相关论文: Computable functions, quantum measurements, and qu…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit.…
We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical,…
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
Quantum measurement is universal for quantum computation. Two models for performing measurement-based quantum computation exist: the one-way quantum computer was introduced by Briegel and Raussendorf, and quantum computation via projective…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
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…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always…
In this work we consider a dynamic system consisting of a damped harmonic oscillator and we formalize a Turing Machine whose definition in terms of states, alphabet and transition rules, can be considered equivalent to that of the…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…