Quantum dynamics in classical thermal baths

Blind Review

When admissible states and dynamics are restricted to pure states and reversible dynamics, the BBBV theorem largely prohibits exponential speedup of quantum search over classical search. However, the recent Chen-Huang-Preskill-Zhou (CHPZ) quantum (thermal) gradient descent proposal suggests system-heat bath interactions may offer more by leveraging irreversible dynamics. We simplify the complex CHPZ analysis by casting everything in terms of quantum equilibrium thermodynamics with some loss of generality. The key point is that different initial system temperatures arise depending on the answer of a decision problem despite sharing the same initial n-qubit system (thermal) state - infinite temperature (for the yes answer) versus the heat bath temperature (for the no answer). By tracing dynamics of either the n-qubit system or heat baths, the decision problem may be solved efficiently - quantum thermal search. Some issues with the efficiency conclusion are explored, in terms of either simulating thermal interactions with polynomially-scaling inverse bath temperature or accuracy of heat bath approximations.

Smitha Vishveshwara, Aashish A. Clerk, P. Nalbach

Alessandro Sergi

A novel method is introduced in order to treat the dissipative dynamics of quantum systems interacting with a bath of classical degrees of freedom. The method is based upon an extension of the Nosè–Hoover chain (constant temperature) dynamics to quantum-classical systems. Both adiabatic and nonadiabatic numerical calculations on the relaxation dynamics of the spin-boson model show that the quantum-classical Nosè–Hoover chain dynamics represents the thermal noise of the bath in an accurate and simple way. Numerical comparisons, both with the constant-energy calculation and with the quantum-classical Brownian motion treatment of the bath, show that the quantum-classical Nosè–Hoover chain dynamics can be used to introduce dissipation in the evolution of a quantum subsystem even with just one degree of freedom for the bath. The algorithm can be computationally advantageous in modelling, within computer simulation, the dynamics of a quantum subsystem interacting with complex molecular environments.

Peter J. Rossky

Dario Patanè, Alessandro Silva, Fernando Sols +1 more

We investigate the dissipative dynamics of a quantum critical system in contact with a thermal bath, focusing on the response of the system to a sudden change of the bath temperature, in analogy to studies of aging. The specific example of the XY model in a transverse magnetic field whose spins are locally coupled to a set of bosonic baths is considered. We analyze the spin-spin correlations and block correlations and identify some universal features in the out-of-equilibrium dynamics. Two distinct regimes, characterized by different time and length scales, emerge. The initial transient dynamics is characterized by the same critical exponents as those of the equilibrium quantum phase transition and resembles the dynamics of thermal phase transitions. At long times equilibrium is reached through the propagation along the chain of a thermal front in a manner similar to the classical Glauber dynamics.