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arXiv:2402.07653 · Physical Review A

Variational protocols for emulating digital gates using analog control with always-on interactions

Claire Chevallier, Joseph Vovrosh, Julius de Hond, Mario Dagrada, Alexandre Dauphin, Vincent E. Elfving

Published Jun 10, 2024• 4 citations
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Abstract

We design variational pulse sequences tailored for neutral atom quantum simulators and show that we can engineer layers of single-qubit and multiqubit gates. As an application, we discuss how the proposed method can be used to perform refocusing algorithms, swap networks, and ultimately quantum chemistry simulations. While the theoretical protocol we develop still has experimental limitations, it paves the way, with further optimization, for the use of analog quantum processors for variational quantum algorithms, including those not previously considered compatible with analog mode.

DOI
10.1103/physreva.109.062604

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We design variational pulse sequences tailored for neutral atom quantum simulators and show that we can engineer layers of single-qubit and multiqubit gates. As an application, we discuss how the proposed method can be used to perform refocusing algorithms, swap networks, and ultimately quantum chemistry simulations. While the theoretical protocol we develop still has experimental limitations, it paves the way, with further optimization, for the use of analog quantum processors for variational quantum algorithms, including those not previously considered compatible with analog mode.
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We consider a hybrid digital-analog quantum computing approach, which allows implementing any quantum algorithm without standard two-qubit gates. This approach is based on the always-on interaction between qubits, which can provide an alternative to such gates. We show how digital-analog approach can be applied to simulate the dynamics of fermionic systems, in particular, the Fermi-Hubbard model, using fermionic SWAP network and refocusing technique. We concentrate on the effects of connectivity topology, the spread of interaction constants as well as on errors of entangling operations. We find that an optimal connectivity topology of qubits for the digital-analog simulation of fermionic systems of arbitrary dimensionality is a chain for spinless fermions and a ladder for spin 1/2 particles. Such a simple connectivity topology makes digital-analog approach attractive for the simulation of quantum materials and molecules.
We show that optimal control of the electron dynamics is able to prepare molecular ground states, within chemical accuracy, with evolution times approaching the bounds imposed by quantum mechanics. We propose a specific parameterization of the molecular evolution only in terms of interaction already present in the molecular Hamiltonian. Thus, the proposed method solely utilizes quantum simulation routines, retaining their favorable scalings. Due to the intimate relationships between variational quantum algorithms and optimal control, we compare, when possible, our results with state-of-the-art methods in the literature. We found that the number of parameters needed to reach chemical accuracy and algorithmic scaling is in line with compact adaptive strategies to build variational Ansätze. The algorithm, which is also suitable for quantum simulators, is implemented by emulating a digital quantum processor (up to 16 qubits) and tested on different molecules and geometries spanning different degrees of electron correlation.
Harnessing the analog capacity of quantum processors at the algorithmic level is key to solving computationally hard problems. Neutral atoms offer analog capabilities supporting hundreds of qubits, but state-of-the-art adiabatic protocol struggles with nonadiabatic errors, restricting scalability due to finite coherence times. To address this, we propose and experimentally demonstrate a tailored analog counterdiabatic quantum computing (ACQC) protocol to enhance the computational capabilities of neutral atoms by mitigating non-adiabatic transitions and facilitating rapid and high-quality solutions. We apply it to solve the maximum independent set problem with up to 100 qubits, achieving over 3-fold speedup in convergence time and solution quality within a short evolution time of the processor, as compared to adiabatic method. Our method shows scalibility of the application of neutral atom processors establishing ACQC as a promising pathway toward quantum advantage for real-world industrial applications.
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.