Variational Approaches to the Dynamics of Mixed Quantum States

Seogjoo Jang

Christina V. Kraus, Tobias J. Osborne

We extend the time-dependent variational principle to the setting of dissipative dynamics. This provides a locally optimal (in time) approximation to the dynamics of any Lindblad equation within a given variational manifold of mixed states. In contrast to the pure-state setting, there is no canonical information geometry for mixed states, and this leads to a family of possible trajectories---one for each information metric. We focus on the case of the operationally motivated family of monotone Riemannian metrics and show further that, in the particular case where the variational manifold is given by the set of fermionic Gaussian states, all of these possible trajectories coincide. We illustrate our results in the case of the Hubbard model subject to spin decoherence.

T. Matsui

Xiao Yuan, Suguru Endo, Qi Zhao +2 more

The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.

Philipp O. J. Scherer

M. Yamamura, A. Kuriyama, Y. Tsue

To appear in those proceedings.OCR Output 'Invited talk presented by M. Y. at the conference on "Many-Body Physics", Coimbra, Portugal, mixed states in highly excited nucleus.5•°•7 been formulated as the Dirac canonical formalism with constraints in order to describe the time-dependent variational principle and thermo field dynamics.This theory has Fiolhais, have also developed a microscopic theory for mixed states based on both is investigated.4Two of the authors (M.Y. and A.K.), together with Providéncia and based on the thermo field dynamics and the variation of the thermodynamic potential the thermo field dynamicsz has progressed,3 and the relation between the treatments description of mixed states in many-fermion systems.}Also, the treatment based on For example, the thermal boson expansion theory has been studied in the microscopic various attempts to describe the systems in the excited states have been developed.particle physics.In the field of microscopic theory in nuclear many-body systems, in highly excited states, has been one of the interesting problems in quantum many-The theoretical study of systems in highly excited states, such as nucleus observed a correct classical counterpart is examined and explicitly constructed as "mixed-means of time-dependent variational procedure, a possible state which can offerIn order to investigate quantal systems governed by su(1,1)-algebra by