Related papers: Algorithmic complexity of quantum states
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating the process of preparation, transmission through the channel, and subsequent measurement of a quantum…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
An important and usual problem is to search all states we want from a database with a large number of states. In such, recall is vital. Grover's original quantum search algorithm has been generalized to the case of multiple solutions, but…
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…
We analyze the complexity of synthesizing random states and unitary operators in a multi-qudit system in two paradigms. In one case, we consider the situation in which we manipulate the system by applying a sequence of one- and two-qudit…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…
We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical…
This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations,…
Quantum information refers to the distinctive information-processing properties of quantum systems, which arise when information is stored in or retrieved from nonorthogonal quantum states. More information is required to prepare an…
State preparation is a process encoding the classical data into the quantum systems. Based on quantum phase estimation, we propose the specific quantum circuits for a deterministic state preparation algorithm and a probabilistic state…
We analyze the complexity of quantum state verification in the context of solving systems of linear equations of the form $A \vec x = \vec b$. We show that any quantum operation that verifies whether a given quantum state is within a…
Given two events $A$ and $B$, Bayes' law is based on the argument that the probability of $A$ given $B$ is proportional to the probability of $B$ given $A$. When probabilities are interpreted in the Bayesian sense, Bayes' law constitutes a…
Computational problems can be classified according to their algorithmic complexity, which is defined based on how the resources needed to solve the problem, e.g. the execution time, scale with the problem size. Many problems in…
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…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
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,…
In our thesis, we try to shed more light onto the complexity of quantum complexity classes by refining the related part of the hierarchy. First, we review the basic concepts of quantum computing in general. Then, inspired by BQP, we define…