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).
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).
Coupling-selective quantum optimal control in weak-coupling NV-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 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 C nuclear spins through weak-coupling with the NV center. In the experiments, the iSWAP † † gate with selective optimal quantum control is implemented in a time-span of Tctrl T ctrl = 170.25 μ μ s, which is comparable to the phase decoherence time T2 T 2 = 203 μs μ s . The two-qubit controlled rotation gate is also completed in a strikingly 1020(80) μ μ s, which is five times of the phase decoherence time. These results could find important applications in the NISQ era.
Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen-vacancy (NV) center in diamond, are among the most promising systems to implement quantum computing, provided the control of the different types of qubits can be efficiently implemented. In the case of the NV center, the anisotropic hyperfine interaction allows one to control the nuclear spins indirectly, through gate operations targeting the electron spin, combined with free precession. Here, we demonstrate that this approach allows one to implement a full quantum algorithm, using the example of Grover's quantum search in a single NV center, whose electron is coupled to a carbon nuclear spin.
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.
Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme for circumventing this problem by indirect control: we apply a small number of short pulses only to the electron and let the full system undergo free evolution under the hyperfine coupling between the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system, including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin as the target qubit. The durations of these gates are shorter than the electron coherence time, and thus additional operations to extend the system coherence time are not needed. Our demonstration serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems, such as nitrogen vacancy centers in diamond. Our scheme is still applicable when the nuclear spins are only weakly coupled to the electron.
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.
Hybrid quantum registers consisting of different types of qubits offer a range of advantages as well as challenges. The main challenge is that some types of qubits react only slowly to external control fields, thus considerably slowing down the information processing operations. Here, we propose and demonstrate an indirect control scheme that allows us to control the nuclear spins of an NV center indirectly, by control operations applied to the electron spin, combined with free precession under the anisotropic hyperfine interaction. The scheme provides universal control and we present two typical applications : polarizing the nuclear spin and measuring nuclear spin free induction decay signal, both without applying radio-frequency pulses. This scheme is versatile as it can be implemented over a wide range of magnetic field strengths and at any temperature.