[Paper Review] Gate Optimization via Efficient Two-Qubit Benchmarking for NV Centers in Diamond

Alessandro Marcomini, Philipp J. Vetter+4 more|arXiv (Cornell University)|Mar 9, 2026

Diamond and Carbon-based Materials Research0 citations

TL;DR

The paper develops an efficient closed-loop benchmarking protocol to optimize a two-qubit gate in NV centers by preparing only two states and performing four measurements, reducing tomography overhead by orders of magnitude, and demonstrates this with NV–13C spins.

ABSTRACT

High-fidelity gate implementation requires sophisticated control pulses that steer the quantum system to undergo the desired transformation. Quantum Optimal Control allows to derive these control pulses in an open-loop fashion based on numerical simulations. However, their precision can be limited by incomplete knowledge of the system. Closed-loop optimization overcomes this limitation by incorporating feedback from measurements, provided a suitable and efficient measure of the gate performance can be defined. In this article, we present an efficient method to evaluate the performance of a two-qubit gate by preparation and measurement of only two quantum states, enabling experimental closed-loop optimization with a metric previously believed to be limited to open-loop control. We tailor the approach to nitrogen-vacancy centers in diamond and, through numerical simulations, demonstrate how the method can optimize a two-qubit gate while reducing the number of required measurements by two orders of magnitude compared to standard process tomography under realistic experimental settings.

Motivation & Objective

• Motivate high-fidelity gate control for fragile quantum systems via closed-loop optimization.
• Develop a minimal-state benchmarking protocol to evaluate two-qubit gate performance.
• Tailor the benchmarking method to NV centers coupled to a 13C nuclear spin.
• Show, through simulations, how closed-loop calibration handles parameter uncertainty.
• Quantify gains in measurement efficiency compared to standard process tomography.

Proposed method

• Use a CnNOTe-style two-qubit gate target implemented via microwave control on the NV electron spin.
• Adopt the dressed Chopped RAndom Basis (dCRAB) quantum optimal control framework in open- and closed-loop modes.
• Define a gate performance metric F_J based on three probe states to avoid full process tomography.
• Show how averaging over phase-tuned preparations of a mixed-state rho_1 enables efficient F_J evaluation.
• Parametrize the microwave control with an envelope g(t) and a dCRAB expansion f(t) and optimize using Nelder-Mead within QuOCS.]
• Model a realistic NV–13C system with H_d and H_hf under secular approximation and include experimental constraints on drive amplitudes.

Figure 1: System level scheme . An NV center in the diamond lattice is coupled to a nearby 13 C spin, with the magnetic field aligned along the defect’s symmetry axis (structure in the inset). The two Zeeman levels $m_{s}=0$ and $m_{s}=-1$ on the electron and the two nuclear spin states $m_{I}=1/2$

Experimental results

Research questions

• RQ1 Can a two-state preparation and four-measurement protocol reliably benchmark and optimize a two-qubit gate in NV centers?
• RQ2 How much measurement overhead can be reduced relative to standard process tomography while preserving gate fidelity optimization?
• RQ3 Does closed-loop calibration using the proposed F_J metric reliably adapt open-loop-optimized pulses to parameter-uncertain, realistic NV–13C systems?
• RQ4 What are the practical SPAM considerations and readout strategies to extract F_J in NV-based two-qubit gates?

Key findings

• An efficient benchmarking protocol based on two prepared states and four measurements enables experimental closed-loop optimization of a two-qubit gate.
• Open-loop optimization achieved a gate fidelity F_sm of 99.97% for the target gate.
• State preparation for the rho_1 probe achieves a diagonal-entries fidelity of 99.9993%.
• State preparation for rho_2 achieves a fidelity of 99.93% with the ideal rho_2.
• Readout strategies yield a high-contrast measurement (C = 99.96%) for the diagonal components relevant to the F_J evaluation.
• Closed-loop adaptation across twenty sample NV–13C systems improves performance relative to the open-loop solution, illustrating robustness to parameter uncertainty.

Figure 2: Full pulse sequences for (a) state preparation and (b) optical readout. We illustrate the full pulse sequences to experimentally compute ${F}_{\text{J}}$ . Green pulses represent the initialization/readout action induced by a laser, while blue pulses are required to prepare correctly the p