Abstract
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated by the systems’ underlying Hamiltonian. Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on one-dimensional (1D) chains and two-dimensional (2D) square lattices, which, in an appropriate reference frame, results in a purely two-local Hamiltonian. By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians. We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, , and Heisenberg spin models. Our dynamics simulations are Trotter error-free for the Ising and models in 1D. We also show that the Trotter errors for 2D and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor. In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations. We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians, which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.
- Received 10 December 2020
- Revised 9 March 2021
- Accepted 7 April 2021
DOI:https://doi.org/10.1103/PRXQuantum.2.020328
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers aim to solve hard problems by leveraging the laws of quantum mechanics for computation. The programming of small-scale noisy devices has followed that of the proposed future large-scale fault-tolerant architectures by defining computation in terms of a minimal universal gate set. Such a gate set is typically partitioned into logical operations affecting single qubits and operations entangling pairs of qubits. However, current hardware imperfections and implementation errors limit the complexity of quantum computations. This begs the question: are there novel logical operations, outside of the universal gate set, which can be efficiently implemented in order to extend the computational power of near-term quantum devices? We answer this question in the affirmative by illustrating how a set of many-qubit entangling operations, which arise naturally in superconducting architectures, can be used to solve important archetypal quantum-simulation problems.
Our work begins by considering the multiqubit generalization of the cross-resonance interaction, which is commonly used to entangle pairs of fixed-frequency superconducting transmon qubits. Employing the same set of approximations used to derive the cross-resonance interaction, we propose a multiqubit generalization, which is applicable for one- and two-dimensional arrays of qubits. This multiqubit interaction is analog in the sense that it is not contained within a universal gate set and is realized at the physical level. Composing our analog interaction with digital single-qubit operations we then derive a broad set of digital-analog sequences useful for the quantum simulation of magnetic models. By analyzing the resulting circuit complexity, we find that our digital-analog sequences outperform their digital counterparts by significantly reducing, and even sometimes fully eliminating, compilation errors.
Our results show that hardware-specific analog interactions, used in conjunction with common digital operations, can significantly extend the computational power of superconducting quantum devices with respect to a broad range of important applications. While answering previous questions, our work leads to new questions regarding the fundamental minimal complexities of quantum computation in the digital-analog paradigm.
