Thermo Field Dynamics on a Quantum Computer

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 Hamiltonians with encoded temperature dependence. The method works normally for fermions, which have a finite representation, but needs some modification to work with bosons. These Hamiltonians 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.

Quantum Computing of Schwarzschild-de Sitter Black Holes and Kantowski-Sachs Cosmology

“…One can can take an approach of thermodynamics using Hamiltonian quantum cosmology [56] [57] [58] [59] [60] or the thermodynamics of Matrix models [61]. In either case quantum computing should be a useful tool to examine the states and thermodynamic observables [62] [63] [64] [65].…”

Z3 gauge theory coupled to fermions and quantum computing

“…Because of the presence of sign problems, finite density, non zero chemical potential and time evolution the Z 3 gauge theory coupled to fermions is an excellent model to pursue quantum advantage over classical computers especially with the increase in the number of qubits and improved development of noise mitigation techniques. It will also be interesting to explore the finite temperature equation of state for this model as well perhaps using a thermo-double approach to realizing finite temperature on a quantum computer [15] [16] [17] [18]. Finally it will be interesting see if the variational Schrodinger wave function approach to higher dimensional QCD [19] [20] [21] [22] [23] [24] can realized in terms of quantum computing by adapting the classical variational techniques to the quantum computing variational approaches in terms of gates on near term quantum hardware.…”

Quantum AI and hybrid simulators for a Universal Quantum Field Computation Model

“…2], by using quantum computational methods to simulate thermodynamic systems and events [7] , [8] , [9] , [10] , [11] , [12] , 23] . Among which are systems in condensed matter physics, e.g., BEC [25] , in HEP, e.g., the Hadron Collider (LHC) [13 , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , 48] , in chemistry and nuclear physics, NMR [16] . To predict new matter forms and system states, the system’s PT or ST is simulated and observed on quantum and classical scales.…”

“…1 displays an imaginary plot projection on such predictive models in some areas of science and technology, including experiments conducted on QFThs, such as LHC, and laser interferometer gravitational-wave observatory (LIGO). The plot shows where in-demand devices for users require greater performance in processing massive amounts of data available on the internet and media, such as Google and IBM [12 , 15 , [22] , [23] , [24] . Nowadays, devices are hybridized between the quantum mechanical and classical computation models [18 , 43 , 44] , as discussed earlier (or see Graphical Abstract, step 5).…”