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 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.
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its digital gate-based counterpart, designing digital-analog circuits that employ optimal quantum resources often requires an exceedingly large classical computational time. In this work we find a suboptimal solution to this exponentially large problem, showing that it can be solved within polynomial computational time. In particular, we provide an exact solution for the problem of expressing arbitrary two-body Hamiltonians as the sum of local unitary transformations of an arbitrary Ising Hamiltonian, with the total number of required terms being at most quadratic in system size. This allows us to design a digital-analog simulation protocol that avoids employing numerical optimization over a large parameter space at the preprocessing stage, minimizing computational resources and allowing for further scaling.
Abstract We introduce a hardware-specific, problem-dependent digital-analog quantum algorithm of a counterdiabatic quantum dynamics tailored for optimization problems. Specifically, we focus on trapped-ion architectures, taking advantage from global Mølmer–Sørensen gates as the analog interactions complemented by digital gates, both of which are available in the state-of-the-art technologies. We show an optimal configuration of analog blocks and digital steps leading to a substantial reduction in circuit depth compared to the purely digital approach. This implies that, using the proposed encoding, we can address larger optimization problem instances, requiring more qubits, while preserving the coherence time of current devices. Furthermore, we study the minimum gate fidelity required by the analog blocks to outperform the purely digital simulation, finding that it is below the best fidelity reported in the literature. To validate the performance of the digital-analog encoding, we tackle the maximum independent set problem, showing that it requires fewer resources compared to the digital case. This hybrid co-design approach paves the way towards quantum advantage for efficient solutions of quantum optimization problems.
Preparing stabilizer-code states with shallow circuits is an important primitive for near-term quantum error correction in superconducting circuits, where logical-state initialization requires four-body stabilizer correlations from native one- and two-body controls. We introduce a digital-analog method for the preparation of surface-code ground-state manifolds. The method exploits a structural property of the adiabatic gauge potential, mapping stabilizer-local counterdiabatic terms to digital-analog blocks on the superconducting layout using fixed-angle two-qubit XY gates, single-qubit rotations, and analog exchange-interaction evolutions. The dressed blocks generate higher-order operators used as the variational ansatz to determine the counterdiabatic terms within the Sels-Polkovnikov adiabatic-gauge-potential framework. We benchmark checkerboard plaquette-stabilizer grids up to 4 x 4; the square-grid instances correspond to rotated surface codes, while the rectangular cases probe the scaling of the method. For all grids, the proposed method generates the dominant four-body counterdiabatic basis and, at short evolution times, substantially improves ground-state preparation compared with bare adiabatic evolution. We further generalize the construction to n x m stabilizer lattices and show that digital-analog synthesis can reduce the entangling depth by an order of magnitude. Together, these results establish a direct connection between stabilizer geometry, the structure of the counterdiabatic gauge potential, and digital-analog control for measurement-free preparation of stabilizer-code states on near-term superconducting architectures.
Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.
While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms.
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.