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arXiv:2401.10622

Digital-Analog Quantum Computing and Algorithms

Martin, Ana

Published Jan 19, 2024• 0 citations
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Abstract

This Thesis delves into the development and implementation of quantum algorithms using the digital-analog quantum computing (DAQC) paradigm. It provides a comparative analysis of the performance of DAQC versus traditional digital approaches, particularly in the presence of noise sources from current noisy intermediate-scale quantum (NISQ) devices. The DAQC paradigm combines the strengths of digital and analog quantum computing, offering greater efficiency and precision for implementing quantum algorithms on real hardware. The Thesis focuses on the comparison of four relevant quantum algorithms using digital and digital-analog approaches, and the results show significant advantages in favor of the latter. Furthermore, the Thesis investigates the cross-resonance effect to achieve efficient and high-precision Hamiltonian simulations. The findings indicate that the digital-analog paradigm is promising for practical quantum computing applications. Its ability to deliver greater efficiency and accuracy in implementing quantum algorithms on real hardware is a significant advantage over traditional digital approaches.

DOI
10.48550/arxiv.2401.10622

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This Thesis delves into the development and implementation of quantum algorithms using the digital-analog quantum computing (DAQC) paradigm. It provides a comparative analysis of the performance of DAQC versus traditional digital approaches, particularly in the presence of noise sources from current noisy intermediate-scale quantum (NISQ) devices. The DAQC paradigm combines the strengths of digital and analog quantum computing, offering greater efficiency and precision for implementing quantum algorithms on real hardware. The Thesis focuses on the comparison of four relevant quantum algorithms using digital and digital-analog approaches, and the results show significant advantages in favor of the latter. Furthermore, the Thesis investigates the cross-resonance effect to achieve efficient and high-precision Hamiltonian simulations. The findings indicate that the digital-analog paradigm is promising for practical quantum computing applications. Its ability to deliver greater efficiency and accuracy in implementing quantum algorithms on real hardware is a significant advantage over traditional digital approaches.
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.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that outperforms digital quantum computation by combining the flexibility of single-qubit gates with the robustness of analog simulations. This work explores the impact of noise on both digital and DAQC paradigms and demonstrates DAQC’s effectiveness in error mitigation. We compare the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single and two-qubit noise sources in superconducting processors. DAQC consistently surpasses digital approaches in fidelity, particularly as processor size increases. Moreover, zero-noise extrapolation further enhances DAQC by mitigating decoherence and intrinsic errors, achieving fidelities above 0.95 for 8 qubits, and reducing computation errors to the order of 10 −3 . These results establish DAQC as a viable alternative for quantum computing in the NISQ era.
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.
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.
The authors introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. The paper shows that, under sensible assumptions about noise sources, the fidelity of the quantum Fourier transformation improves considerably with this approach when compared against digital quantum computing. This suggests that hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach quantum advantage in the Noisy Intermediate-Scale Quantum era.
Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.