Thermo Field Dynamics on a Quantum Computer
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Abstract
In this project we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we implemented a real-time therom field dynamics formalism, which has the added benefit of being able to compute quantities that are both time-and temperature-dependent. To implement thermo field dynamics we apply a unitary transformation [1] to discrete quantum mechanical operators to make new Hamiltoni-ans with encoded temperature dependence. The method works normally for fermions, which have a finite representation, but needs some modification to work with bosons. These Hamilto-nians are then processed into a Pauli matrix representation in order to be used as input for IBM's Qiskit package [2]. We then use IBM's quantum simulator to calculate an approximation to the Hamiltonaian's ground state energy via the variational quantum eigensolver (VQE) algorithm [3]. This approximation is then compared to a classically calculated value for the exact energy. The thermo field dynamics quantum algorithm has general applications to material science, high-energy physics and nuclear physics, particularly in those situations involving realtime evolution at high temperature.