Abstract Quantum error correction (QEC) is crucial for protecting quantum information from the decoherence caused by the interaction between the system and the environment. Many QEC techniques and algorithms have been proposed and demonstrated in various physical platforms at low temperatures, such as superconducting circuits, Rydberg’s atoms, and trapped ions. At room temperature, the QEC realization with nitrogen-vacancy (NV) centers in diamond has become very attractive due to the promising nature of the centers that have a relatively long spin coherence time and can be initialized and read out optically. Here, we investigate the potential realization of a simple repetitive three-qubit QEC scheme in which three NVs are coupled via dipolar coupling. A single NV qubit has been protected using two other coupled NVs which act as ancilla qubits. In this configuration of three NVs, a single NV qubit is protected from bit or phase-flip errors. This work paves the way for realizing five-qubit QEC with NVs at room temperature to preserve a qubit against any arbitrary single-qubit error.
Abstract Quantum error correction (QEC) is crucial for protecting quantum information from the decoherence caused by the interaction between the system and the environment. Many QEC techniques and algorithms have been proposed and demonstrated in various physical platforms at low temperatures, such as superconducting circuits, Rydberg’s atoms, and trapped ions. At room temperature, the QEC realization with nitrogen-vacancy (NV) centers in diamond has become very attractive due to the promising nature of the centers that have a relatively long spin coherence time and can be initialized and read out optically. Here, we investigate the potential realization of a simple repetitive three-qubit QEC scheme in which three NVs are coupled via dipolar coupling. A single NV qubit has been protected using two other coupled NVs which act as ancilla qubits. In this configuration of three NVs, a single NV qubit is protected from bit or phase-flip errors. This work paves the way for realizing five-qubit QEC with NVs at room temperature to preserve a qubit against any arbitrary single-qubit error.
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.
Quantum computing and quantum sensing have received much attention in recent years. As an atomic quantum system with super-long coherence time and spin-dependent optical transitions at room temperature, nitrogen-vacancy (NV) center in diamond is one of the well-studied physical systems in quantum information science. In this review, we brief the working principles and quantum control techniques of this single spin system, and also several experimental demonstrations. We focus on the following points:1) coherent manipulation of single spins with optically detected magnetic resonance; 2) main mechanism of NV election spin decoherence and schemes of coherence protection; 3) quantum sensing and quantum computing applications of spin quantum control techniques. Some open questions are discussed at the end of this review.
This work investigates the applicability of the nitrogen-vacancy (NV) defect center in diamond for quantum computation and metrology purposes. The NV center is a molecule like defect in the diamond lattice which is optically active and possesses an electron spin in its ground state. The spin can be used as a quantum bit and as a field sensor. The NV center has three major properties enabling individual control of single defects. Its optical properties depend on the spin state, the spin can be polarized optically and the spin state has an exceptionally long lifetime. Single NV centers can be controlled by optical and microwave radiation. Generally, the research on individually controllable quantum systems is not only motivated by quantum computation and communication. With the ongoing miniaturization nowadays electronic and electro-optic devices will soon reach the limit of single quantum building blocks. While in these applications the full complexity of single quantum systems might not be needed, small sensors based on single atoms or molecules might very well take advantage of the susceptibility of quantum coherences to environmental conditions. Major challenges for all approaches towards single quantum system control are the individual addressing, the measurement of the quantum state and the protection of quantum coherence from environmental noise. Today, there is a variety of systems (including the NV center) that allow control on the single quantum level. These are for example single photons, single ions and atoms in traps, single spins in semiconductors or single molecules in solid state systems. Rather mesoscopic examples are superconducting devices, nanomechanical oscillators or surface plasmon polaritons. Regarding the NV center it has been shown that the magnetic moment of its electron spin allows individual sensing and coupling to other surrounding electron and nuclear spins. Especially single nuclear spins were shown to be exceptional quantum memories. In this work small quantum registers of up to 5 spins have been used to test major requirements for a feasible quantum processor. Therefore, mainly artificially created high purity diamond samples with controlled spin and impurity concentration were used. The NV centers were either grown in or created via ion implantation techniques in a controlled fashion. As a first requirement for quantum computation entanglement among up to three spins has been generated and was verified by quantum state tomography. This proves the access of the full Hilbert space. Especially, entanglement among nuclear