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arXiv:2604.00802

Unitary Encoding of Thermal States via Thermofield Dynamics on Quantum Computers

G. X. A. Petronilo, M. R. Araújo, A. B. M. Souza, Clebson Cruz

quant-phSubmitted Apr 1, 2026• Announced Apr 2, 2026• 0 citations
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Abstract

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.

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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.
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.
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.
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.
The efficient preparation of correlated thermal states, such as the Thermofield Double (TFD) state, is a fundamental prerequisite for simulating quantum gravity models and many-body thermodynamics on quantum processors. In this work, we investigate the ground state preparation of the Two Coupled Sachdev-Ye-Kitaev model, known as the Maldacena-Qi model, which is dual to a traversable wormhole in AdS2AdS_2AdS2​, utilizing feedback-based quantum algorithms. We demonstrate that the standard feedback-based quantum algorithm (FALQON) and its time-rescaled variant (TR-FALQON) face severe kinetic limitations in this system, failing to converge to the highly entangled ground state when initialized in trivial product states. To overcome these barriers, we propose the hybrid ITE-TR-FALQON protocol, which integrates the imaginary-time evolution present in imaginary-time-enhanced FALQON (ITE-FALQON) with the time-rescaling mechanism. Our numerical results indicate that the introduction of non-unitary dynamics is strictly necessary to break symmetry traps and filter out excited states, while time-rescaling drastically accelerates algorithm convergence. The proposed method achieves fidelities close to unity and reproduces the von Neumann and Rényi entropy spectra of the exact TFD state with high precision.
We present a variational approach for quantum simulators to realize finite temperature Gibbs states by preparing thermofield double (TFD) states. Our protocol is motivated by the quantum approximate optimization algorithm and involves alternating time evolution between the Hamiltonian of interest and interactions which entangle the system and its auxiliary counterpart. As a simple example, we demonstrate that thermal states of the 1D classical Ising model at any temperature can be prepared with perfect fidelity using L/2 iterations, where L is system size. We also show that a free fermion TFD can be prepared with nearly optimal efficiency. Given the simplicity and efficiency of the protocol, our approach enables near-term quantum platforms to access finite temperature phenomena via preparation of thermofield double states.
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.