Quantum algorithms to detect ODMR-active defects for quantum sensing applications

TL;DR

This work introduces two quantum algorithms to identify ODMR-active spin defects by detecting imbalances between axial and non-axial ISC rates, avoiding costly direct ISC-rate calculations via SOC. The evolution-proxy method uses short-time SOC-driven proxies, while the spectroscopy-based approach leverages SOC-induced changes in emission spectra, with an improved optical-response scheme built on QDET and Trotter-based time evolution. Applied to the VB$^-$ defect in hBN, the methods are validated against classical results and enable resource estimates showing feasibility on near-term fault-tolerant hardware, with hundreds of qubits and Toffoli counts around 10^8–10^13 depending on the algorithm and active-space size. Collectively, these quantum-simulation strategies offer a scalable path to screen defects for ODMR activity and accelerate the design of quantum sensors.

Abstract

Spin defects in two-dimensional materials are a promising platform for quantum sensing. Simulating the defect's optical response and optically detected magnetic resonance (ODMR) contrast is key to identifying suitable candidates. However, existing simulation methods are typically unable to supply the required accuracy. Here, we propose two quantum algorithms to detect an imbalance in the triplet-to-singlet intersystem crossing (ISC) rates between excited states with the same and different spin projections -- a necessary condition for nonzero ODMR response. The lowest-cost approach evaluates whether the evolution of an $S=0$ state under the spin-orbit coupling induces ISC to $S=1$, and also whether there is an imbalance in its intensity depending on the final state spin projection. The second approach works by comparing the emission spectrum of a spin defect with and without the spin-orbit coupling operator, inferring ISC intensity for different spin transition channels from spectrum intensity changes. Additionally, we present an improved scheme to evaluate the defect's optical response, building upon previous work. We study these quantum algorithms in the context of the negatively charged boron vacancy in hexagonal boron nitride. We generate an embedded active space of 18 spatial orbitals using quantum defect embedding theory (QDET) and show that the ISC rate imbalance can be detected with as few as 105 logical qubits and $4.41 \times 10^8$ Toffoli gates. By avoiding direct and costly rate calculations, our methods enable faster screening of candidate defects for ODMR activity, advancing the prospect of using quantum simulations to aid the development of high-performing sensing devices.

Figures (17)

• Figure 1: Schematic representation of the workflow used to identify ODMR-active defects. (a) A laser pumps optical excitations in the defect while a microwave field induces transitions between the spin sublevels with $M=0$ and $M=\pm 1$. (b) A schematic representation of the observed ODMR contrast measured experimentally, where the dashed and solid curves correspond to different applied magnetic field strengths (see \ref{['eq:odmr_contrast']} for the definition of this quantity) (c) The defect's low-lying energy spectrum, coming from a QDET effective Hamiltonian, showing both radiative transitions and ISC transitions mediated by SOC, with non-axial ($k^{\text{ISC},\perp}$) and axial ($k^{\text{ISC},z}$) rates highlighted. (d) The spectroscopy-based algorithm detects ODMR activity by detecting drops in spectral intensity indicative of nonzero ISC rates, then comparing the deduced ISC rates between spin-preserving and spin-flipping channels and inferring ODMR activity from an imbalance. (e) The evolution-proxy algorithm computes ISC rate proxies by time evolving under the SOC operator for the different spin channels, and compares the relative strengths of those proxies to deduce an ISC rate imbalance and thus ODMR-activity.
• Figure 2: Sketch of the lowest-lying energy spectrum of a quantum defect with a triplet ground state with spin quantum numbers $S, M$. The spin-conserving emission rate, and the axial and non-axial intersystem crossing rates are respectively denoted by $k^r$, $k^{\text{ISC},z}$ and $k^{\text{ISC},\perp}$. Rabi frequency of the microwave radiation inducing magnetic transitions between the spin sublevels of the excited states is denoted by $\omega_\text{MW}$.
• Figure 3: Transitions between spin subspaces enabled by the spin tensor components of the full $H_\text{SOC}$ operator. The definitions of $H_\text{SOC}^{S,M}$ are indicated in \ref{['eq:h_soc_decomp']}. We depict $S=1, M=\pm 1$ together despite them being different spin sectors, because no spin tensor from those depicted allows $M$ to change by more than $\pm 1$, so there are no transitions between them.
• Figure 4: Quantum signal processing polynomial approximating a Heaviside function, syntesized with pyqspmrtc_unification_21cdghs_finding_qsp_angles_20haah_decomposition_19gslw_qsvt_19dmwl_efficient_phases_21. The Heaviside function can be used to probabilistically project an ancilla to $\ket{0}$ or $\ket{1}$ depending on the sign of the energy of the eigenstate.
• Figure 5: Assume $\bm{D}\ket{E_0}$ has support over $[E_0, E_{\max}]$, and we are interested in projecting into an energy window $[E_0, E']$. We can pad the smaller segment to make them of equal size. Then, we can project both energy ranges to 0 and 1, so that a single qubit suffices to identify whether the state belongs to the desired energy window or is outside of it.