Introduction to Double State

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]