Designing quantum technologies with a quantum computer

TL;DR

This work addresses the challenge of designing and analyzing solid-state quantum devices based on spin defects by introducing a quantum computer–aided framework that simulates ESR Hamiltonians with zero-field splitting, Zeeman, hyperfine, dipole–dipole, and spin–phonon couplings. It combines Gray encoding, qubit-wise commuting partitioning, and the multi-reference selected Quantum Krylov Fast-Forwarding (sQKFF) algorithm to access long-time dynamics within the constraints of NISQ and early fault-tolerant hardware. Key results show accurate autocorrelation functions, microwave absorption spectra, and the $\ell_1$-norm of coherence for NV$^-$ configurations while achieving 18–30% reductions in gate counts and circuit depth compared to unoptimized approaches; reference-state selection emerges as a primary driver of long-time accuracy. The framework provides a flexible blueprint for using quantum computers to design, compare, and optimize solid-state spin-qubit technologies under realistic conditions, with practical implications for quantum sensing, memories, and processors.

Abstract

Interacting spin systems in solids underpin a wide range of quantum technologies, from quantum sensors and single-photon sources to spin-defect-based quantum registers and processors. We develop a quantum-computer-aided framework for simulating such devices using a general electron spin resonance Hamiltonian incorporating zero-field splitting, the Zeeman effect, hyperfine interactions, dipole-dipole spin-spin terms, and electron-phonon decoherence. Within this model, we combine Gray-encoded qudit-to-qubit mappings, qubit-wise commuting aggregation, and a multi-reference selected quantum Krylov fast-forwarding (sQKFF) hybrid algorithm to access long-time dynamics while remaining compatible with NISQ and early fault-tolerant hardware constraints. Numerical simulations demonstrate the computation of autocorrelation functions up to $\sim100$ ns, together with microwave absorption spectra and the $\ell_1$-norm of coherence, achieving 18-30$\%$ reductions in gate counts and circuit depth for Trotterized time-evolution circuits compared to unoptimized implementations. Using the nitrogen vacancy center in diamond as a testbed, we benchmark the framework against classical simulations and identify the reference-state selection in sQKFF as the primary factor governing accuracy at fixed hardware cost. This methodology provides a flexible blueprint for using quantum computers to design, compare, and optimize solid-state spin-qubit technologies under experimentally realistic conditions.

Figures (6)

• Figure 1: The quantum computer-aided design framework proposed in this work. The process begins by defining a quantum system (a) by specifying spin-defect species, the host material, the presence of nuclear spin species, applied magnetic fields, and the geometry of the spin ensemble (configurations 1, 2, and 3 in Table \ref{['tab:TableParameters']} are examples of such a specification). Next, the system Hamiltonian is constructed, with its parameters obtained either computationally or experimentally, as depicted in (b). With the Hamiltonian defined, the sQKFF algorithm can be executed by specifying the system’s initial state. (c) is divided into two parts: the quantum component, which computes the elements of the $H$ and $S$ matrices via Hadamard tests and performs the optimization step through QWC aggregation; and the classical component, which solves the Schrödinger equation within the Krylov subspace. Finally, as shown in (d), the outputs of (c) enable the estimation of quantum resource requirements and the computation of key system properties such as the system’s autocorrelation function, microwave absorption spectrum, and time-dependent $\ell_1$-norm of coherence of other dynamics-derived properties.
• Figure 2: Layout of the three configurations of $NV^{-}$ centers, represented as yellow and red elements, and $^{14}N$ impurities, represented as purple elements.
• Figure 3: Trotterization error $\varepsilon_{T}$, bounded with the Hamiltonian's 1-norm $\|\hat{H}\|_{1}$, as a function of the number of Trotter steps, shown for different values of $M$: the Krylov subspace order.
• Figure 4: Microwave absorption spectra comparison for Configuration 1. The plot shows the spectrum computed using QuTiP versus spectra calculated using sQKFF, for different numbers of reference states and Trotterization error thresholds. All spectra are normalized by the maximum intensity value of the spectrum computed using QuTiP.
• Figure 5: Time evolution of the absolute value of the difference between the $\ell_{1}$-norm of coherence computed with QuTiP, $C_{\ell_{1}}^{Q}$, and those computed using the sQKFF algorithm, $C_{\ell_{1}}^{Q}$, for Configuration 1 and for different values of Trotterization thresholds and numbers of reference states, $R$.