In this thesis we deal with two different topics.In the first half we investigate how the Bayesian formalism can be introduced into the problem of quantum thermometrya field which exploits the high level of control in coherent devices to offer enhanced precision for temperature estimation.In particular, we investigate concrete estimation strategies, with focus on collisional thermometry, a protocol where a series of ancillae are sent sequentially to probe the system's temperature.We put forth a complete framework for analyzing collisional thermometry using Bayesian inference.The approach is easily implementable and experimentally friendly.Moreover, it is guaranteed to always saturate the Cramér-Rao bound in the long-time limit.Subtleties concerning the prior information about the system's temperature are also discussed and analyzed in terms of a modified Cramér-Rao bound associated with Van Trees and Schützenberger.Meanwhile, in the last part of the thesis we approach the problem of non-adiabatic holonomic computation.Namely, we investigate the implementation based on Λ-systems.It is known that a three-level system can be used in a Λ-type configuration in order to construct a universal set of quantum gates through the use of non-Abelian nonadiabatic geometrical phases.Such construction allows for high-speed operation times which diminish the effects of decoherence.This might be, however, accompanied by a breakdown of the validity of the rotating-wave approximation (RWA) due to the comparable timescale between counter-rotating terms and the pulse length, which greatly affects the dynamics.Here, we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.
In this thesis we deal with two different topics.In the first half we investigate how the Bayesian formalism can be introduced into the problem of quantum thermometrya field which exploits the high level of control in coherent devices to offer enhanced precision for temperature estimation.In particular, we investigate concrete estimation strategies, with focus on collisional thermometry, a protocol where a series of ancillae are sent sequentially to probe the system's temperature.We put forth a complete framework for analyzing collisional thermometry using Bayesian inference.The approach is easily implementable and experimentally friendly.Moreover, it is guaranteed to always saturate the Cramér-Rao bound in the long-time limit.Subtleties concerning the prior information about the system's temperature are also discussed and analyzed in terms of a modified Cramér-Rao bound associated with Van Trees and Schützenberger.Meanwhile, in the last part of the thesis we approach the problem of non-adiabatic holonomic computation.Namely, we investigate the implementation based on Λ-systems.It is known that a three-level system can be used in a Λ-type configuration in order to construct a universal set of quantum gates through the use of non-Abelian nonadiabatic geometrical phases.Such construction allows for high-speed operation times which diminish the effects of decoherence.This might be, however, accompanied by a breakdown of the validity of the rotating-wave approximation (RWA) due to the comparable timescale between counter-rotating terms and the pulse length, which greatly affects the dynamics.Here, we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.
In this thesis we deal with two different topics. In the first half we investigate how the Bayesian formalism can be introduced into the problem of quantum thermometry -- a field which exploits the high level of control in coherent devices to offer enhanced precision for temperature estimation. In particular, we investigate concrete estimation strategies, with focus on collisional thermometry, a protocol where a series of ancillae are sent sequentially to probe the system's temperature. We put forth a complete framework for analyzing collisional thermometry using Bayesian inference. The approach is easily implementable and experimentally friendly. Moreover, it is guaranteed to always saturate the Cramér-Rao bound in the long-time limit. Subtleties concerning the prior information about the system's temperature are also discussed and analyzed in terms of a modified Cramér-Rao bound associated with Van Trees and Schützenberger. Meanwhile, in the last part of the thesis we approach the problem of non-adiabatic holonomic computation. Namely, we investigate the implementation based on Λ-systems. It is known that a three-level system can be used in a Λ-type configuration in order to construct a universal set of quantum gates through the use of non-Abelian nonadiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating-wave approximation (RWA) due to the comparable timescale between counter-rotating terms and the pulse length, which greatly affects the dynamics. Here, we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.
Quantum thermometry exploits the high level of control in coherent devices to offer enhanced precision for temperature estimation. This highlights the need for constructing concrete estimation strategies. Of particular importance is collisional thermometry, where a series of ancillae are sent sequentially to probe the system's temperature. In this paper we put forth a complete framework for analyzing collisional thermometry using Bayesian inference. The approach is easily implementable and experimentally friendly. Moreover, it is guaranteed to always saturate the Cram\'er-Rao bound in the long-time limit. Subtleties concerning the prior information about the system's temperature are also discussed and analyzed in terms of a modified Cram\'er-Rao bound associated with Van Trees and Sch\"utzenberger.
