2020
DOI: 10.1103/physrevd.101.126007
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Circuit complexity for generalized coherent states in thermal field dynamics

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Cited by 30 publications
(27 citation statements)
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“…While the inverse metric of a degenerate metric cannot be defined, we will use what we refer to as the equivalent metric method to define its substitute. 18 To this end, consider first the problem of geodesic motion on a finite-dimensional degenerate metric, i.e. a metric g µν with det(g) = 0 and hence an eigenvector k µ with eigenvalue zero: k µ g µν = 0.…”
Section: Jhep12(2020)091mentioning
confidence: 99%
See 1 more Smart Citation
“…While the inverse metric of a degenerate metric cannot be defined, we will use what we refer to as the equivalent metric method to define its substitute. 18 To this end, consider first the problem of geodesic motion on a finite-dimensional degenerate metric, i.e. a metric g µν with det(g) = 0 and hence an eigenvector k µ with eigenvalue zero: k µ g µν = 0.…”
Section: Jhep12(2020)091mentioning
confidence: 99%
“…The approach elucidated above was originally introduced in [1][2][3] as a way of bounding qubit circuits preparing unitary transformations of interest in the context of quantum computing and currently serves as our best definition of complexity in the QFT setting. In the course of the past three years starting with [4,5] many results were delivered on complexity of quantum fields by focusing in the vast majority of cases on free QFTs soluble via Gaussian techniques [6], see [7][8][9][10][11][12][13][14][15][16][17][18] for sample developments.…”
Section: Jhep12(2020)091 Introductionmentioning
confidence: 99%
“…Various studies have explored the complexity of quantum circuits made by pure Gaussian states in lattice models [17][18][19][20][21][22][23][24][25][26][27]. In these cases the gates implement only unitary transformations of the state.…”
Section: Jhep12(2020)101mentioning
confidence: 99%
“…Besides the reference state, the target state and the set of allowed gates, the circuit complexity can depend also on the tolerance parameter for the target state. Many results have been obtained for the complexity of quantum circuits made by pure states constructed through lattice models [17][18][19][20][21][22][23][24][25] and in the gravitational side of the holographic correspondence. Some proposals have been done also to study the circuit complexity in quantum fields theories [26][27][28][29][30][31][32][33][34][35][36][37][38].…”
Section: Introductionmentioning
confidence: 99%