The Quantum Approximate Optimisation Algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the post-supremacy, noisy, intermediate scale era of quantum computing. In this work, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the variational quantum approximate optimisation algorithm, due to its inherent resilience against coherent errors, by performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation times. We observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over non-variational counterparts.
The Quantum Approximate Optimisation Algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the post-supremacy, noisy, intermediate scale era of quantum computing. In this work, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the variational quantum approximate optimisation algorithm, due to its inherent resilience against coherent errors, by performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation times. We observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over non-variational counterparts.
The quantum approximate optimization algorithm was proposed as a heuristic method for solving combinatorial optimization problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the postsupremacy, noisy, intermediate-scale era of quantum computing. In this work we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the quantum approximate optimization algorithm due to the algorithm's variational resilience against the coherent errors introduced by the scheme. By performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation time we observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over nonvariational counterparts in the digital-analog scheme.
Quantum simulation and computing traditionally has been based on two main paradigms, namely, digital and analog. In the digital paradigm, usually single and two-qubit gates (where qubit is an acronym for quantum bit) are employed as building blocks for scalable, universal quantum computing, although errors add up fast and error correction will be ultimately needed for scaling up. In the analog paradigm, large analog blocks are normally employed for a unitary dynamics that carries out the computation, enabling quantum operations on many qubits with reduced errors, but with the drawback of a limited choice of evolutions and lack of universality. In the past decade, a new paradigm has emerged, showing interesting possibilities for quantum simulation and computing in the near and mid term. This is the paradigm of digital-analog quantum technologies, which proposes to combine the best of both paradigms: large analog blocks, provided by native interactions of the employed quantum platform, enabling scalability, combined with digital gates, allowing for more versatility and, ultimately, universality. In this Perspective, I give an overview of the evolution of the field along the past decade, and an outlook for its future possibilities.
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the noisy intermediate-scale quantum era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.
Optimisation plays a central role in a wide range of scientific and industrial applications, and quantum computing has been widely proposed as a means to achieve computational advantages in this domain. To date, research into the design of noise-resilient quantum algorithms has been dominated by variational approaches, while alternatives remain relatively unexplored. In this work, we introduce a novel class of quantum optimisation heuristics that forgo this variational framework in favour of a hybrid quantum-classical approach built upon Markov Chain Monte Carlo (MCMC) techniques. We introduce Quantum-enhanced Simulated Annealing (QeSA) and Quantum-enhanced Parallel Tempering (QePT), before validating these heuristics on hard Sherrington-Kirkpatrick instances and demonstrate their superior scaling over classical benchmarks. These algorithms are expected to exhibit inherent robustness to noise and support parallel execution across both quantum and classical resources with only classical communication required. As such, they offer a scalable and potentially competitive route toward solving large-scale optimisation problems with near-term quantum devices.
Abstract Quantum computing uses quantum resources provided by the underlying quantum nature of matter to enhance classical computation. However, the current Noisy Intermediate-Scale Quantum (NISQ) era in quantum computing is characterized by the use of quantum processors comprising from a few tens to, at most, a few hundreds of physical qubits without implementing quantum error correction techniques. This limits the scalability in the implementation of quantum algorithms. Digital-analog quantum computing (DAQC) has been proposed as a more resilient alternative quantum computing paradigm to outperform digital quantum computation within the NISQ era framework. It arises from adding the flexibility provided by fast single-qubit gates to the robustness of analog quantum simulations. Here, we perform a careful comparison between the digital and digital-analog paradigms under the presence of noise sources. The comparison is illustrated by comparing the performance of the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single- and two-qubit noise sources. Indeed, we obtain that when the different noise channels usually present in superconducting quantum processors are considered, the fidelity of these algorithms for the digital-analog paradigm outperforms the one obtained for the digital approach. Additionally, this difference grows when the size of the processor scales up, making DAQC a sensible alternative paradigm in the NISQ era. Finally, we show how to adaptthe DAQC paradigm to quantum error mitigation techniques for canceling different noise sources, including the bang error.
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.