Model-aware reinforcement learning for high-performance Bayesian experimental design in quantum metrology

The recent advances in Machine Learning hold great promises for the field of quantum sensing and metrology. With the help of reinforcement learning, we can tame the complexity of quantum systems and solve the problem of optimal experimental design. Reinforcement learning is a powerful model-free technique that allows an agent, which is typically a neural network, to learn the best strategy to reach a certain goal in a completely a priori unknown environment. However, in general, we know something about the quantum system the agent is interacting with, at least that it follows the rules of quantum mechanics. In quantum metrology, we typically have a model for the system and only some parameters of the evolution or of the initial state are unknown. We present here a general Machine Learning technique that can optimize the precision of quantum sensors, and in doing so it exploits the knowledge we have on the system. We have developed a Python package to automate a broad class of optimizations that can be found in the tasks of quantum parameter estimation, quantum metrology and quantum hypothesis testing. What the agent is learning here is an optimal adaptive strategy, that, on the basis of the previous outcomes, decides the next measurements to perform. It works both for Bayesian estimation and for frequentist estimation. The user is required to implement the physics of the system to be studied and state which parameters in the experiment are controllable and which are unknowns. The functions of the library allow then to easily train a neural network agent for optimizing the precision of the sensor, by simulating the experiment. We have explored some applications of this technique to magnetometry on NV centers (both DC and AC), to state discrimination in quantum optics and to phase estimation. So far, we were able to certify better results than the current state-of-the-art controls for many examples. The Machine Learning technique developed here can be applied in all those scenarios where the quantum system is well characterized and relatively simple and small. In these cases, we can squeeze every last bit of information from a quantum sensor by controlling it with a neural network appropriately trained.

We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.

In this paper, we study the dynamical behavior and quantum metrology in a rotating Nitrogen-Vacancy(NV) center system which is subject to an external magnetic field. Based on the recently realized rapid rotation of nano-rotor [J. Ahn, et. al., Phys. Rev. Lett. 121, 033603 (2018) and R. Reimann, et. al., Phys. Rev. Lett. 121, 033602 (2018)], the frequency of the rotation is close to that of the intrinsic frequency of the NV center system, we predict the quantum beats phenomenon in the time domain and show that the quantum metrology can be enhanced by the superposition effect in our system.

Emerging quantum technologies, such as quantum information processing and quantum metrology, require quantum systems that provide reliable toolsets for initialization, readout, and coherent manipulation as well as long coherence times. The coherence of these systems, however, is usually limited by uncontrolled interactions with the surrounding environment. In particular, innovations building on solid-state spin systems like the Nitrogen-Vacancy (NV) center in diamond ordinarily involve the use of magnetic field-sensitive states. In this case, ambient magnetic field fluctuations constitute a serious impediment that shortens the coherence time considerably. Thus, the protection of individual quantum systems from environmental perturbations constitutes a fundamentally important but also a challenging task for the further development of quantum appliances. In this thesis, we address this challenge by extending the widely used approach of dynamical decoupling to protect a quantum system from decoherence. Specifically, we study three-level dressed states that emerge under continuous, `closed-contour' interaction driving. To implement and investigate these dressed states, we exploit well-established methods for coherent microwave and strain manipulation of the NV center spin in a hybrid spin-mechanical system. Our results reveal that this novel continuous decoupling mechanism can overcome external magnetic fluctuations in a robust way. We demonstrate experimentally that the dressed states we created are long-lived and find coherence times nearly two orders of magnitude longer than the inhomogeneous dephasing time of the NV spin, even for moderate driving strengths. To realize direct and efficient access to the coherence-protected dressed states under closed-contour driving, we further demonstrate the use of state transfer protocols for their initialization and readout. In addition to an adiabatic approach, we apply recently developed protocols based on `shortcuts to adiabaticity' to accomplish the initialization process, which ultimately accelerates the transfer speed by a factor of $2.6$ compared to the fastest adiabatic protocol with similar fidelity. Moreover, we show bidirectionality of the accelerated state transfer, which allows us to directly read out the dressed state population and to quantify the transfer fidelity of $\approx$$\,99\,\%$. By employing the methods to prepare and read out the dressed states, we lay the foundation to meet the remaining key requirement for quantum systems -- coherent quantum control. We present direct, coherent manipulation of the dressed states in their own manifold and exploit this for extensive characterization of the dressed states' properties. Thus, our results constitute an elementary step to establish the dressed states as a powerful resource in prospective quantum sensing applications. Harnessing quantum systems like the dressed states as nanoscale sensors of external fields requires the detailed characterization of the local internal environment. In the final part of this thesis, we report on the determination of intrinsic effective fields of individual NV center spins. We study single NVs in high purity diamond and find that local strain dominates over local electric fields. In addition, we experimentally demonstrate and theoretically describe a new technique for performing single spin-based polarization analysis of microwave fields in a tunable, linear basis.

