiabatic gauge potential. In this paper, we propose a universal method of digitized counterdiabatic driving, constructing the adiabatic gauge potential in a digital way with the idea of universal counterdiabatic driving. This method has three advantages over existing universal counterdiabatic driving and/or digitized counterdiabatic driving: it does not introduce any many-body and/or nonlocal interactions to an original target Hamiltonian; it can incorporate infinite nested commutators, which constitute the adiabatic gauge potential; and it gives explicit expression of rotation angles for digital implementation. We show the consistency of our method to the exact theory in an analytical way and the effectiveness of our method with the aid of numerical simulations.