Very recently, interferometric methods have been proposed to measure the full statistics of work performed on a driven quantum system [Dorner et al., Phys. Rev. Lett. 110, 230601 (2013) and Mazzola et al., Phys. Rev. Lett. 110, 230602 (2013)]. The advantage of such schemes is that they replace the necessity to make projective measurements by performing phase estimation on an appropriately coupled ancilla qubit. These proposals are one possible route to the tangible experimental exploration of quantum thermodynamics, a subject which is the center of much current attention due to the current control of mesoscopic quantum systems. In this Rapid Communication we demonstrate that a modification of the phase estimation protocols can be used in order to measure the heat distribution of a quantum process. In addition, we demonstrate how our scheme maybe implemented using ion trap technology. Our scheme should pave the way for experimental explorations of the Landauer principle and hence the intricate energy to information conversion in mesoscopic quantum systems.
Very recently, interferometric methods have been proposed to measure the full statistics of work performed on a driven quantum system [Dorner et al., Phys. Rev. Lett. 110, 230601 (2013) and Mazzola et al., Phys. Rev. Lett. 110, 230602 (2013)]. The advantage of such schemes is that they replace the necessity to make projective measurements by performing phase estimation on an appropriately coupled ancilla qubit. These proposals are one possible route to the tangible experimental exploration of quantum thermodynamics, a subject which is the center of much current attention due to the current control of mesoscopic quantum systems. In this Rapid Communication we demonstrate that a modification of the phase estimation protocols can be used in order to measure the heat distribution of a quantum process. In addition, we demonstrate how our scheme maybe implemented using ion trap technology. Our scheme should pave the way for experimental explorations of the Landauer principle and hence the intricate energy to information conversion in mesoscopic quantum systems.
Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola {\it et al}, Phys. Rev. Lett. {\bf 110} 230602 (2013)]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancillary qubit. Here, we expand that work in two important directions. We first apply the protocol to an interesting specific physical example consisting of a superconducting qubit dispersively coupled to the field of a microwave resonator, thus enlarging the class of situations for which our scheme would be key in the task highlighted above. We then account for the interaction of the system with an additional one (which might embody an environment), and generalise the protocol accordingly.
We study an interferometric method for measuring the statistics of work performed on a driven quantum system, which has been put forward recently (Dorner et al 2013 Phys. Rev. Lett. 110 230601, Mazzola et al 2013 Phys. Rev. Lett. 110 230602). This method allows the replacement of two projective measurements of the energy of the driven system with qubit tomography of an ancilla that is appropriately coupled to it. We highlight that this method could be employed to obtain the work statistics of closed as well as open driven system, even in the strongly dissipative regime. We then illustrate an implementation of the method in a circuit QED setup, which allows one to experimentally obtain the work statistics of a parametrically driven harmonic oscillator. Our implementation is an extension of the original method, in which two ancilla-qubits are employed and the work statistics are retrieved through two-qubit state tomography. Our simulations demonstrate the experimental feasibility.
Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola et al., Phys. Rev. Lett.110 (2013) 230602]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancillary qubit. Here, we expand that work in two important directions. We first apply the protocol to an interesting specific physical example consisting of a superconducting qubit dispersively coupled to the field of a microwave resonator, thus enlarging the class of situations for which our scheme would be key in the task highlighted above. We then account for the interaction of the system with an additional one (which might embody an environment), and generalize the protocol accordingly.
Inspired by the idea that quantum computers can be useful in advancing basic science, we use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics, that were not (or were very little) corroborated so far.In order to do so, we first put forward a novel method to implement the so called two-point measurement scheme, which is at the basis of the study of nonequilibrium energetic exchanges in quantum systems.Like previously established methods, our method uses an ancillary system, but at variance with them, it provides direct access to the energy exchange statistics, and is, accordingly more effective, at least when applied to small quantum systems.Using a quantum computer as a remotely programmable experimental platform, we first validate our ancilla-assisted two-point measurement scheme, and then apply it to (i) experimentally verify that fluctuation theorems are robust against projective measurements, a theoretical prediction, which was not validated so far; (ii) experimentally verify the so-called heat-engine fluctuation relation, by implementing a SWAP quantum heat engine; (iii) experimentally verify that the heat-engine fluctuation relation holds for measurement-fueled quantum heat engines, by implementing the design at the basis of the so-called quantum-measurement-cooling concept.For both engines, we report the measured average heat and work exchanged and single out their operation mode.Our experiments constitute an experimental basis for the understanding of the nonequilibrium energetics of quantum computation and for the implementation of energy-management devices on quantum processors.
Thermodynamical properties of quantum systems have been the object of study from many recent papers. In this dissertation, we begin with a brief review of quantum thermodynamics papers, where we focus on the rst law. We show that there are many different denitions of work and heat on quantum systems. We focus on one of the most usual denitions andwe present a recent work from Augusto Roncaglia et al. [1]. On this paper, they propose a method to measure the variation of the internal energy of a quantum system between two instants of time with a single measure by making the system interact with an ancilla twice. This method will be used as a starting point for this dissertation. We will explain how totransform the measurement protocol into one that continuously monitors a system and we will describe some conditions that the system must obey to make this monitoring possible. We show how the ancilla, which will also serve as the measurement apparatus, work and we will dene a quality factor for the measures. At last, we will study a specic system and will show how to use the protocol to obtain the time-dependance of an unknown hamiltonian. In order to do this, we use an algorithm that simulates the measurements proposed here and show that the protocol can not only effectively reconstruct the unknown hamiltonian but also obtain the total work and heat exchanged between the system and a reservoir.
The thermodynamics of quantum processes is a recent field of study and it has been growing in recent years. Previously thought of as an emergent phenomenon for macroscopic systems, thermodynamics started being applied to quantum systems considering quantities such as heat and work as stochastics. The peculiarity of these systems is that, in addition to studying energetic resources, we must also take into account quantum informational resources such as entanglement and coherence. In this scenario, entropy becomes an important quantity, because in addition to being related to the irreversibility of a process, it can also be used as a measure of the amount of information in the system to which we have access. Entropy, unlike energy, is not a conserved quantity; that is, in a closed system, there is not only an entropy flow between it\'s parts, but also, in general, entropy production. According to the principle of Landauer [IBM Journal of Research and Development, vol. 5, no. 3, pp. 183191 (1961)], it is the entropy produced that causes the loss of information. Studying, then, the production of entropy becomes important for areas such as quantum computing, where you want to have control over information gains and losses. In quantum processes, entropy is produced due both to changes in the energy of the system and to fluctuations in coherence [Phys. Rev. E 99, 042105 (2019); npj Quantum Information 5, 23 (2019)], a purely quantum resource. In this project, we propose to study the statistics of entropy production due to coherence. For this, we will investigate two different splittings of the entropy production: the one proposed in [Phys. Rev. E, vol. 99, 042105 (2019); npj Quantum Information 5, 23 (2019)] and a most recent one proposed in [Phys. Rev. Research 2, 023377 (2020); New Journal of Physics 23, 063027 (2021)]. For simplicity, we will analyse a unitary quantum process, using the two-point measurement (TPM) scheme [Phys. Rev. E 75, 050102 (2007)]. We will apply both formalisms for two specific quantum systems: a macrospin model and the Lipkin-Meshkov-Glick (LMG) model [Nuclear Physics, vol. 62, no. 2, pp. 188 224 (1965)]. We will analyse, in these cases, how the distribution of coherence depends on parameters such as system dimension, temperature, evolution in time, etc.