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Nummerical Optimization of Control of Multiple Carbon Qubits near a Nitrogen-Vacancy Center

Tim Dikland

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

The NV-center in diamond is a promising system for quantum information processing. The typical qubits are the electron spin in the NV-center and the surrounding 13C nuclear spins. Fast and precise control of many 13C spins is desirable but challenging due to crosstalk. Crosstalk is the unwanted effect of a control pulse on the other qubits. The coupled NV-13C system is explored, and numerical techniques to optimize the control of multiple and single qubits are used. In this report the effect of the Bloch-Siegert shift in the weak driving regime is investigated first. This is done by studying the effect of a π-pulse when two carbon qubits are driven at the same time on resonance. It turns out that in this weak driving regime the effect of the off resonance is very small, and changes the fidelity not more than 0.3%. Furthermore the effect of a square πpulse on 4 nearby qubits is studied. If the pulse is not optimized (thus square), the pulse cannot be done in less than 100µs while retaining at least 99% fidelity. By optimizing the envelope of the driving field using constrained optimization the pulse can be done in 22µs while retaining at least 99% fidelity.

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The NV-center in diamond is a promising system for quantum information processing. The typical qubits are the electron spin in the NV-center and the surrounding 13C nuclear spins. Fast and precise control of many 13C spins is desirable but challenging due to crosstalk. Crosstalk is the unwanted effect of a control pulse on the other qubits. The coupled NV-13C system is explored, and numerical techniques to optimize the control of multiple and single qubits are used. In this report the effect of the Bloch-Siegert shift in the weak driving regime is investigated first. This is done by studying the effect of a π-pulse when two carbon qubits are driven at the same time on resonance. It turns out that in this weak driving regime the effect of the off resonance is very small, and changes the fidelity not more than 0.3%. Furthermore the effect of a square πpulse on 4 nearby qubits is studied. If the pulse is not optimized (thus square), the pulse cannot be done in less than 100µs while retaining at least 99% fidelity. By optimizing the envelope of the driving field using constrained optimization the pulse can be done in 22µs while retaining at least 99% fidelity.
Individual nuclear spins in diamond can be optically detected through hyperfine couplings with the electron spin of a single nitrogen-vacancy (NV) center; such nuclear spins have outstandingly long coherence times. Among the hyperfine couplings in the NV center, the nearest neighbor 13C nuclear spins have the largest coupling strength. Nearest neighbor 13C nuclear spins have the potential to perform fastest gate operations, providing highest fidelity in quantum computing. Herein, we report on the control of coherences in the NV center where all three nearest neighbor carbons are of the 13C isotope. Coherence among the three and four qubits are generated and analyzed at room temperature.
Coupling-selective quantum optimal control in weak-coupling NV-13^{13}13C system
Abstract Quantum systems are under various unwanted interactions due to their coupling with the environment. Efficient control of quantum system is essential for quantum information processing. Weak-coupling interactions are ubiquitous, and it is very difficult to suppress them using optimal control method, because the control operation is at a time scale of the coherent life time of the system. Nitrogen-vacancy (NV) center of diamond is a promising platform for quantum information processing. The 13^{13}13 13 C nuclear spins in the bath are weakly coupled to the NV, rendering the manipulation extremely difficulty. Here, we report a coupling selective optimal control method that selectively suppresses unwanted weak coupling interactions and at the same time greatly prolongs the life time of the wanted quantum system. We applied our theory to a 3 qubit system consisting of one NV electron spin and two 13^{13}13 13 C nuclear spins through weak-coupling with the NV center. In the experiments, the iSWAP †^{\dagger }† † gate with selective optimal quantum control is implemented in a time-span of TctrlT_{ctrl}Tctrl​ T ctrl = 170.25 μ\muμ μ s, which is comparable to the phase decoherence time T2T_2T2​ T 2 = 203 μs\mu sμs μ s . The two-qubit controlled rotation gate is also completed in a strikingly 1020(80) μ\muμ μ s, which is five times of the phase decoherence time. These results could find important applications in the NISQ era.
Indirect control of qubits by a quantum actuator has been proposed as an appealing strategy to manipulate qubits that couple only weakly to external fields. While universal quantum control can be easily achieved when the actuator-qubit coupling is anisotropic, the efficiency of this approach is less clear. Here we analyze the time-efficiency of the quantum actuator control. We describe a strategy to find time-optimal control sequence by the quantum actuator and compare their gate times with direct driving, identifying regimes where the actuator control performs faster. As an example, we focus on a specific implementation based on the Nitrogen-Vacancy center electronic spin in diamond (the actuator) and nearby carbon-13 nuclear spins (the qubits).
A negatively charged nitrogen-vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits, and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.
We investigate the theoretically achievable fidelities when coherently controlling an effective three-qubit system consisting of a negatively charged nitrogen vacancy ( 15 NV − ) center in diamond with an additional nearby carbon 13 C spin via square and two frequency component radio and microwave frequency pulses in different magnetic field regimes. Such a system has potentially interesting applications in quantum information-related tasks such as distributed quantum computation or quantum repeater schemes. We find that the best fidelities can be achieved in an intermediate magnetic field regime. However, with only square pulses it will be challenging to reach the fidelity threshold(s) predicted by current models of fault-tolerant quantum computing.
Abstract A nitrogen-vacancy (NV) center in a diamond enables the access to an electron spin, which is expected to present highly sensitive quantum sensors. Although exploiting a nitrogen nuclear spin improves the sensitivity, manipulating it using a resonant pulse requires a long gate time owing to its small gyromagnetic ratio. Another technique to control nuclear spins is a conditional rotation gate based on dynamical decoupling, which is faster but unavailable for nitrogen spins owing to the lack of transverse hyperfine coupling with the electron spin. In this study, we generated effective transverse coupling by applying a weak off-axis magnetic field. An effective coupling depends on the off-axis field; the conditional rotation gate on the nitrogen-14 spins of an NV center was demonstrated within 4.2 μs under an 1.8% off-axis field and a longitudinal field of approximately 280 mT. We estimated that a population transfer from the electron to nitrogen spins can be implemented with 8.7 μs. Our method is applicable to an ensemble of NV centers, in addition to a single NV center.