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Digital-Analog Quantum Simulation of Spin Systems in Trapped Ions

Iñigo Arrazola Maiztegui

Published Oct 2, 2015• 0 citations
OpenAlex

Abstract

We propose a method to simulate spin models in trapped ions, using digital-analog techniques. With a suitable multiqubit gate decomposition in terms of analog blocks and digital steps, we show that the dynamics of the spin-1/2 Heisenberg chain can be implemented in a linear ion array. This digital-analog proposal involves substantially less number of gates than a fully digital approach, making it a good candidate for experimental implementations. Our work may be adapted to different quantum platforms.

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We propose a method to simulate spin models in trapped ions, using digital-analog techniques. With a suitable multiqubit gate decomposition in terms of analog blocks and digital steps, we show that the dynamics of the spin-1/2 Heisenberg chain can be implemented in a linear ion array. This digital-analog proposal involves substantially less number of gates than a fully digital approach, making it a good candidate for experimental implementations. Our work may be adapted to different quantum platforms.
We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation in trapped-ion technologies.
Universal digital quantum computers are able to approximate any Hamiltonian evolution as a digital quantum circuit consisting of discrete time steps. Strongly interacting physics models, for example in high-energy physics or materials science, make this a challenging task for near-term devices as they place a high demand on the quantum resources required [1]. One alternative is analog quantum simulation where the native evolution of a quantum system can be tailored to mimic that of the model of interest. While more efficient at specific problems, there are limits on the types of evolution available and on the observables that can be measured. In this conference paper we present first results towards unifying these two concepts in a trapped-ion experiment. Trapped atomic ions are one of the most advanced experimental platforms for both analog quantum simulation and digital quantum computing. Typically, the internal spin degrees of freedom are used qubits or for the simulation of spin models. The harmonic oscillator modes given by the motion of the ions in the trap are only employed transiently to create quantum gates or spin-spin interactions. However, these motional modes constitute a large Hilbert space themselves and present a bosonic degree of freedom, which is costly to model with qubits. Many systems of interest, for example Lattice gauge theories, require both spin and boson degrees of freedom. It was recently shown that they can be encoded more efficiently using the harmonic oscillator modes directly [2].
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up ways for simulating complex dynamics of, e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.
We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.