We experimentally demonstrate high degree of polarization of 13C nuclear spins weakly interacting with nitrogen-vacancy (NV) centers in diamond. We combine coherent microwave excitation pulses with optical illumination to provide controlled relaxation and achieve a polarity-tunable, fast nuclear polarization of degree higher than 85% at room temperature for remote 13C nuclear spins exhibiting hyperfine interaction strength with NV centers of the order of 600 kHz. We show with the aid of numerical simulation that the anisotropic hyperfine tensor components naturally provide a route to control spin mixing parameter so that highly efficient nuclear polarization is enabled through careful tuning of nuclear quantization axis by external magnetic field. We further discuss spin dynamics and wide applicability of this method to various target 13C nuclear spins around the NV center electron spin. The proposed control method demonstrates an efficient and versatile route to realize, for example, high-fidelity spin register initialization and quantum metrology using nuclear spin resources in solids.

The ready optical detection and manipulation of bright nitrogen vacancy center spins in diamond plays a key role in contemporary quantum information science and quantum metrology. Other optically dark defects such as substitutional nitrogen atoms (`P1 centers') could also become potentially useful in this context if they could be as easily optically detected and manipulated. We develop a relatively straightforward continuous wave protocol that takes advantage of the dipolar coupling between nitrogen vacancy and P1 centers in type 1b diamond to detect and polarize the dark P1 spins. By combining mutual spin flip transitions with radio frequency driving, we demonstrate the simultaneous optical polarization and detection of the electron spin resonance of the P1 center. This technique should be applicable to detecting and manipulating a broad range of dark spin populations that couple to the nitrogen vacancy center via dipolar fields, allowing for quantum metrology using these spin populations.

Photon–phonon entanglement and spin squeezing via dynamically strain-mediated Kerr nonlinearity in dressed nitrogen–vacancy centers

We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation. The approach allows to optimize practically any computable functional and is implemented in two open source Julia packages,GRAPE.jlandKrotov.jl, part of theQuantumControl.jlframework. Our method is based on formally rewriting the optimization functional in terms of propagated states, overlaps with target states, or quantum gates. An analytical application of the chain rule then allows to separate the time propagation and the evaluation of the functional when calculating the gradient. The former can be evaluated with great efficiency via a modified GRAPE scheme. The latter is evaluated with automatic differentiation, but with a profoundly reduced complexity compared to the time propagation. Thus, our approach eliminates the prohibitive memory and runtime overhead normally associated with automatic differentiation and facilitates further advancement in quantum control by enabling the direct optimization of non-analytic functionals for quantum information and quantum metrology, especially in open quantum systems. We illustrate and benchmark the use of semi-automatic differentiation for the optimization of perfectly entangling quantum gates on superconducting qubits coupled via a shared transmission line. This includes the first direct optimization of the non-analytic gate concurrence.

