Related papers: Exact Gravity Duals for Simple Quantum Circuits
Motivated by recent studies of quantum computational complexity in quantum field theory and holography, we discuss how weighting certain classes of gates building up a quantum circuit more heavily than others does affect the complexity.…
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a…
We investigate a large-$N$ CFT in a high-energy pure state coupled to a small auxiliary system of $M$ weakly-interacting degrees of freedom, and argue the relative state complexity of the auxiliary system is holographically dual to an…
We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories with a view that they provide the simplest setting to find a gravity dual to complexity. Our work pursues a geometric understanding of complexity…
We study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the "complexity = volume" and "complexity = action" conjectures. We…
We derive a holographic dual description of free quantum field theory in arbitrary dimensions, by reinterpreting the exact renormalization group, to obtain a higher spin gravity theory of the general type which had been proposed and studied…
Quantum complexity of conformal field theory (CFT) states has recently gained significant attention, both as a diagnostic tool in condensed matter systems and in connection with holographic observables probing black hole interiors. Previous…
We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we…
This thesis develops recent work on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, geometric quantities can be defined in some holographic gravitational theories that can be mapped…
We propose that holographic spacetimes can be regarded as collections of quantum circuits based on path-integrals. We relate a codimension one surface in a gravity dual to a quantum circuit given by a path-integration on that surface with…
We investigate the first law of complexity proposed in arXiv:1903.04511, 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…
We consider the holographic dual of SQCD in the conformal phase. It is based on a higher derivative gravity theory, which ensures the correct field theory anomalies. This is then related to a six dimensional gravity theory via S^1…
We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\bar T$ deformed holographic CFTs. In Nielsen's geometric…
We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the…
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open…
A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the…
We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as unitary circuits. We show that the complexity functional can be…
Quasi-topological gravity is a new gravitational theory including curvature-cubed interactions and for which exact black hole solutions were constructed. In a holographic framework, classical quasi-topological gravity can be thought to be…
Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's…
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…