Abstract Decoherence has been observed to be one of the main limitations to build a practical quantum computer. This is because the qubits that conform it rapidly lose the entanglement and correlations existent among them due to interactions with the environment. In this work, the relaxation time of a Transmon qubit interacting with an environment is predicted by using the steepest-entropy-ascent quantum thermodynamics framework and the Lindblad master equation. For the study it is considered that the environment behaves as a thermal bath composed of a collection of harmonic oscillators. Results show that the qubit processes from a non-equilibrium state to a state of stable equilibrium, exchanging energy with the thermal bath during the process. In addition, the prediction of the relaxation time of the qubit is in agreement with experimental results obtained from the literature. The decoherence time is also accurately predicted by the models.
Abstract Decoherence has been observed to be one of the main limitations to build a practical quantum computer. This is because the qubits that conform it rapidly lose the entanglement and correlations existent among them due to interactions with the environment. In this work, the relaxation time of a Transmon qubit interacting with an environment is predicted by using the steepest-entropy-ascent quantum thermodynamics framework and the Lindblad master equation. For the study it is considered that the environment behaves as a thermal bath composed of a collection of harmonic oscillators. Results show that the qubit processes from a non-equilibrium state to a state of stable equilibrium, exchanging energy with the thermal bath during the process. In addition, the prediction of the relaxation time of the qubit is in agreement with experimental results obtained from the literature. The decoherence time is also accurately predicted by the models.
Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation.
The current stage of quantum computing technology, called noisy intermediate-scale quantum technology, is characterized by large errors that prohibit it from being used for real applications. In these devices, decoherence, one of the main sources of error, is generally modeled by Markovian master equations such as the Lindblad master equation. In this paper, the decoherence phenomena are addressed from the perspective of the steepest-entropy-ascent quantum thermodynamics framework in which the noise is in part seen as internal to the system. The framework is as well used to describe changes in the energy associated with environmental interactions. Three scenarios, an inversion recovery demonstration, a Ramsey demonstration, and a two-qubit entanglement-disentanglement demonstration, are used to demonstrate the applicability of this framework, which provides good results relative to the demonstrations and the Lindblad equation; it does so, however, from a different perspective as to the cause of the decoherence. These demonstrations are conducted on the IBM superconducting quantum device ibmqbogota.
The thermodynamics of a qubit undergoing dephasing due to the coupling with the external environment is discussed. First of all, we assume the dynamics of the system to be described by a master equation in Lindblad form. In this framework, we review a standard formulation of the first and second law of thermodynamics that has been known in literature for a long time. After that, we explicitly model the environment with a set of quantum harmonic oscillators choosing the interaction such that the global dynamics of system and bath is analytically solvable and the Lindblad master equation is recovered in the weak-coupling limit. In this generalized setting, we can show that the correlations between system and bath play a fundamental role in the heat exchange. Moreover, the internal entropy production of the qubit is proven to be positive for arbitrary coupling strength.
The quantum Mpemba effect describes the unusual relaxation of a quantum system where if starting from a state far from equilibrium reaches equilibrium faster than starting from a closer state. In this work, the steepest-entropy ascent quantum thermodynamics framework is used to model this effect in a three-level ion system coupled to a short-life level which acts as an environment. The four-level Hilbert space is reduced to an effective three-dimensional description via the Feshbach projection, where the resulting model parameters are determined by a differential evolution algorithm. Predictions of both the steepest-entropy-ascent and Lindblad frameworks agree well with experimental data for all three initial conditions considered. In addition it is shown that, independently of the Mpemba condition, the relaxation parameter τD is an emergent thermodynamic quantity whose step-function time dependence arises from a near-indetermination at the metastable state, resolved by the two-timescale structure of the dissipative dynamics, with a step height τD+/τD−(∣λf∣/∣λs∣)r set by the ratio of the linearised relaxation rates at the metastable state times a geometric factor r fixed by the curvature of the entropy and free-energy-variance surfaces there. Furthermore, it is also established the correspondence between the Lindblad and steepest-entropy-ascent order parameters as spectral and geometric suppression of the same slow dissipative mode, and it is shown that for isolated systems with a negative nonequilibrium inverse temperature, as realized in the case studied here, the genuine Mpemba free-energy ordering is equivalent to an entropy ordering.
The equation of motion of steepest-entropy-ascent quantum thermodynamics (SEA-QT) was first postulated in the early 1980s with the intent of modeling the non-linear dynamic behavior encountered in nature, which the unitary (linear) dynamics of the Schrödinger-von Neumann equation cannot. The SEA-QT equation is used here to model the decoherence phenomenon between two distinguishable and indivisible elementary constituents of type spin–½ (e.g., quantum bits or qubits). The resulting set of non-linear, first-order differential equations is solved with a fourth-order-Runge-Kutta routine provided by Matlab®. The time evolution of the state of the composite system as well as that of the reduced and locally-perceived states of the two constituents are traced from an initial non-equilibrium state of the composite along its relaxation towards stable equilibrium at constant system energy. An entangled and generally coherent, initial non-equilibrium state of the composite quantum system is prepared using a heuristic approach, which consists of randomly and homogeneously generating an initial point on the Bloch sphere for each of the constituents and then using a weighted average of their projections to arrive at an initial state for the composite. Results show how the initial entanglement and coherence between the two spin–½ constituents are reduced during relaxation towards a state of stable equilibrium. When the two particles are non-interacting, the initial coherence is lost once stable equilibrium is reached. When they are interacting, the coherence in the final stable equilibrium state is only that due to the interaction.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2 with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.