Quantum Gates via Dynamical Decoupling of Central Qubit on IBMQ and 15NV Center in Diamond

TL;DR

This work presents a hardware-agnostic protocol for realizing fast, high-fidelity gates by dynamical decoupling a central qubit that interacts with one or more target qubits. It develops a minimal, general model and validates it on the IBMQ digital quantum simulator, then extends to a realistic $^{15}$NV center in diamond to demonstrate hardware-relevant gate performance and a potential nuclear-spin polarization technique. The DD-gate shows near-unity fidelity for a single target and substantial speedups relative to direct control, while multi-target gates reveal challenges from time-dependent dynamics and Trotterization on current quantum hardware. The study provides open-source tools and a framework to simulate time-dependent qubit dynamics on NISQ-era processors, with implications for scalable quantum control and diamond-based quantum technologies.

Abstract

We demonstrate a hardware-agnostic protocol for realizing fast, high-fidelity gates through dynamical decoupling (DD) pulse sequences applied to a central qubit coupled to target qubits. The target qubits are controlled by leveraging their intrinsic interaction with the central qubit, eliminating the need for slow, error-prone direct control. We develop and implement the DD-gate protocol within two distinct frameworks: a general model with minimal assumptions, benchmarked on a gate-based digital quantum simulator given by the IBMQ; and an experimentally realistic case with a nitrogen-15 vacancy center ($^{15}$NV) in diamond. Using IBMQ, we are able to elucidate the underlying quantum dynamics of the DD-gates and test them, independently of experimental constraints. For $^{15}$NV, we realize the protocol considering system-specific properties, which could represent a significant reduction in gate duration and improved technological scalability compared with current dynamical-decoupling-based control. We also propose a simple application for high-efficiency polarization of the $^{15}$N nuclear spin that could potentially be less technically demanding than current methods. Altogether, this work provides a robust strategy for quantum control that can be implemented in arbitrary systems fitting the central-target qubit architecture. Beyond these results, our open-source simulations and implementations for both platforms provide a practical framework for simulating time-dependent qubit dynamics on NISQ-era gate-based quantum processors.

Figures (10)

• Figure 1: (a) The $^{15}$NV center in the diamond lattice consists of an electron spin $S$ (control qubit) and the $^{15}$N nuclear spin $I$ (target qubit). These are surrounded by a $^{13}$C nuclear spin bath. The IBMQ is employed as a digital quantum simulator to emulate these dynamics, without complex bath interactions and other experimental constraints. (b) CPMG dynamical decoupling sequence. By changing the separation $\tau$ between consecutive $\pi_x$ pulses applied on the control qubit, the sequence filters out signals which are not in resonance with the frequency $\omega=1/(2\tau)$ and its odd multiples. In this way, the target-qubit expectation value $\langle \hat{I} \rangle(t)$ averages to zero in the laboratory frame, but adds constructively in the control qubit's reference frame. (c) Demonstrated and simulated time evolution of the control qubit under a CPMG-10 sequence in IBMQ. The $\langle \hat{S}_z \rangle$ observable shows resonances due to its interaction with the target qubit at odd multiples of $1/(2\omega_{0, 1})$, with pronounced sidebands at larger $\tau$ values.
• Figure 2: (a) CPMG-$N$ sequences applied to the control qubit implemented in IBMQ and simulated with Qiskit. The target qubit observable $\langle \hat{I}_z \rangle$ has a time-evolution opposite to the control qubit $\langle \hat{S}_z \rangle$, with a resonance at $\tau=1/(2\omega_{0, 1})=0.5$ [time]. As the number of pulses $N$ increases, the amplitude of the resonance varies and sidebands become more pronounced. (b) Rabi-like oscillations of the central and target qubits. By taking $\tau=0.5$ [time] fixed and varying $N$, the two observables perform opposite harmonic oscillations, due to opposite phase accumulations at the equator of the Bloch sphere by the end of the DD sequence. This variation of the $\langle \hat{I}_z \rangle$ observable is the basis for the DD-gates.
• Figure 3: (a) Bloch sphere representation of the target qubit under the DD-gate implemented with IBMQ. During the CPMG-$N$ sequences, the subsystem state obtained from a partial trace of the two-qubits occupies points inside the sphere, which does not qualify the gate as a proper rotation. Full density matrices $\hat{\rho}$ at (b)$N=0$, (c)$N=6$ and (d)$N=12$ pulses, demonstrated by quantum state tomography. These points are represented in (a) by the green stars. At $N=0$ the system is well initialized in the $\ket{00}$ state, with small readout errors. In the middle of the gate at $N=6$, the diagonal population term is distributed into off-diagonal terms representing entanglement, which results in mixed states for the single qubits when taking the partial traces of $\hat{\rho}$. At $N=12$, the entanglement terms are reverted back into diagonal terms, resulting in a population inversion for the target qubit with fidelity 0.948, limited by the discretized nature of $N$.
• Figure 4: (a) Central qubit coupled to two target qubits represented with IBMQ. (b) Implemented and simulated CPMG-10 sequence applied to the central qubit coupled with two target qubits. The central qubit observable $\langle \hat{S}_z \rangle$ shows resonances at both of the target qubits resonant $\tau$ values, while each of the target qubits has its own resonance determined by $\tau=1/(2\omega_{0, j})$. (c) DD-mediated gates obtained with $\tau$ fixed to each qubit's resonance, showing a significant signal decay. (d) Implemented tomography of the reduced density matrix of the target qubits, with a partial trace over the control qubit. By applying a CPMG-16($\tau=0.5$) sequence followed by a CPMG-11($\tau=1.0$), both target qubits populations are inverted with a low fidelity of 0.659 with respect to the ideal state $\ket{11}$, while taking a partial trace of the control qubit. This poor performance of the DD-gate protocol with two target qubits suggests a fundamental limitation for a digital gate-based quantum simulator to emulate a time-dependent Hamiltonian.
• Figure 5: (a) XYN spectra of $^{15}$NV for different number of pulses $N$. A small misalignment of $\mathbf{B}_0$ causes the precession of the $^{15}$N nuclear spin to be sensed by the electron spin observable $\langle \hat{S}_z \rangle$, experimentally measured and simulated. Although the experimental measurement of the $\langle \hat{I}_z \rangle$ observable was not possible in this work, its simulations indicate resonances opposite to $\langle \hat{S}_z \rangle$. As $N$ increases, the experimental data starts to deviate from the simulations, due to decoherence and pulse errors ambiguous_resonances. (b) DD-gate with $^{15}$NV. By taking $\tau=0.364$ µ s fixed and varying $N$, we observe Rabi-like oscillations of the two observables. With 24 pulses, a complete inversion of the population is observed, totaling $T_\pi=9.04$ µ s, which can represent a speed-up of nearly 10 times compared to direct excitation of the $^{15}$N nuclear spin.