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

In recent years, quantum detector tomography (QDT) is widely used in many fields, such as non-Gaussian states preparation, quantum metrology, quantum communication and so forth. In this paper, we used QDT to completely characterize a photon-number-resolving detector (PNRD) based on a multi-pixel photon counter (MPPC) at 650 nm, which operated in continuous wave (CW) mode. Reconstructing the positive operator-valued measure (POVM) accurately by QDT could help us theoretically derived the operation performance of MPPC in quantum sensing with nitrogen-vacancy (NV) center ensemble. The reconstruction fidelity of MPPC is larger than 99.94%, which means that QDT is very reliable. Comparing with conventional silicon avalanche photodiode (Si-APD), the fluorescent contrast of optically detected magnetic resonance (ODMR) spectrum of NV center ensemble detected by MPPC could be significantly improved. Since its excellent linearity and outstanding photon-number-resolving capability, MPPC could be further used in the DC magnetometry of NV center ensemble. We can infer that the magnetic field sensitivity can be effectively improved by replacing Si-APD with MPPC. Reportedly, this is an extremely rare research on the application of MPPC in NV center magnetometry.

The Nitrogen-Vacancy (NV) center is becoming a promising qubit for quantum information processing. The defect has a long coherence time at room temperature and it allows spin state initialized and read out by laser and manipulated by microwave pulses. It has been utilized as a ultra sensitive probe for magnetic fields and remote spins as well. Here, we review the recent progresses in experimental demonstrations based on NV centers. We first introduce our work on implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond. Then the quantum nature of the bath around the center spin is revealed and continuous wave dynamical decoupling has been demonstrated. By applying dynamical decoupling, a multi-pass quantum metrology protocol is realized to enhance phase estimation. In the final, we demonstrated NV center can be regarded as a ultra-sensitive sensor spin to implement nuclear magnetic resonance (NMR) imaging at nanoscale.

A quantumnetwork would allow the distribution of a quantum state over many spatially separated quantum nodes which individually possess the ability to generate, process and store quantum information. Connecting these nodes through quantum communication channels would enable sending quantum information over arbitrarily long distances, secret key distribution with guaranteed secure communication and distributed quantum computing. An appealing platform for implementation of quantum networks is the nitrogen-vacancy (NV) center in diamond. An NV center is an optically active defect in diamond created by the substitution of two adjacent carbon atoms in the diamond crystal matrix by a nitrogen atom and a neighboring vacancy. The NV center fits remarkably well in the described quantum network framework. Its electronic spin can be optically initialized, read out in a single shot, coherently manipulated and coupled to the nearby carbon-13 nuclear spins. These properties represent necessary ingredients of a multi-qubit quantum node. The possibility of the entanglement between the state of the NV center spin and a photon establishes a photonic quantum link which can enable the entanglement of the quantum nodes, forming a quantum network. First building blocks of the proposed quantum networks based on NV centers were demonstrated by performing entanglement between two distant NV centers separated by more than a kilometer. However, the current success rate of the entangling protocols is greatly reduced due to the low emission probability of the NV center photons into the resonant zero phonon line (ZPL) and the inefficient photon extraction from the diamond. This is the central problem which prevents promoting our experiments beyond proof-of-principle demonstration towards practical implementation of the proposed quantumnetworks. The goal of this thesis is tackling these issues by coupling NV centers to optical cavities which would greatly increase the rate of generation and collection of the ZPL photons through themechanism of Purcell enhancement. The design and the fabrication of the components constituting a diamond-basedFabry-Perot microcavity, as used in this thesis, are described in Chapter 4. For large enhancement of the NV center resonant emission, a low cavity mode volume is necessary. This is achieved by inserting a micrometers thin diamond slab into the cavity architecture; we present the fabrication details of such samples. Chapter 5 describes the fabrication of an integrated platform for microwave signal delivery to the NV centers within a diamond membrane in the cavity architecture. Microwave striplines and arrays of unique markers are embedded in the mirror onto which the diamond is bonded. We investigate the mirror optical properties post fabrication and find that the fabrication method preserves the mirror optical performance. We describe the diamond bonding method and demonstrate addressing of the NV center spin. In Chapter 6 we probe the properties of the cavity with the embedded diamond membrane through measurements of the cavity finesse. We investigate the cavity finesse dependence on length, mode structure and temperature. We further explore the operation at cryogenic temperatures by probing the effect of cryostation vibration on the cavity linewidth. Finally, in Chapter 7 we discuss ways of improving the existing experimental capabilities, outline the first steps for demonstrating enhancement of the NV center resonant emission and suggest future experiments that can be performed with this system. We conclude that coupling of the NV centers to the cavities developed in this research could lead to an increase of remote entanglement success rates by more than three orders of magnitude.

