相关论文: Quantum Kolmogorov Complexity Based on Classical D…

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…

The concept of \emph{complexity} has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on \emph{Krylov…

An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…

As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…

A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query…

In this paper, we study the Krylov complexity in quantum field theory and make a connection with the holographic "Complexity equals Volume" conjecture. When Krylov basis matches with Fock basis, for several interesting settings, we observe…

A common way of stating the non-cloning theorem -- one of distinguishing characteristics of quantum theory -- is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing…

In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…

In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…

We provide tight upper and lower bounds on the expected minimum Kolmogorov complexity of binary classifiers that are consistent with labeled samples. The expected size is not more than complexity of the target concept plus the conditional…

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…

Quantum cloning is a fundamental protocol of quantum information theory. Perfect universal quantum cloning is prohibited by the laws of quantum mechanics, only imperfect copies being reachable. Symmetric quantum cloning is concerned with…

The ultimate goal of the classicality programme is to quantify the amount of quantumness of certain processes. Here, classicality is studied for a restricted type of process: quantum information processing (QIP). Under special conditions,…

An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…

From the perspective of quantum information theory, a system so simple as one restricted to just two nonorthogonal states can be surprisingly rich in physics. In this paper, we explore the extent of this statement through a review of three…

We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…

Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…

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…