Related papers: The Complexity Geometry of a Single Qubit
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
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…
In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions…
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
We define a semantic complexity class based on the model of quantum computing with just one pure qubit (as introduced by Knill and Laflamme) and discuss its computational power in terms of the problem of estimating the trace of a large…
The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' 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…
The notion of a qubit is ubiquitous in quantum information processing. In spite of the simple abstract definition of qubits as two-state quantum systems, identifying qubits in physical systems is often unexpectedly difficult. There are an…