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arXiv:2401.15303 · Physical Review Research

Feedback-based quantum algorithm inspired by counterdiabatic driving

Rajesh K. Malla, Hiroki Sukeno, Hongye Yu, Tzu-Chieh Wei, Andreas Weichselbaum, Robert Konik

Published Oct 25, 2024• 14 citations
arXivHTMLPDF

Abstract

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043068

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In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems. Published by the American Physical Society 2024
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We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground-state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization. Published by the American Physical Society 2024
Abstract We introduce a quantum algorithm that integrates counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to address combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces dependence on extensive higher-order CD terms and on classical optimization techniques, making it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum devices.
Abstract Counterdiabatic driving can suppress diabatic losses during adiabatic ground state preparation. As its implementation necessitates the generation of an adiabatic gauge potential, which requires knowledge of the spectral gap of instantaneous Hamiltonians and involves highly non-local controls in many-body systems, local counterdiabatic driving with approximate adiabatic gauge potential has been widely adopted. In this work, using transverse-field Ising model as an example, we present an in-depth study of the performance of local counterdiabatic protocols and provide a closed-form analysis of ground-state-fidelity optimization. We then propose a two-stage protocol based on local counterdiabatic and simple local single-body control to further improve the performance. The practical implementation of these protocols does not require diagonalization of instantaneous Hamiltonians or spectral gaps, and only additional local single-body driving is involved. To benchmark their performance, we experimentally implement digitized adiabatic quantum evolution in a trapped-ion system. We characterize the quality of the prepared states and explore the scaling behavior with system size up to 14 qubits. Our demonstration of quantum shortcut to adiabaticity opens a path towards preparing ground states of complex systems with accessible local controls.
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 propose a quantum-inspired classical algorithm for combinatorial optimization problems, named the counterdiabaticity-assisted classical algorithm for optimization (CACAO). In this algorithm, a solution of a given combinatorial optimization problem is heuristically searched with classical spin dynamics based on quantum Lyapunov control of local counterdiabatic driving. We compare the performance of CACAO with that of quantum time-evolution algorithms, i.e., quantum annealing, the feedback-based algorithm for quantum optimization (known as FALQON), and the counterdiabatic feedback-based quantum algorithm (known as CD-FQA). We also study the performance of CACAO applied to large systems up to 10000 spins.