Circuit complexity in quantum field theory

Jefferson, Ro; Myers, Robert C.

doi:10.1007/jhep10(2017)107

Cited by 447 publications

(1,021 citation statements)

References 81 publications

Supporting

Mentioning

991

Contrasting

Order By: Relevance

“…Further, the complexity in the QFT quench showed a strong dependence on the mass scale M associated with the unentangled reference state. In [44,45], it was suggested the dependence on M could be associated with dependence of the holographic complexity α, which seems to be traded for the dependence on scale ct with the addition of the boundary counterterm [60]. However, the holographic growth rate, e.g., in eq.…”

Section: Jhep06(2018)046mentioning

confidence: 99%

“…Of course, one might ask if one proposal is correct while the other is wrong. However, at present, it seems equally likely that both proposals simply encode different definitions of complexity, e.g., see discussion in [34,44,45]. The precise numerical value of the complexity will depend on a number of choices at the microscopic level, e.g., the set of universal gates used in preparing the states, and therefore the latter is an inherently ambiguous quantity.…”

Section: Jhep06(2018)046mentioning

confidence: 99%

“…Some initial studies of this question appear in [98,99], which examine the evolution of the complexity through a mass quench in a free scalar field theory (analogous to those studied in [86][87][88]). A remarkable feature of these quenches is that the scalar field remains in a Gaussian state throughout the entire process, and so methods developed in [44][45][46] can still be applied to evaluate the complexity. The comparison of our holographic results with those in [98] is not straightforward since, e.g., the initial and final masses are nonvanishing (i.e., neither the initial nor final scalar theories are CFTs).…”

Section: Future Directionsmentioning

confidence: 99%

See 2 more Smart Citations

Holographic complexity in Vaidya spacetimes. Part I

Chapman

Marrochio

Myers

2018

J. High Energ. Phys.

Self Cite

151

222

View full text Add to dashboard Cite

We examine holographic complexity in time-dependent Vaidya spacetimes with both the complexity=volume (CV) and complexity=action (CA) proposals. We focus on the evolution of the holographic complexity for a thin shell of null fluid, which collapses into empty AdS space and forms a (one-sided) black hole. In order to apply the CA approach, we introduce an action principle for the null fluid which sources the Vaidya geometries, and we carefully examine the contribution of the null shell to the action. Further, we find that adding a particular counterterm on the null boundaries of the Wheeler-DeWitt patch is essential if the gravitational action is to properly describe the complexity of the boundary state. For both the CV proposal and the CA proposal (with the extra boundary counterterm), the late time limit of the growth rate of the holographic complexity for the one-sided black hole is precisely the same as that found for an eternal black hole.

show abstract

Section: Jhep06(2018)046mentioning

confidence: 99%

Section: Jhep06(2018)046mentioning

confidence: 99%

Section: Future Directionsmentioning

confidence: 99%

See 1 more Smart Citation

Holographic complexity in Vaidya spacetimes. Part I

Chapman

Marrochio

Myers

2018

J. High Energ. Phys.

Self Cite

151

222

View full text Add to dashboard Cite

show abstract

“…We will follow [38], which defines complexity of a quantum circuit and also describe the closely related notion of complexity of a state (see e.g. [39]). …”

Section: Defining Complexitymentioning

confidence: 99%

“…In other words, as the tolerance becomes smaller, we should also choose our gates to make finer changes to the wavefunction. This is the strategy employed in [39,41], where the gates are chosen G i = e i Q i , for some fixed set Q i . In other words, all gates are chosen to approach the identity as the tolerance vanishes.…”

Section: Defining Complexitymentioning

confidence: 99%

Complexity is simple!

Cottrell

2018

J. High Energ. Phys.

View full text Add to dashboard Cite

In this note we investigate the role of Lloyd's computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd's proof into the bulk language. In particular, we discuss the distinction between orthogonalizing and 'simple' gates and argue that these notions are useful for diagnosing holographic complexity. We show that large black holes constructed from series circuits necessarily employ simple gates, and thus do not satisfy Lloyd's assumptions. We also estimate the degree of parallel processing required in this case for elementary gates to orthogonalize. Finally, we show that for small black holes at fixed chemical potential, the orthogonalization condition is satisfied near the phase transition, supporting a possible argument for the Weak Gravity Conjecture first advocated in [1].

show abstract

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Alvarez‐Jimenez¹,

González²,

Gutiérrez‐Ruiz³

et al. 2019

Annalen der Physik

View full text Add to dashboard Cite

The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed matter physics. Classical integrable systems are considered and a new approach is reported to obtain the classical analogs of the quantum metric tensor and the Berry curvature. An advantage of this approach is that it can be applied to a wide variety of classical systems corresponding to quantum systems with bosonic and fermionic degrees of freedom. The approach used arises from the semiclassical approximation of the Berry curvature and the quantum metric tensor in the Lagrangian formalism. This semiclassical approximation is exploited to establish, for the first time, the relation between the quantum metric tensor and its classical counterpart. The approach described is illustrated and validated by applying it to five systems: the generalized harmonic oscillator, the symmetric and linearly coupled harmonic oscillators, the singular Euclidean oscillator, and a spin‐half particle in a magnetic field. Finally, some potential applications of this approach and possible generalizations that can be of interest in the field of condensed matter physics are mentioned.

show abstract

Circuit complexity in quantum field theory

Cited by 447 publications

References 81 publications

Holographic complexity in Vaidya spacetimes. Part I

Holographic complexity in Vaidya spacetimes. Part I

Complexity is simple!

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Contact Info

Product

Resources

About