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Physics Letters B

Thermo field boson realizations for operators of the finite temperature random phase approximation

Nguyen Dinh Dang

Published Oct 1, 1989• 3 citations
Publisher
DOI
10.1016/0370-2693(89)91153-2

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A comparative study of the random phase approximation is reported in the case of the following three approaches based on the thermo field dynamics formalism: (A) the Tanabe approach, (B) the Hatsuda approach and (C) the approach developed by the present authors. The basic viewpoint is to formulate the random phase approximation by picking up the quadratic terms with respect to bosons in the boson expansion theory for the thermo field dynamics formalism. It is concluded that the approach (C) appears to be superior to the other two approaches.
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.