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arXiv:2410.10622 · npj Quantum Information

High dimensional counterdiabatic quantum computing

Diego Tancara, F. Albarrán-Arriagada

Published Jul 8, 2025• 5 citations
arXivHTMLPDF

Abstract

The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we explore the extension of this paradigm to high-dimensional systems. Specifically, we consider qutrits in the context of quadratic problems, obtaining the qutrit Hamiltonian codifications and the counterdiabatic drivings. Our findings show that qutrits can improve the solution quality up to 90 times compared to the qubit counterpart. We tested our proposal on 1000 random instances of the multiway number partitioning, max 3-cut, and portfolio optimization problems, demonstrating that, in general, without prior knowledge, it is better to use qutrits and, apparently, high-dimensional systems in general instead of qubits. Finally, considering the state-of-the-art quantum platforms, we show the experimental feasibility of our high-dimensional counterdiabatic quantum algorithms at least in a fully digital form. This work paves the way for the efficient codification of optimization problems in high-dimensional spaces and their efficient implementation using counterdiabatic quantum computing.

DOI
10.1038/s41534-025-01070-5

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The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we explore the extension of this paradigm to high-dimensional systems. Specifically, we consider qutrits in the context of quadratic problems, obtaining the qutrit Hamiltonian codifications and the counterdiabatic drivings. Our findings show that qutrits can improve the solution quality up to 90 times compared to the qubit counterpart. We tested our proposal on 1000 random instances of the multiway number partitioning, max 3-cut, and portfolio optimization problems, demonstrating that, in general, without prior knowledge, it is better to use qutrits and, apparently, high-dimensional systems in general instead of qubits. Finally, considering the state-of-the-art quantum platforms, we show the experimental feasibility of our high-dimensional counterdiabatic quantum algorithms at least in a fully digital form. This work paves the way for the efficient codification of optimization problems in high-dimensional spaces and their efficient implementation using counterdiabatic quantum computing.
We propose a faster digital quantum algorithm for portfolio optimization using the digitized counterdiabatic quantum optimization paradigm in the impulse regime, that is, where the counterdiabatic terms are dominant. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We apply this protocol to a real-case scenario of portfolio optimization with 20 assets, using purely quantum and hybrid classical-quantum paradigms. We demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer. By benchmarking our method against the standard quantum approximate optimization algorithm and finite-time digitized adiabatic algorithms, we obtain a significant reduction in the circuit depth by factors of 2.5 to 40, while minimizing the dependence on the classical optimization subroutine. Besides portfolio optimization, the proposed method is applicable to a large class of combinatorial optimization problems.
We introduce a digital-analog quantum computing framework that enables counterdiabatic protocols to be implemented at constant circuit depth, allowing fast and resource-efficient quantum state preparation on current quantum hardware. Counterdiabatic protocols suppress diabatic excitations in finite-time adiabatic evolution, but their practical application is limited by the non-local structure of the required Hamiltonians and the resource overhead of fully digital implementations. Counterdiabatic terms can be expressed as truncated expansions of nested commutators of the adiabatic Hamiltonian and its parametric derivative. Here, we show how this algebraic structure can be efficiently realized in a digital-analog setting using commutator product formulas. Using native multi-qubit analog interactions augmented by local single-qubit rotations, this approach enables higher-order counterdiabatic protocols whose implementation requires a constant number of analog blocks for any fixed truncation order, independent of system size. We demonstrate the method for two-dimensional spin models and analyze the associated approximation errors. These results show that digital-analog quantum computing enables a qualitatively new resource scaling for counterdiabatic protocols and related quantum control primitives, with direct implications for quantum simulation, optimization, and algorithmic state preparation on current quantum devices.
We consider digitized-counterdiabatic quantum computing as an advanced paradigm to approach quantum advantage for industrial applications in the NISQ era. We apply this concept to investigate a discrete mean-variance portfolio optimization problem, showing its usefulness in a key finance application. Our analysis shows a drastic improvement in the success probabilities of the resulting digital quantum algorithm when approximate counterdiabatic techniques are introduced. Along these lines, we discuss the enhanced performance of our methods over variational quantum algorithms like QAOA and DC-QAOA.
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Shortcuts to adiabaticity are well-known methods for controlling the quantum dynamics beyond the adiabatic criteria, where counterdiabatic (CD) driving provides a promising means to speed up quantum many-body systems. In this work, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We study the state evolution of an Ising spin chain using the digitized version of the standard CD driving and its variants derived from the variational approach. We apply this technique in the preparation of Bell and Greenberger-Horne-Zeilinger states with high fidelity using a very shallow quantum circuit. We implement this proposal on the IBM quantum computer, proving its usefulness for the speed up of adiabatic quantum computing in noisy intermediate-scale quantum devices.
Abstract Quantum computing holds the potential for quantum advantage in optimization problems, which requires advances in quantum algorithms and hardware specifications. Adiabatic quantum optimization is conceptually a valid solution that suffers from limited hardware coherence times. In this sense, counterdiabatic quantum protocols provide a shortcut to this process, steering the system along its ground state with fast-changing Hamiltonian. In this work, we take full advantage of a digitized-counterdiabatic quantum optimization algorithm to find an optimal solution of the p -spin model up to four-local interactions. We choose a suitable scheduling function and initial Hamiltonian such that a single-layer quantum circuit suffices to produce a good ground-state overlap. By further optimizing parameters using variational methods, we solve with unit accuracy two-spin, three-spin, and four-spin problems for 100%, 93%, and 83% of instances, respectively. As a particular case of the latter, we also solve factorization problems involving 5, 9, and 12 qubits. Due to the low computational overhead, our compact approach may become a valuable tool towards quantum advantage in the NISQ era.