Related papers: Quantum Computational Complexity -- From Quantum I…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
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…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that…
We portray the structure of quantum gravity emerging from recent progress in understanding the quantum mechanics of an evaporating black hole. Quantum gravity admits two different descriptions, based on Euclidean gravitational path integral…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
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…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with…
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…
Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries…
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the "Wheeler-DeWitt" patch). We provide calculations for the…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
This is the contribution to Quarks'2018 conference proceedings. This contribution is devoted to the holographic description of chaos and quantum complexity in the strongly interacting systems out of equilibrium. In the first part of the…
We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields…