Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1211.0933 · International Journal of Modern Physics B

QUANTUM INFORMATION, THERMOFIELD DYNAMICS AND THERMALIZED BOSONIC OSCILLATOR

Marco A. S. Trindade, Lourival M. S. Filho, Larissa Couto dos Santos, M. GRAÇAS R. MARTINS, J. D. M. Vianna

Published Aug 16, 2013• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217979213501336

Related papers

Thermofield qubits, generalized expectations and quantum information protocols

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

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.

arXiv:1404.5542•Apr 22, 2014•2 citations

Unitary Encoding of Thermal States via Thermofield Dynamics on Quantum Computers

G. X. A. Petronilo, M. R. Araújo, A. B. M. Souza +1 more

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-$1/2$ particle in a magnetic field agrees with the exact result $M(β)=\tanh(βω/2)$ 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.

quant-pharXiv:2604.00802•Apr 2, 2026•0 citations

Negativity of the Wigner function and thermal effects of Bell-cat states

Vinícius N. A. Lula-Rocha, Sérgio Floquet, Marco A. S. Trindade +2 more

Abstract We applied the thermofield dynamics formalism to analyze how the non-classical properties of the Bell-cat states are influenced by a gradual change of temperature values, in a thermal equilibrium system. To this purpose we calculate the thermal Wigner functions for these states, whose negative volume is associated with non-classical properties, and we evaluate how these non-classical features vary with temperature. Our results indicate that these properties are almost absent for temperatures of around 2 K.

arXiv:2006.16439•Journal of Physics A Mathematical and Theoretical•Aug 17, 2020•1 citation

Quantum computation with logical gates between hot systems

Ferran Riera-Sàbat, Pavel Sekatski, Wolfgang Dür

We consider quantum computer architectures where interactions are mediated between hot qubits that are not in their mechanical ground state. Such situations occur, e.g., when not cooling ideally, or when moving ions or atoms around. We introduce quantum gates between logically encoded systems that consist of multiple physical ones and show how the encoding can be used to make these gates resilient against such imperfections. We demonstrate that, in this way, one can improve gate fidelities by enlarging the logical system, and counteract the effect of unknown positions or position fluctuations of involved particles. We consider both a classical treatment of positions, in terms of probability distributions, and a quantum treatment using mechanical eigenmodes. We analyze different settings including a cool logical system mediating interactions between two hot systems, as well as two logical systems consisting of hot physical systems whose positions fluctuate collectively or individually. In all cases, assuming ideal local control to logical systems, we demonstrate a significant improvement in gate fidelities, which provides a platform-independent tool to mitigate thermal noise in the context of trapped-particle-based architectures. Published by the American Physical Society 2024

arXiv:2311.06588•Physical Review Research•Jul 24, 2024•1 citation

Thermal CNOT gate based on Silicon quantum dots using Tsallis statistics

Behzad Lari, E. Mohammadikhabaz, elham eilkhas +1 more

Abstract We consider a CNOT gate based on Silicon semiconductor quantum dots in thermal non-equilibrium conditions (TNEC). By applying Tsallis statistics, we analyze the time evolution of fidelity between the dot state and Bell state in TNEC, considering the effects of control magnetic fields on the left and right dots, exchange interaction, and microwave frequencies in the presence of environmental exposure. We present a thermal model for the time-dependent behavior of exchange interaction in silicon and compare our findings with experimental data. Our model incorporates physical dimensions and highlights the trade-off between achieving high fidelity near absolute zero temperatures and generating strong, high-frequency point magnetic fields to stabilize the CNOT gate. We determine that q > 1 is the optimal geometric region for extending gate lifetime. Utilizing quantum materials to generate strong point fields and topological manipulation of the qubit could be a viable approach to achieve such a gate. We aim to manipulate states to achieve high fidelity using control magnetic fields to create a functional CNOT gate in thermal noise, simultaneously ensuring strong entanglement between the dots.

Physica Scripta•Oct 1, 2025•2 citations

Thermofield Theory for Finite-Temperature Electronic Structure

Gaurav Harsha, Thomas M. Henderson, Gustavo E. Scuseria

Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. They also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.

arXiv:2303.12318•The Journal of Physical Chemistry A•Apr 5, 2023•10 citations
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.
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.
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.
Abstract We applied the thermofield dynamics formalism to analyze how the non-classical properties of the Bell-cat states are influenced by a gradual change of temperature values, in a thermal equilibrium system. To this purpose we calculate the thermal Wigner functions for these states, whose negative volume is associated with non-classical properties, and we evaluate how these non-classical features vary with temperature. Our results indicate that these properties are almost absent for temperatures of around 2 K.
We consider quantum computer architectures where interactions are mediated between hot qubits that are not in their mechanical ground state. Such situations occur, e.g., when not cooling ideally, or when moving ions or atoms around. We introduce quantum gates between logically encoded systems that consist of multiple physical ones and show how the encoding can be used to make these gates resilient against such imperfections. We demonstrate that, in this way, one can improve gate fidelities by enlarging the logical system, and counteract the effect of unknown positions or position fluctuations of involved particles. We consider both a classical treatment of positions, in terms of probability distributions, and a quantum treatment using mechanical eigenmodes. We analyze different settings including a cool logical system mediating interactions between two hot systems, as well as two logical systems consisting of hot physical systems whose positions fluctuate collectively or individually. In all cases, assuming ideal local control to logical systems, we demonstrate a significant improvement in gate fidelities, which provides a platform-independent tool to mitigate thermal noise in the context of trapped-particle-based architectures. Published by the American Physical Society 2024
Abstract We consider a CNOT gate based on Silicon semiconductor quantum dots in thermal non-equilibrium conditions (TNEC). By applying Tsallis statistics, we analyze the time evolution of fidelity between the dot state and Bell state in TNEC, considering the effects of control magnetic fields on the left and right dots, exchange interaction, and microwave frequencies in the presence of environmental exposure. We present a thermal model for the time-dependent behavior of exchange interaction in silicon and compare our findings with experimental data. Our model incorporates physical dimensions and highlights the trade-off between achieving high fidelity near absolute zero temperatures and generating strong, high-frequency point magnetic fields to stabilize the CNOT gate. We determine that q > 1 is the optimal geometric region for extending gate lifetime. Utilizing quantum materials to generate strong point fields and topological manipulation of the qubit could be a viable approach to achieve such a gate. We aim to manipulate states to achieve high fidelity using control magnetic fields to create a functional CNOT gate in thermal noise, simultaneously ensuring strong entanglement between the dots.
Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. They also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.