## What is/are Double State?

Double State - Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation.^{[1]}We obtain an entanglement renormalization scheme for finite-temperature (Gibbs) states by applying the multiscale entanglement renormalization ansatz to their canonical purification, the thermofield double state.

^{[2]}So far, most of the studies have found singe topological element of different types and the coexistence of double states in a sole material is very scarce, not to mention the three types together.

^{[3]}For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian.

^{[4]}A pair of identical Sachdev-Ye-Kitaev (SYK) models with bilinear coupling forms a quantum dual of a traversable wormhole, with a ground state close to the so called thermofield double state.

^{[5]}In this contribution, we present an improved robust filter with a double state model on the basis of the chi-square distribution of the square of the Mahalanobis distance.

^{[6]}We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state.

^{[7]}The fidelity between the initial and time-evolving thermofield double states exhibits as a function of time a decay, dip, ramp, and plateau.

^{[8]}The exponential stability problem for impulsive systems subject to double state-dependent delays is studied in this paper, where state-dependent delay (SDD) is involved in both continuous dynamics and discrete dynamics and the boundedness of it with respect to states is prior unknown.

^{[9]}It is also argued that several artifacts, such as the unphysical negative-time interval, can be removed by truly considering the bulk dual of the thermofield double state.

^{[10]}We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static patches.

^{[11]}Profound threats to national security – such as 9/11 – thus stipulate the authoritative exertion of extraconstitutional competency-manifested in the unique conditions of President Bush’s declaration of double state emergency.

^{[12]}As an example, we consider the complexity of a charged thermofield double state constructed from two free massive complex scalar fields in the presence of a chemical potential.

^{[13]}In this way, we can answer the question that lies at the bottom of this double statement, and that rests on the perplexity that its concept of equality awakens: What does it do, how does it work, in short, how does his concept of equality act?.

^{[14]}In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao, Jafferis and Wall.

^{[15]}The two leading conjectures on this subject hold that the quantum complexity of the boundary thermofield double state should be dual to either the volume of the Einstein-Rosen bridge connecting the two sides (CV conjecture) or to the action of the Wheeler-de-Witt patch of the bulk spacetime (CA conjecture).

^{[16]}We study Nielsen’s circuit complexity for a charged thermofield double state (cTFD) of free complex scalar quantum field theory in the presence of background electric field.

^{[17]}We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS$_3$ black holes, both for the action and the volume conjectures.

^{[18]}Given the simplicity and efficiency of the protocol, our approach enables near-term quantum platforms to access finite temperature phenomena via preparation of thermofield double states.

^{[19]}In four bulk dimensions, we propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the two boundaries Hilbert spaces, whereby the Gibbons--Hawking formula arises as the holographic entanglement entropy between the past and future conformal infinities.

^{[20]}We study traversable wormholes by considering the duality between BTZ black holes and two-dimensional conformal field theory on the thermofield double state.

^{[21]}In this paper, we study the thermofield double states in group field theories.

^{[22]}The states are constructed by adding sources for a scalar operator to the path integral that constructs the thermofield double state.

^{[23]}We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states.

^{[24]}Likewise, this critical coupling also corresponds to the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest.

^{[25]}The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entanglement entropy.

^{[26]}The newly constructed class of thermal vacua are entangled, two-mode squeezed, thermofield double states.

^{[27]}Here we propose to realize this protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state.

^{[28]}Motivated by the holographic complexity proposals, in this paper, we investigate the time dependence of the complexity for the Fermionic thermofield double state (TFD) using the Nielsen approach and Fubini-Study (FS) approach separately.

^{[29]}We give a dual large c CFT description in terms of a thermofield double state with different temperatures for left and right moving modes that is perturbed by a local operator.

^{[30]}Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space.

^{[31]}

## Thermofield Double State

Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation.^{[1]}We obtain an entanglement renormalization scheme for finite-temperature (Gibbs) states by applying the multiscale entanglement renormalization ansatz to their canonical purification, the thermofield double state.

^{[2]}For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian.

^{[3]}A pair of identical Sachdev-Ye-Kitaev (SYK) models with bilinear coupling forms a quantum dual of a traversable wormhole, with a ground state close to the so called thermofield double state.

^{[4]}We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state.

^{[5]}The fidelity between the initial and time-evolving thermofield double states exhibits as a function of time a decay, dip, ramp, and plateau.

^{[6]}It is also argued that several artifacts, such as the unphysical negative-time interval, can be removed by truly considering the bulk dual of the thermofield double state.

^{[7]}We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static patches.

^{[8]}As an example, we consider the complexity of a charged thermofield double state constructed from two free massive complex scalar fields in the presence of a chemical potential.

^{[9]}In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao, Jafferis and Wall.

^{[10]}The two leading conjectures on this subject hold that the quantum complexity of the boundary thermofield double state should be dual to either the volume of the Einstein-Rosen bridge connecting the two sides (CV conjecture) or to the action of the Wheeler-de-Witt patch of the bulk spacetime (CA conjecture).

^{[11]}We study Nielsen’s circuit complexity for a charged thermofield double state (cTFD) of free complex scalar quantum field theory in the presence of background electric field.

^{[12]}We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS$_3$ black holes, both for the action and the volume conjectures.

^{[13]}Given the simplicity and efficiency of the protocol, our approach enables near-term quantum platforms to access finite temperature phenomena via preparation of thermofield double states.

^{[14]}In four bulk dimensions, we propose an holographic description of an inertial observer in terms of a thermofield double state in the tensor product of the two boundaries Hilbert spaces, whereby the Gibbons--Hawking formula arises as the holographic entanglement entropy between the past and future conformal infinities.

^{[15]}We study traversable wormholes by considering the duality between BTZ black holes and two-dimensional conformal field theory on the thermofield double state.

^{[16]}In this paper, we study the thermofield double states in group field theories.

^{[17]}The states are constructed by adding sources for a scalar operator to the path integral that constructs the thermofield double state.

^{[18]}We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states.

^{[19]}Likewise, this critical coupling also corresponds to the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest.

^{[20]}The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entanglement entropy.

^{[21]}The newly constructed class of thermal vacua are entangled, two-mode squeezed, thermofield double states.

^{[22]}Here we propose to realize this protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state.

^{[23]}Motivated by the holographic complexity proposals, in this paper, we investigate the time dependence of the complexity for the Fermionic thermofield double state (TFD) using the Nielsen approach and Fubini-Study (FS) approach separately.

^{[24]}We give a dual large c CFT description in terms of a thermofield double state with different temperatures for left and right moving modes that is perturbed by a local operator.

^{[25]}Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space.

^{[26]}