A three-level system can be used in a Λ-type configuration in order to construct auniversal set of non-adiabatic quantum gates through the use of non-Abelian non-adiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating wave approximation (RWA) due to the comparable timescale between the counter-rotating terms and the pulse length, which greatly affects the dynamics. Here we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.
A three-level system can be used in a $\mathrm{\ensuremath{\Lambda}}$-type configuration in order to construct a universal set of quantum gates through the use of non-Abelian nonadiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating-wave approximation (RWA) due to the comparable timescale between counter-rotating terms and the pulse length, which greatly affects the dynamics. Here, we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.
Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. However, temperature is not a quantum observable, and most theoretical studies have therefore concentrated on analyzing fundamental precision limits set by the quantum Fisher information through the quantum Cramer-Rao bound. In contrast, whether a direct temperature readout can be achieved in quantum thermometry remains largely unexplored, particularly under the nonequilibrium conditions prevalent in real-world applications. To address this, we develop a direct temperature readout scheme based on a thermodynamic inference strategy. The scheme integrates two conceptual developments: (i) By applying the maximum entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive semi-definite error functions that lower-bound the deviation of the reference temperature from the true temperature-in analogy to the quantum Cramer-Rao bound for the mean squared error-and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature readout under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout.
Quantum computation has been shown to be superior to classical computation in solving some problems, and therefore can substantially change our life. However, the realization of quantum computation is still challenging, even if quantum technologies have been improved significantly. Two main obstacles to the realization of practical quantum computation are control errors and decoherence. Control errors are caused by inaccurate manipulations of quantum systems and decoherence is caused by the inevitable interaction between the system and its environment. Geometric phases are only dependent on evolution paths of quantum systems but independent of the evolution details and therefore quantum computation based on geometric phases, i.e., geometric quantum computation, is robust against control errors, benefiting the realization of practical quantum computation. The early proposals of geometric quantum computation are based on adiabatic geometric phases. These proposals require quantum systems to undergo adiabatic evolution, which makes quantum systems evolve for a long time. To circumvent this, nonadiabatic geometric quantum computation based on nonadiabatic Abelian geometric phases was proposed soon after. In 2012, nonadiabatic holonomic quantum computation based on nonadiabatic non-Abelian geometric phases was proposed, which also circumvents long-time evolutions. Moreover, compared with nonadiabatic geometric quantum computation that uses the geometric phase as one parameter of a quantum gate, nonadiabatic holonomic quantum computation uses the holonomic matrix itself as a quantum gate. This makes nonadiabatic holonomic quantum computation possess whole-geometric property. Due to the merits of both geometric robustness and high-speed implementation without the limit of adiabatic evolution, nonadiabatic holonomic quantum computation has been attracting much attention. Until now, much progress has been achieved in the field of nonadiabatic holonomic quantum computation. On one hand, various methods have been proposed to design more efficient nonadiabatic holonomic gates. Nonadiabatic holonomic gates were first realized by using resonant laser fields to drive a three-level system. After this, the single-shot proposal and the single-loop proposal were proposed, allowing us to realize one-qubit gates by a shorter path and thereby reducing the exposure time of nonadiabatic holonomic gates to the environment. To further shorten the exposure time, the path-shortening protocol was put forward, where nonadiabatic holonomic gates can be realized based on a class of extended evolution paths that are shorter than the former ones. Recently, a general approach of constructing Hamiltonians for nonadiabatic holonomic quantum computation was put forward, by using which one can easily find a Hamiltonian making the quantum system evolve along a desired path so that nonadiabatic holonomic gates can be realized with an economical evolution time. On the other hand, various methods have been proposed to combine nonadiabatic holonomic gates and various decoherence-resilient methods, making the resulting schemes robust against both control errors and decoherence. The first proposal in this aspect is combining nonadiabatic holonomic gates and decoherence-free subspaces. Gradually, proposals combining nonadiabatic holonomic gates with noiseless subsystems, dynamical decoupling and surface codes were put forward. Last but not least, various proposals suitable for specific physical systems have been proposed and particularly various experimental platforms have been used to demonstrate nonadiabatic holonomic gates. This also significantly improves the development of nonadiabatic holonomic quantum computation. In this paper, we review the above research advances on nonadiabatic holonomic quantum computation, aiming to help readers understand the main developments of nonadiabatic holonomic quantum computation.