spins was very long-living. In further experiments this processor was used for first quantum algorithms like super-dense coding and the Deutsch algorithm. In addition, this work demonstrates new methods to initialize nuclear spin qubits into a desired quantum state. This is particularly important as improper initialization inhibits quantum computation. One of these methods is related to dynamic nuclear spin polarization and the other to measurement based state preparation. Nuclear spins in the diamond lattice originate mainly from the C-13 isotope. By artificially altering its content the influence on the NV center spin was investigated. The coherence times of the NV center were increasing inversely with the nuclear spin density. Even increasing nuclear spin density to offer more nuclear spin qubits to an operational quantum register was possible. As an alternative route of scaling up the quantum register pairs of closely spaced NV centers were investigated. For the first time two qubit gates among two NV centers mediated by magnetic dipolar coupling have been realized. Furthermore the sensing ability was demonstrated by measuring the relative distance of the two centers (10 nm) with sub-nm precision. Eventually, this work contains new insight into the electronically excited state of the NV center which allowed a more advanced control of the electron and nuclear spins. A comparably high magnetic field was used to decouple electron and nuclear spins. Finally, this allowed quantum nondemolition measurements on single nuclear spins which manifests in the observation of quantum jumps. The new insight was used to drastically improve the performance of quantum state readout. Summarizing, it was shown that single NV centers and proximal nuclear spins form versatile small quantum registers which can be interconnected with neighboring such NV quantum registers. Although the number of qubits used in this work is still small the experimental results propose a way of how to proceed when building a quantum computer. Regarding quantum metrology, however, the use of such a small register which can sense fields and store and process the results would already outperform a single NV electron spin by orders of magnitude.
The nitrogen vacancy (NV) center in diamond is a unique quantum system that combines solid state spin qubits with coherent optical transitions. The spin states of the NV center can be initialized, read out, and controlled with RF fields at room temperature. It can be coupled to other spin systems in the environment while at the same time maintaining an extraordinary degree of quantum coherence. Experiments utilizing the NV center's spin states have led to a wide range of demonstrations from quantum error correction to high-sensitivity magnetometry. This thesis, however, focuses on creating an interface between NV centers and light in the visible domain by making use of its optical transitions. Such an interface connects the quantum system consisting of NV centers and nuclear spins to photons, which can then be used to both manipulate the spin qubits themselves or transport quantum information over large distances.
Abstract Quantum state readout is a key component of quantum technologies, including applications in sensing, computation, and secure communication. Readout fidelity can be enhanced by repeating readouts. However, the number of repeated readouts is limited by measurement backaction, which changes the quantum state that is measured. This detrimental effect can be overcome by storing the quantum state in an ancilla qubit, chosen to be robust against measurement backaction and to allow error correction. Here, we protect the electronic-spin state of a diamond nitrogen-vacancy center from measurement backaction using a robust multilevel 14N nuclear-spin memory and perform repetitive readout, as demonstrated in previous work on bulk diamond devices. We achieve additional protection using error correction based on the quantum logic of coherent feedback to reverse measurement backaction. The repetitive spin readout scheme provides a 13-fold enhancement of readout fidelity over conventional readout and the error correction a 2-fold improvement in the signal. These experiments demonstrate full quantum control of a nitrogen-vacancy center electronic-spin coupled to its host 14N nuclear spin inside a ~25 nm nanodiamond, creating a sensitive and biologically compatible platform for nanoscale quantum sensing. Our error-corrected repetitive readout scheme is particularly useful for quadrupolar nuclear magnetic resonance imaging in the low magnetic field regime where conventional repetitive readout suffers from strong measurement backaction. More broadly, methods for correcting longitudinal (bit-flip) errors described here could be used to improve quantum algorithms that require non-volatile local memory, such as correlation spectroscopy measurements for high resolution sensing.
Nitrogen–vacancy (NV) center in diamond is one of the most promising candidates to implement room temperature quantum computing. In this review, we briefly discuss the working principles and recent experimental progresses of this spin qubit. These results focus on understanding and prolonging center spin coherence, steering and probing spin states with dedicated quantum control techniques, and exploiting the quantum nature of these multi-spin systems, such as superposition and entanglement, to demonstrate the superiority of quantum information processing. Those techniques also stimulate the fast development of NV-based quantum sensing, which is an interdisciplinary field with great potential applications.