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Digital-Analog Quantum Simulation and Computing: A Perspective on Past and Future Developments

Lucas Lamata

Abstract

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.

Digital-Analog Quantum Simulation and Computing: A Perspective on Past and Future Developments

Abstract

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.

Paper Structure

This paper contains 9 sections, 1 figure.

Table of Contents

  1. Digital-Analog Quantum Technologies
  2. Digital-Analog Quantum Simulations
  3. Digital-Analog Quantum Computing and Machine Learning
  4. Towards Quantum Advantage with the Digital-Analog Quantum Paradigm
  5. Implementations of the Digital-Analog Quantum Paradigm: Current Status
  6. Trapped Ions
  7. Superconducting Circuits
  8. Cold Atoms
  9. Outlook

Figures (1)

  • Figure 1: Scheme of an instance of a basic digital-analog quantum computation. It consists of digital gates, here represented as a single-qubit $R_x$ rotation and a two-qubit Controlled-Z $CZ$ gate, and analog blocks given by time evolutions of the quantum simulator with native interactions, in this particular example provided by the Hamiltonians $\tilde{H}_a^{(1)}$ evolved a time $t_1$, and $\tilde{H}_a^{(2)}$ evolved a time $t_2$. Adapted from Ref. [3].