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 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.

Revista Brasileira de Ensino de FísicaJan 1, 20231 citation

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.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:2604.00802Apr 2, 20260 citations

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.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:1404.5542Apr 22, 20142 citations

Double-bracket quantum algorithms for thermal state preparation

Andrew Wright, Reyhaneh Aghaei Saem, Supanut Thanasilp +2 more

We propose quantum algorithms for preparing thermal states via the simulation of the thermofield double states. The key idea is to leverage double-bracket quantum algorithms to implement imaginary-time evolution on thermofield double states, whose reduced state realizes the Gibbs state. Our method, termed double-bracket thermofield double (DB-TFD), introduces two variants. The first, the vanilla DB-TFD algorithm, directly implements imaginary-time evolution using double-bracket quantum imaginary-time evolution. The second, poly DB-TFD, employs double-bracket quantum signal processing to approximate the imaginary-time evolution operator via a polynomial transformation. We demonstrate that the complexity of the poly DB-TFD algorithm scales exponentially with the inverse temperature in a broad practical regime. This scaling is consistent with existing methods, and numerical simulations support the corresponding theoretical bound. We further demonstrate the utility of DB-TFD in quantum Boltzmann machines for generative modeling, achieving improved performance compared with variational imaginary-time evolution approaches. These results establish DB-TFD as a promising route for thermal state preparation in the near-term and early-fault-tolerant regimes.We propose quantum algorithms for preparing thermal states via the simulation of the thermofield double states. The key idea is to leverage double-bracket quantum algorithms to implement imaginary-time evolution on thermofield double states, whose reduced state realizes the Gibbs state. Our method, termed double-bracket thermofield double (DB-TFD), introduces two variants. The first, the vanilla DB-TFD algorithm, directly implements imaginary-time evolution using double-bracket quantum imaginary-time evolution. The second, poly DB-TFD, employs double-bracket quantum signal processing to approximate the imaginary-time evolution operator via a polynomial transformation. We demonstrate that the complexity of the poly DB-TFD algorithm scales exponentially with the inverse temperature in a broad practical regime. This scaling is consistent with existing methods, and numerical simulations support the corresponding theoretical bound. We further demonstrate the utility of DB-TFD in quantum Boltzmann machines for generative modeling, achieving improved performance compared with variational imaginary-time evolution approaches. These results establish DB-TFD as a promising route for thermal state preparation in the near-term and early-fault-tolerant regimes.

quant-pharXiv:2606.05947Jun 5, 20260 citations

Thermal Schrödinger Equation: Efficient Tool for Simulation of Many‐Body Quantum Dynamics at Finite Temperature

Maxim F. Gelin, Raffaele Borrelli

Abstract We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.Abstract We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.

Annalen der PhysikSep 6, 201737 citations

Teaching quantum computing to computer science students: Review of a hands-on quantum circuit simulation practical

Florian Krötz, Xiao-Ting Michelle To, Korbinian Staudacher +1 more

We present a practical course targeting graduate students with prior knowledge of the basics of quantum computing. The practical aims to deepen students' understanding of fundamental concepts in quantum computing by implementing quantum circuit simulators. Through hands-on experience, students learn about different methods to simulate quantum computing, including state vectors, density matrices, the stabilizer formalism, and matrix product states. By implementing the simulation methods themselves, students develop a more in-depth understanding of fundamental concepts in quantum computing, including superposition, entanglement, and the effects of noise on quantum systems. This hands-on experience prepares students to do research in the field of quantum computing and equips them with the knowledge and skills necessary to tackle complex research projects in the field. In this work, we describe our teaching approach and the structure of our practical, and we discuss evaluations and lessons learned.We present a practical course targeting graduate students with prior knowledge of the basics of quantum computing. The practical aims to deepen students' understanding of fundamental concepts in quantum computing by implementing quantum circuit simulators. Through hands-on experience, students learn about different methods to simulate quantum computing, including state vectors, density matrices, the stabilizer formalism, and matrix product states. By implementing the simulation methods themselves, students develop a more in-depth understanding of fundamental concepts in quantum computing, including superposition, entanglement, and the effects of noise on quantum systems. This hands-on experience prepares students to do research in the field of quantum computing and equips them with the knowledge and skills necessary to tackle complex research projects in the field. In this work, we describe our teaching approach and the structure of our practical, and we discuss evaluations and lessons learned.

physics.ed-phCross-listedarXiv:2511.17218IEEE International Conference on Quantum Computing and Engineering (QCE)Nov 24, 20250 citations

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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.