Related papers: Termination of Nondeterministic Quantum Programs
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
Programmability is a unifying paradigm for enacting families of quantum transformations via fixed processors and program states, with a fundamental role and broad impact in quantum computation and control. While there has been a shift from…
A discrete quantum process is defined as a sequence of local states $\rho_t$, $t=0,1,2,...$, satisfying certain conditions on an $L_2$ Hilbert space $H$. If $\rho =\lim\rho_t$ exists, then $\rho$ is called a global state for the system. In…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
In support of the growing interest in quantum computing experimentation, programmers need new tools to write quantum algorithms as program code. Compared to debugging classical programs, debugging quantum programs is difficult because…
We present quantum observable Markov decision processes (QOMDPs), the quantum analogues of partially observable Markov decision processes (POMDPs). In a QOMDP, an agent's state is represented as a quantum state and the agent can choose a…
Parallelism is often required for performance. In these situations an excess of non-determinism is harmful as it means the program can have several different behaviours or even different results. Even in domains such as high-performance…
Consider a situation in which a quantum system is secretly prepared in a state chosen from the known set of states. We present a principle that gives a definite distinction between the operations that preserve the states of the system and…
We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict…
We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
A deterministic model with a large number of continuous and discrete degrees of freedom is described, and a statistical treatment is proposed. The model exactly obeys a Schrodinger equation, which has to be interpreted exactly according to…