Circuit complexity and 2D bosonisation

Ge, Dongsheng; Policastro, Giuseppe

doi:10.1007/jhep10(2019)276

Cited by 19 publications

(18 citation statements)

References 37 publications

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“…In this section we adapt the analysis of [6,41] (see also [42][43][44][45][46]) to study the complexity of the ground state of the harmonic chain on a segment with Dirichlet boundary conditions with respect to a particular factorized Gaussian state. The method, first developed by Nielsen et al [2][3][4], boils down to the calculation of the length of geodesics in the "space of circuits", namely that of unitary transformations connecting the states at hand.…”

Section: Complexity In the Harmonic Chain With Dirichlet Boundary Conmentioning

confidence: 99%

Complexity in the presence of a boundary

Paolo

Cotrone

Tonni

2020

J. High Energ. Phys.

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The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual of the complexity, including the "Complexity = Volume" (CV) and "Complexity = Action" (CA) prescriptions, and in the harmonic chain with Dirichlet boundary conditions. In all the cases considered except for CA, the boundary introduces a subleading logarithmic divergence in the expansion of the complexity as the UV cutoff vanishes. Holographic subregion complexity is also explored in the CV case, finding that it can change discontinuously under continuous variations of the configuration of the subregion.

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Section: Complexity In the Harmonic Chain With Dirichlet Boundary Conmentioning

confidence: 99%

Complexity in the presence of a boundary

Paolo

Cotrone

Tonni

2020

J. High Energ. Phys.

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“…Evaluating complexity of mixed states in quantum field theories remains an important challenge. The complexity of pure states in quantum field theories has been explored in various studies [21,[30][31][32][33][34][35][36][37][38][39][40][41][42][43] and it would be instructive to extend these analyses to mixed states. The tools of Information Geometry, that we have largely employed in our analysis, could provide further tools to handle this interesting problem [163].…”

Section: Jhep12(2020)101mentioning

confidence: 99%

Complexity of mixed Gaussian states from Fisher information geometry

Giulio

Tonni

2020

J. High Energ. Phys.

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We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.

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“…This approach was first applied to a concrete quantum field theory calculation in [57], where the authors adapted Nielsen's approach to evaluate the complexity of the vacuum state of a free scalar field theory. These calculations have been extended in a number of interesting ways in the past few years, e.g., [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], but we will be particularly interested in [65] where the same techniques were applied to explore the complexity of coherent states in the same QFT.…”

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confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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We investigate the first law of complexity proposed in [1], i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

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Circuit complexity and 2D bosonisation

Cited by 19 publications

References 37 publications

Complexity in the presence of a boundary

Complexity in the presence of a boundary

Complexity of mixed Gaussian states from Fisher information geometry

Aspects of the first law of complexity

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