Complexity as a Novel Probe of Quantum Quenches: Universal Scalings and Purifications

Camargo, Hugo A.; Caputa, Paweł; Das, Diptarka; Heller, Michał; Jefferson, Ro

doi:10.1103/physrevlett.122.081601

Cited by 127 publications

(161 citation statements)

References 80 publications

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“…Before proceeding further, we must acknowledge that the purification complexity of a single oscillator is briefly considered using the F 2 cost function (see eq. (2.11)) in [38]. This overlaps somewhat with the discussion in section 2, where we consider the purification complexity for the same system but focus on the F 1 cost function.…”

mentioning

confidence: 64%

“…Before proceeding, we must note that the authors of [38] have considered the purification complexity for one-mode Gaussian mixed states using the F 2 cost function in their appendix C, as we will do below. They considered the most general purification consisting of a six real (or three complex) parameter family of two-mode pure Gaussian states as purifications.…”

Section: Other Cost Functionsmentioning

confidence: 99%

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Complexity of mixed states in QFT and holography

Cáceres

Chapman

Couch

et al. 2020

J. High Energ. Phys.

108

227

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We study the complexity of Gaussian mixed states in a free scalar field theory using the 'purification complexity'. The latter is defined as the lowest value of the circuit complexity, optimized over all possible purifications of a given mixed state. We argue that the optimal purifications only contain the essential number of ancillary degrees of freedom necessary in order to purify the mixed state. We also introduce the concept of 'mode-by-mode purifications' where each mode in the mixed state is purified separately and examine the extent to which such purifications are optimal. We explore the purification complexity for thermal states of a free scalar QFT in any number of dimensions, and for subregions of the vacuum state in two dimensions. We compare our results to those found using the various holographic proposals for the complexity of subregions. We find a number of qualitative similarities between the two in terms of the structure of divergences and the presence of a volume law. We also examine the 'mutual complexity' in the various cases studied in this paper.

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mentioning

confidence: 64%

Section: Other Cost Functionsmentioning

confidence: 99%

Complexity of mixed states in QFT and holography

Cáceres

Chapman

Couch

et al. 2020

J. High Energ. Phys.

108

227

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show abstract

“…The study of the effects of the boundaries on the complexity deserves further analysis. Interesting directions concern scenarios involving higher dimensions [20], non trivial time dependence [12,36,62,63], mixed states [55] and the role of spacetime singularities [64][65][66]. It is also interesting to explore the effects of the boundaries in the connections between complexity with the laws of thermodynamics [67,68].…”

Section: Discussionmentioning

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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“…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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Complexity as a Novel Probe of Quantum Quenches: Universal Scalings and Purifications

Cited by 127 publications

References 80 publications

Complexity of mixed states in QFT and holography

Complexity of mixed states in QFT and holography

Complexity in the presence of a boundary

Aspects of the first law of complexity

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