Coherent control of the nitrogen-vacancy (NV) center in diamond’s triplet spin state has traditionally been accomplished with resonant ac magnetic fields. Here, we show that high-frequency stress resonant with the spin state splitting can also coherently control NV center spins. Because this mechanical drive is parity non-conserving, controlling spins with stress enables direct access to the magnetically forbidden |−1〉↔|+1〉 spin transition. Using a bulk-mode mechanical microresonator fabricated from single-crystal diamond, we apply intense ac stress to the diamond substrate and observe mechanically driven Rabi oscillations between the |−1〉 and |+1〉 states of an NV center spin ensemble. Additionally, we measure the inhomogeneous spin dephasing time (T2*) of the spin ensemble within this {−1,+1} subspace using a mechanical Ramsey sequence and compare it to the dephasing times measured with a magnetic Ramsey sequence for each of the three spin qubit combinations available within the NV center ground state. These results demonstrate coherent control of a spin with a mechanical resonator and could lead to the creation of a phase-sensitive Δ-system inside the NV center ground state with potential applications in quantum optomechanics and metrology.

Spin squeezing has received much attention due to the interesting physics and important applications such as quantum metrology and quantum information processing. We here present a scheme to engineer stable spin squeezing in an array of nitrogen vacancy centers (NVCs) coupled to a rectangular hollow metallic waveguide. The remarkable feature of the waveguide as the common environment media is that one can switch on/off either the waveguide induced dipole-dipole interactions or correlated spontaneous emissions among the NVCs by designing their spatial separation. It permits us to achieve a dissipative Dicke model after the dipole-dipole interactions vanish due to destructive interference. With the external driving lasers on each NVC, a second-order phase transition is triggered, separating the steady state into two phases with and without collective spin squeezing. Supplying a physical realization of the dissipative Dicke model, our study gives a bridge between the generation of the stable spin squeezing and the phase transition physics.

The new field of quantum information technology uses qubits (quantum bits) instead of classical bits to carry out certain computation operations or for secure transfer of information (quantum cryptography). There are a number of physical systems that can act as qubits including a wide range of materials and technologies, e.g. ions in traps, local defect states in crystal lattices, superconducting junctions, etc. All these material systems offer different challenges and opportunities for the creation of qubit-based quantum devices. The search for defect states in solids with a capability to store and manipulate quantum information represents a exciting area of research. One of the most promising (and maybe the best studied) defects are the so-called nitrogen-vacancy (NV) centers in diamond, which are perspective candidates for a number of applications, including quantum computation and cryptography. A NV center represents a nitrogen atom in the diamond crystalline lattice adjacent to a vacancy, i.e. a site with a missing carbon atom. The attractiveness of this system stems from the long-lived quantum coherence, which can be initialized, acted upon, and measured using readily available techniques. A particularly exciting feature of these defects is the persistence of long coherence times even at room temperature. Single NV centers can be patterned on demand, and much like atomic defects surrounded by a stable environment (the crystalline lattice), they have highly reproducible properties. In order to exploit the outstanding properties of NV centers by increasing both the photon emission yield and the collection efficiency of the emitted photons, they should be embedded in an optical cavity, e.g. in all-diamond devices like nanopillars, photonic crystals, microrings, etc.