Decoherence and errors appear among the main challenges to implement successful quantum technologies. In this thesis I discuss the application of some general tools and principles that may be valuable resources to develop robust technologies, with applications in quantum sensing and quantum simulation. Firstly, we employ suitable periodically driving fields acting on the Ising model in order to tailor spin-spin interactions depending on the spatial direction of the bonds. In this way, we are able to simulate the quantum compass model on a square lattice. This system exhibits topological order and a doubly degenerate ground state protected against local noise. A possible implementation of this proposal is outlined for atomic quantum simulators. Secondly, we exploit two general working principles based on spontaneous symmetry breaking and criticality that may be beneficial to achieve robust quantum sensors, particularly appropriate for quantum optical dissipative systems. A concrete application is given for a minimal model: a single qubit laser. It is shown how the precision in parameter estimation is enhanced as the incoherent pumping acting on the qubit increases, and also when the system is close to the lasing critical point. Finally, classical long-range correlations in lattice systems are shown to provide us with an additional resource to be used in robust sensing schemes. The previous setup is extended to a lattice of single qubit lasers where interactions are incoherent. Under the right conditions, we show that a Heisenberg scaling with the number of probes can be accomplished.
Decoherence and errors appear among the main challenges to implement successful quantum technologies. In this thesis I discuss the application of some general tools and principles that may be valuable resources to develop robust technologies, with applications in quantum sensing and quantum simulation. Firstly, we employ suitable periodically driving fields acting on the Ising model in order to tailor spin-spin interactions depending on the spatial direction of the bonds. In this way, we are able to simulate the quantum compass model on a square lattice. This system exhibits topological order and a doubly degenerate ground state protected against local noise. A possible implementation of this proposal is outlined for atomic quantum simulators. Secondly, we exploit two general working principles based on spontaneous symmetry breaking and criticality that may be beneficial to achieve robust quantum sensors, particularly appropriate for quantum optical dissipative systems. A concrete application is given for a minimal model: a single qubit laser. It is shown how the precision in parameter estimation is enhanced as the incoherent pumping acting on the qubit increases, and also when the system is close to the lasing critical point. Finally, classical long-range correlations in lattice systems are shown to provide us with an additional resource to be used in robust sensing schemes. The previous setup is extended to a lattice of single qubit lasers where interactions are incoherent. Under the right conditions, we show that a Heisenberg scaling with the number of probes can be accomplished.
Quantum systems cannot always be treated as isolated from their surroundings since this is an idealization which is not always true. Though theoretical analysis of open quantum systems poses great challenges as one needs to treat many-particle quantum systems as a whole, the system-environment interactions often lead to many interesting effects that are not observed in closed systems. The dissipation of a quantum system is not always a disadvantage and, in fact, if exploited properly in combination of coherent driving, one can steer the system into a desired state. This dissipation driven quantum state engineering technique finds its applications in novel technologies such as quantum computing, quantum simulation, and quantum metrology. In this thesis, we focus on the latter two, and show that using dissipative channels allows us to build quantum devices that have considerable advantages over their entirely coherent analogues. Simulation of many-body problems on a quantum simulator will unlock the potential to provide great insights into a large number of systems especially those that are computationally intractable or experimentally challenging. The two crucial steps towards the successful functioning of quantum simulation are the initialization of the quantum simulators i.e, preparing the system in a known initial state, and the Hamiltonian engineering. While there have been many experiments demonstrating the implementation of the Hamiltonian dynamics on the quantum simulator, work still needs to be done on the problem of preparing the simulator in a suitable quantum state. This is exactly our aim here and we propose a protocol to cool a given system into the ground state of a black-box spin Hamiltonian. The central idea is to use a dissipatively driven auxiliary spin to pull out the excitations in the system, eventually cooling it to its ground state. We show that already a single auxiliary spin is efficient in cooling the quantum simulator to a low-energy state of largely arbitrary Hamiltonians as the resources scale only polynomially with the system size. We also show that our scheme of sympathetic cooling is robust against additional sources of decoherence. The second part of the thesis deals with nanoscale quantum sensing using dissipative first order transition in the magnetization of a system of nitrogen-vacancy point defect centers in diamond. The sensitivity of a generic quantum sensor with non-interacting particles scales as the square root of the number of particles. Therefore, a sensor with large number of particles displays a better sensitivity. However, in the interest of nanoscale sensing, having a large number of particles implies that they are closely packed next to each other. At such high densities, the particles interact strongly with each other posing great challenges to the sensing process. Here, we show that these interactions can in fact be used to trigger a first order phase transition when coupled with controlled dissipation in the system. We study the properties of the phase transition using two- and three-dimensional setups to build a nanoscale quantum sensor that is especially robust against typical disorder imperfections or additional decoherence processes, with the sensitivity not being severely limited by the T2 decoherence time. Since our sensing protocol does not assume too many microscopic details of the process, one can easily apply this to other areas of quantum sensing and metrology. These results especially highlight the fact that dissipation in quantum systems, that is normally considered unwanted, can in fact be a powerful tool that allows us to enable a large list of quantum technologies in the future.
We study the performance of a single qubit laser as a quantum sensor to measure the amplitude and phase of a driving field. By using parameter estimation theory we show that certain suitable field quadratures are optimal observables in the lasing phase. The quantum Fisher information scales linearly with the number of bosons and thus the precision can be enhanced by increasing the incoherent pumping acting on the qubit. If we restrict ourselves to measurements of the boson number observable, then the optimal operating point is the critical point of the lasing phase transition. Our results point to an intimate connection between symmetry breaking, dissipative phase transitions, and efficient parameter estimation.
Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is , which harnesses the enhanced susceptibility and nonclassical correlations that naturally occur near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.
Atoms in optical lattices are promising candidates to implement quantum information processing. Their behaviour is well understood on a microscopic level, they exhibit excellent coherence properties, and they can be easily manipulated using external fields. In very deep optical lattices, each atom is restricted to a single lattice site and can be used as a qubit. If the lattice is shallow enough such that the atoms can move, their properties can be used to simulate certain condensed matter phenomena such as superconductivity. In this thesis, we show how technical problems of optical lattices such as restricted decoherence times, or fundamental shortcomings such as the lack of phonons or strong spin interactions, can be overcome by using current or near-future experimental techniques. We introduce a scheme that makes it possible to simulate model Hamiltonians known from high-temperature superconductivity. For this purpose, previous simulation schemes to realise the spin interaction terms are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. This scheme makes a large range of parameters accessible, which is difficult to cover with a condensed matter setup. We also investigate the properties of optical lattices submerged into a Bose-Einstein condensate (BEC). A weak-coupling expansion in the BEC-impurity interaction strength is used to derive a model that describes the lattice atoms in terms of polarons, i.e.~atoms dressed by Bogoliubov phonons. This is analogous to the description of electrons in solids, and we observe similar effects such as a crossover from coherent to incoherent transport for increasing temperatures. Moreover, the condensate mediates an attractive off-site interaction, which leads to macroscopic clusters at experimentally realistic parameters. Since the atoms in the lattice can also be used as a quantum register with the BEC mediating a two-qubit gate, we derive a quantum master equation to examine the coherence properties of the atomic qubits. We show that the system exhibits sub- and superdecoherence and that a fast implementation of the two-qubit gate competes with dephasing. Finally, we show how to realise the encoding of qubits in a decoherence-free subspace (DFS) using optical lattices. We develop methods for implementing robust gate operations on qubits encoded in a DFS exploiting collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of the gate operations and show that a robust implementation of quantum repeaters can be achieved using our setup. We compare the robust repeater scheme to one that makes use of conventional qubits only, and show the conditions under which one outperforms the other.
For several decades it has been appreciated that quantum computers hold incredible promise to perform calculations intractable to classical computation. However, this promise has be slow to realize. Dozens of quantum systems are currently being investigated for use in quantum information processing - none of which have yet demonstrated algorithms involving more than a handful of qubits and it remains unclear which, if any, of these systems will ultimately compose a scalable, robust quantum information processing architecture. In this thesis we employ analytical, optimal and algebraic control techniques to evaluate various quantum systems for their potential use in quantum information processing. In doing so, we have additionally identified several novel characterization procedures capable of probing both the coherent and incoherent dynamics of quantum systems. The first part of this thesis discusses work motivated by attempts to utilize donor qubits in silicon as quantum bits. We first propose a measurement of the state of a single donor electron spin using two-dimensional electron gas of a field-effect transistor and electrically detected magnetic resonance. We analyze the potential sensitivity of this measurement and show that it is a quantum nondemolition measurement of an electron-encoded state. We then present the first of two novel qubit characterization procedures. We consider the problem of rapidly characterizing a large number of similarly prepared qubits using techniques from optimal experiment design. All qubits are assumed to evolve according to the same physical processes, though the Hamiltonian parameters may vary from device to device - an inevitability in solid state qubits. We use the Cram\\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Though applied to dipole- and exchange-coupled qubits, this technique is widely applicable to other systems. The second part of the thesis discusses the role that control can play in measuring and mitigating noise in qubit systems. Our first result describes a method for quickly simulating the effects of arbitrary markovian noise on qubit systems through the use of a numerically optimized, multi-state Markovian fluctuator. This ability to rapidly simulate the noisy qubit evolution allows us to compute control sequences capable of maximally decoupling the qubit from the noise source. We then introduce the second characterization procedure of the these, showing that a single measurable and controllable qubit may act as a spectrometer of dephasing noise. We show that the formalism of dynamical decoupling can be used to estimate the short-time correlation function of the noise source, while long time correlations may be estimated by a very simple series of free evolution experiments. This technique is applicable to the wide range of physical implementations which suffer from dephasing noise.The final part of this thesis demonstrates that trapped neutral atoms may be utilized for the robust simulation of complex systems exhibiting a topological phase. We present a method to simulate the toric code Hamiltonian stroboscopically, and demonstrate that our technique preserves the ground state degeneracy . Furthermore, we introduce a dissipative mechanism allowing for thermalization of the system to a finite temperature or direct cooling to the ground state manifold.
Entangled many-body states enable high-precision quantum sensing beyond the standard quantum limit. We develop interferometric sensing protocols based on quantum critical wavefunctions and compare their performance with Greenberger-Horne-Zeilinger (GHZ) and spin-squeezed states. Building on the idea of symmetries as a metrological resource, we introduce a symmetry-based algorithm to identify optimal measurement strategies. We illustrate this algorithm both for magnetic systems with internal symmetries and Rydberg-atom arrays with spatial symmetries. We study the robustness of criticality for quantum sensing under non-unitary deformations, symmetry-preserving and symmetry-breaking decoherence, and qubit loss -- identifying regimes where critical systems outperform GHZ states and showing that non-unitary deformation can even enhance sensing precision. Combined with recent results on log-depth preparation of critical wavefunctions, interferometric sensing in this setting appears increasingly promising.