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arXiv:2408.13349

High fidelity quantum state tomography of electron-$^{14}$N nuclear hybrid spin register in diamond using Rabi oscillations

Abhishek Shukla, Boo Carmans, Petrov, Michael, Daan Vrancken, Miloš Nesládek

Published Aug 23, 2024• 0 citations
arXivHTMLPDF

Abstract

We report on a new quantum state characterisation method, which we call Rabi-based Quantum State Tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) centre in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of density matrix from the measured data sets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere with a maximum fidelity of 0.99992. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrate fidelities of the same order.

DOI
10.48550/arxiv.2408.13349

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High fidelity quantum state tomography of electron-14^{14}14N nuclear hybrid spin register in diamond using Rabi oscillations
We report on a new quantum state characterisation method, which we call Rabi-based Quantum State Tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) centre in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of density matrix from the measured data sets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere with a maximum fidelity of 0.99992. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrate fidelities of the same order.
We report on a quantum state characterization method, which we call Rabi-based quantum state tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) center in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of the density matrix from the measured datasets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrates fidelities of the same order.
The nitrogen-vacancy (NV) center in diamond is one of the advanced candidates for solid-state quantum computing at room temperature and has proven to be competitive in terms of gate fidelity and the availability of quantum error correction codes. Ambient solid-state qubits may therefore provide quantum computing architectures as an alternative to current solutions. The NV center has an associated electronic spin that is conventionally read out via photoluminescence. As an alternative, the electrical readout is not limited by the confocal resolution of quantum microscopes, which is required in the development of NV-based quantum processors to establish a scalable individual single-spin readout on the order of a few nanometers (necessary for strong dipole-dipole coupling). In this work, the performance of photoelectric readout versus traditional optical readout is investigated to perform Quantum State Tomography measurements on a single NV center. A state fidelity of 0.995 ±\pm± 0.006 is achieved using photoelectrical spin-state readout for state reconstruction, comparable to simultaneous optical measurements. We report photocurrent signal delays, which significantly slow down the photocurrent tomography. We develop a model describing their origin, and propose strategies for their mitigation.
Digital information based on the laws of quantum mechanics promisses powerful new ways of computation and communication. However, quantum information is very fragile; inevitable errors continuously build up and eventually all information is lost. Therefore, realistic large-scale quantum information processing requires the protection of quantum bits (qubits) against errors. In this thesis we present the experimental implementation of quantum error correction protocols based on spins in diamond. In such protocols, a quantum state is protected against errors by encoding in multiple qubits. Errors can be detected and corrected by measurement of correlations, so-called stabilizer-measurements, on these qubits.The experimental work presented in this thesis employs multiple spins in diamond as qubits to explore and implement error correction protocols. The nitrogen-vacancy (NV) centre in diamond is a lattice defect consisting of a nitrogen atom (N) and a vacancy (V) on two adjacent diamond lattice sites. This defect effectively results in an electronic spin that can be addressed as a qubit. The spin state can be manipulated by microwave fields and optically read out. At liquid helium temperatures (cryogenic temperature, ~4 K = -269 C), the NV electron spin provides high-fidelity single-shot readout and long coherence times.The NV centre is surrounded by naturally available (1.1% abundance) nuclear C13 spins. As the number of spins that are close enough to the NV centre to be strongly coupled is limited, we employ the weakly coupled nuclear spins in the spin bath of the NV centre. Using dynamical decoupling techniques these nuclear spins can be detected via the NV electron spin through the hyperfine interaction. The nuclear spins are long-lived and robust against optical excitation of the NV electron spin, which can make these spins a robust quantum register for quantum error correction.In Ch. 4 we demonstrate universal control over multiple of such weakly coupled nuclear C13 spins in the environment of the NV centre at ambient temperatures. We demonstrate initialization, control and read-out of individual nuclear spins. Finally, we implement a quantum error correction protocol by encoding a quantum state in the NV electron spin and two nuclear spins. Errors are detected by un-encoding the quantum state back to the electron spin and correction via a double controlled operation.For universal fault-tolerant quantum computations it is essential that the quantum information remains encoded at all times. In Ch. 5 we present multiple rounds of quantum error correction and active feedback on a continuously encoded qubit at cryogenic temperatures. A quantum state is protected by encoding in three weakly coupled spins. Errors are detected via high-fidelity non-demolition readout of the NV electron spin and actively corrected using fast classical electronics. We demonstrate that an actively error-corrected qubit is robust against phase flip errors and show that a superposition state can live longer than the best physical qubit in the encoding.The presented methods and results can be extended to a range of future experiments. In Ch. 6 we propose the implementation of five-qubit quantum error correction, the smallest code to correct for general single-qubit errors on the physical qubits in the encoding, by extending the experimental methods as developed in Chs. 4&5. Besides the exploration and development of larger error correction protocols and fault-tolerant quantum computing, the presented quantum register based in spins in diamond can be employed as a quantum node and combined with recent advances in the realization of quantum entanglement over large distances to form quantum networks. These networks can be used to study both fundamental questions as well as future applications in quantum information technology.
Single-qubit measurements are typically insufficient for inferring arbitrary quantum states of a multiqubit system. We show that, if the system can be fully controlled by driving a single qubit, then utilizing a local random pulse is almost always sufficient for complete quantum-state tomography. Experimental demonstrations of this principle are presented using a nitrogen-vacancy (NV) center in diamond coupled to a nuclear spin, which is not directly accessible. We report the reconstruction of a highly entangled state between the electron and nuclear spin with fidelity above 95% by randomly driving and measuring the NV-center electron spin only. Beyond quantum-state tomography, we outline how this principle can be leveraged to characterize and control quantum processes in cases where the system model is not known.
A collapse and revival shape of Rabi oscillations in an electron spin of a single nitrogen-vacancy centre has been observed in diamond at room temperature. Because of hyperfine interaction between the host 14 N nuclear spin and the nitrogen-vacancy centre electron spin, different orientations of the 14 N nuclear spins lead to a triplet splitting of the transition between ground state ( m s = 0) and excited state ( m s = 1). The manipulation of the single electron spin of nitrogen-vacancy centre is achieved by using a combination of selective microwave excitation and optical pumping at 532 nm. Microwaves can excite three transitions equally to induce three independent nutations and the shape of Rabi oscillations is a combination of the three nutations.