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arXiv:1404.5542

Thermofield qubits, generalized expectations and quantum information protocols

Thiago Prudêncio, T. M. Rocha Filho, Ademir Eugenio de Santana

Published Apr 22, 2014• 2 citations
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Abstract

Thermofield dynamics (TFD) approach is a real time quantum field method for dealing with finite temperature quantum states in a purified version of usual density operator formalism at finite temperature. In the domain of quantum information, TFD represents a quite promising direction for dealing with qubits under thermal influence and can also be associated to Gaussian states. Here, we propose a generalized TFD mean expectation for the case of thermofield qubits considering the action of gate operators. We propose quantum teleportation protocols involving thermofield states, considering thermal-to-thermal and thermal-to-non-thermal transfering cases. In particular, we discuss the case in which Alice and Bob are at different temperatures. Action of gate operators on the result of the Mandel parameter for thermofields and on Gibbs-like density operators are also discussed. The no-cloning and non-broadcasting theorems in TFD are also considered and cases of superposed thermofield states and maps connecting thermofield vacua at different temperatures are also addressed and associated to metastable and non-equilibrium scenarios.

DOI
10.48550/arxiv.1404.5542

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Thermofield dynamics (TFD) approach is a real time quantum field method for dealing with finite temperature quantum states in a purified version of usual density operator formalism at finite temperature. In the domain of quantum information, TFD represents a quite promising direction for dealing with qubits under thermal influence and can also be associated to Gaussian states. Here, we propose a generalized TFD mean expectation for the case of thermofield qubits considering the action of gate operators. We propose quantum teleportation protocols involving thermofield states, considering thermal-to-thermal and thermal-to-non-thermal transfering cases. In particular, we discuss the case in which Alice and Bob are at different temperatures. Action of gate operators on the result of the Mandel parameter for thermofields and on Gibbs-like density operators are also discussed. The no-cloning and non-broadcasting theorems in TFD are also considered and cases of superposed thermofield states and maps connecting thermofield vacua at different temperatures are also addressed and associated to metastable and non-equilibrium scenarios.
Abstract Quantum teleportation of thermofields in the context of thermofield dynamics (TFD) at single and two thermal baths is proposed. We show using TFD that the non-local correlations associated to the quantum channel and temperature effects in each subsystem can be treated separately, allowing teleportation even if the systems A and B are considered at different temperatures. As a consequence, the temperature effect is treated locally in each subsystem, while the quantum correlation protocol is used for non-locality, allowing the systems A and B be separated at long distances at different temperatures for implementation of the protocol.
Quantum computing has attracted the attention of the scientific community in the past few decades. The development of quantum computers promises one path toward safer and faster ways to treat, extract, and transfer information. However, despite the significant advantages of quantum computing, the development of quantum devices operating at room temperature has been compromised by the thermal decoherence process. In addition, in most undergraduate and graduate quantum mechanics courses, the study of thermofield dynamics is usually neglected. In this scenario, this work presents a didactic approach to simulate thermal qubit systems through Thermofield Dynamics (TFD), applied in a quantum computing setup. The results show that the Bloch sphere representation for a qubit can be written in terms of the Bogoliubov transformation, which allows a practical construction for the thermal qubits in a quantum computing setup. Therefore, this work introduces thermofield dynamics through quantum computing to teachers and curious students interested in teaching and learning this important field of studying the temperature impacts on quantum protocols using the TFD technique.
Quantum computing has attracted the attention of the scientific community in the past few decades. The development of quantum computers promises one path toward safer and faster ways to treat, extract, and transfer information. However, despite the significant advantages of quantum computing, the development of quantum devices operating at room temperature has been compromised by the thermal decoherence process. In addition, in most undergraduate and graduate quantum mechanics courses, the study of thermofield dynamics is usually neglected. In this scenario, this work explores a didactic approach to simulate thermal qubit systems through Thermofield Dynamics (TFD), applied in a quantum computing setup. The results show that the Bloch sphere representation for a qubit can be written in terms of the Bogoliubov transformation, which allows a practical construction for the thermal qubits in a quantum computing setup. Therefore, this work introduces thermofield dynamics through quantum computing to teachers and curious students interested in teaching and learning this important field of studying the temperature impacts on quantum protocols using the TFD technique.
Quantum computing has attracted the attention of the scientific community in the past few decades. However, despite some relevant advantages, near-term quantum devices remain severely limited by thermal effects, which induce decoherence and restrict coherent control at finite temperature. In this regard, this work reports a gate-based quantum algorithm that prepares the finite-temperature vacuum of Thermofield Dynamics (TFD) and tracks its real-time evolution. The circuit depth scales linearly with system size and requires only single-qubit rotations and nearest-neighbor CNOT gates, making it NISQ-friendly. We benchmark the protocol on the PennyLane simulator: magnetization of a spin-1/21/21/2 particle in a magnetic field agrees with the exact result M(β)=tanh⁡(βω/2)M(β)=\tanh(βω/2)M(β)=tanh(βω/2) to machine precision, and the coherent precession acquires a temperature-dependent damping that quantitatively matches the analytical TFD prediction. Our work provides a ready-to-deploy toolbox for thermal quantum simulations and opens a route to study dissipative phase transitions, quantum thermodynamics and thermal machine-learning models on near-term devices.
We show through Thermofield Dynamics approach that the action of the thermalized quantum logic gate on the thermalized state is equivalent to thermalization of the state that arise from the application of the nonthermalized quantum logic gate. In particular, we study the effect of temperature on a mixed state associated to a system capable of implementing a controlled-NOT (CNOT) quantum logic gate. According to a proposal in the literature, a way of implementing such a logic gate is by using a representation of the qubit states as elements of the Fock space of a bosonic system. We consider such a proposal and use the Thermofield Dynamics to determine the thermalized qubit states. The temperature acts as a quantum noise on pure states, making them a statistical mixture. In this context, we analyze the fidelity as a function of the temperature and using the Mandel parameter, we determine temperature ranges for which the statistics of the system becomes subpoissonian, poissonian and superpoissonian. Finally, we calculate the Wigner function, allowing an analysis of the thermal state in phase space, and we obtain that the increase of temperature decreases nonclassical properties of the system. The temperature range where one has a subpoissonian statistics and high fidelity is determined.