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arXiv:2512.11619 · Physical Review Research

Tight bound for the total time in digital-analog quantum computation

Mikel Garcia-de-Andoin, Mikel Sanz

quant-phSubmitted Dec 12, 2025• Announced Dec 15, 2025• 0 citations
v1 · Dec 12, 2025v2 · Jun 26, 2026
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Abstract

Digital-analog quantum computing (DAQC) is a universal computational paradigm that combines the evolution under an entangling Hamiltonian with the application of single-qubit gates. Since any unitary operation can be decomposed into a sequence of evolutions generated by two-body Hamiltonians, DAQC is inherently well-suited for realizing such operations. Suboptimal upper bounds for the total time required to perform these evolutions have been previously proposed. Here, we improve these limits by providing a tight bound for this crucial parameter, which shows a linear dependence with the number of couplings. This result enables a precise estimation of the time resources needed for quantum simulations and quantum algorithms implemented within the DAQC framework, facilitating a rigorous comparison with other approaches.

Journal reference
Phys. Rev. Research 8, L022035 (2026)
DOI
10.1103/pkz9-vjkh
Comments
7 pages, 3 figures

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Digital-analog quantum computing (DAQC) is a universal computational paradigm that combines the evolution under an entangling Hamiltonian with the application of single-qubit gates. Since any unitary operation can be decomposed into a sequence of evolutions generated by two-body Hamiltonians, DAQC is inherently well-suited for realizing such operations. Suboptimal upper bounds for the total time required to perform these evolutions have been previously proposed. Here, we improve these limits by providing a tight bound for this crucial parameter, which shows a linear dependence with the number of couplings. This result enables a precise estimation of the time resources needed for quantum simulations and quantum algorithms implemented within the DAQC framework, facilitating a rigorous comparison with other approaches.
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.
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 MMM-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.
Abstract Digital–analog quantum computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation (DQC). DAQC generates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of errors in DAQC implementing Ising Hamiltonians used for arbitrary computations, which was missing from the previous literature, revealing that, overall, DAQC errors scale less favorably compared to those in DQC. As demonstrated, for an all-to-all connectivity, the leading error source for DAQC scales like Θ ( N 4 ) , while for the digital case, it scales like O ( N 2 ) for implementing an arbitrary Hamiltonian evolution. We further illustrate this result with our own simulations of the Quantum Fourier Transform, which in the previous literature were based on unrealistic parameter choices, biasing the result in favor of DAQC, and were limited to system sizes of up to only seven qubits. On the other hand, we develop a specific DAQC protocol for a star connectivity, which shows an advantage for the particular case of a GHZ state generation protocol.
Digital-Analog Quantum Computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation. DAQC creates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of DAQC by extending its implementation to arbitrary connectivities and by performing the first systematic study of its scaling properties. We specify the analysis for three examples of quantum algorithms, showing that except for a few specific cases, DAQC is in fact disadvantageous with respect to the digital case.
Digital-analog quantum computing (DAQC) combines digital gates with analog operations, offering an alternative paradigm for universal quantum computation. This approach leverages the higher fidelities of analog operations and the flexibility of local single-qubit gates. In this paper, we propose a quantum genetic algorithm within the DAQC framework using a Rydberg-atom emulator. The algorithm employs single-qubit operations in the digital domain and a global driving interaction based on the Rydberg Hamiltonian in the analog domain. We evaluate the algorithm performance by estimating the ground-state energy of Hamiltonians, with a focus on molecules such as H2,LiH{\mathrm{H}}_{2}, \mathrm{LiH}H2​,LiH, and BeH2{\mathrm{BeH}}_{2}BeH2​. Our results show energy estimations with less than 1% error and state overlaps nearing 1, with computation times ranging from a few minutes for H2{\mathrm{H}}_{2}H2​ (two-qubit circuits) to one to two days for LiH\mathrm{LiH}LiH and BeH2{\mathrm{BeH}}_{2}BeH2​ (six-qubit circuits). The gate fidelities of global analog operations further underscore DAQC as a promising quantum computing strategy in the noisy intermediate-scale quantum era.
Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. Here, we design a new scheme which employs an arbitrary two-body source Hamiltonian, extending the experimental applicability of this computational paradigm to most quantum platforms. We show that the simulation of an arbitrary two-body target Hamiltonian of nnn qubits requires O(n2)\mathcal{O}({n}^{2})O(n2) analog blocks with guaranteed positive times, providing a polynomial advantage compared to the previous scheme. Additionally, we propose a classical strategy which combines a Bayesian optimization with a gradient descent method, improving the performance by $\ensuremath{\sim}55%$ for small systems measured in the Frobenius norm.