Unitary Encoding of Thermal States via Thermofield Dynamics on Quantum Computers

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.

Figures (4)

• Figure 1: Magnetization $\langle M_z \rangle$ as a function of inverse temperature $\beta$ (blue line) compared to the theoretical result (black dashed line). The $\langle M_x \rangle$ and $\langle M_y \rangle$ components (red and green lines) are zero, as expected for the thermal vacuum state.
• Figure 2: Magnetization components of the superposition state $|+\widetilde{0}\rangle$ at $\beta = 1$. The transverse components $\langle M_x \rangle$ and $\langle M_y \rangle$ show partial amplitude due to thermal damping, while $\langle M_z \rangle$ is negative as expected.
• Figure 3: Time evolution of the expectation values $\langle M_x(t) \rangle$, $\langle M_y(t) \rangle$, and $\langle M_z(t) \rangle$ for $|+\widetilde{0}\rangle$ at $\beta = 1$. The transverse oscillations are damped by $\cos\theta$, while the longitudinal component remains negative.
• Figure 4: Time evolution of the transverse magnetization $\langle M_x(t) \rangle$ for different inverse temperatures $\beta$. The amplitude of oscillation decreases with increasing temperature, consistent with the TFD thermal damping factor $\cos\theta$.