Related papers: Defining and composing big state machines
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…
By combining the beam splitter and the Fresnel transform, a protocol is proposed to generate a new entangled state representation, called the intermediate coherent-entangled state (ICES) representation. The properties, such as eigenvalue…
Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by…
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the…
Given a nondeterministic finite-state automaton (NFA), we aim to estimate the size of an equivalent deterministic finite-state automaton (DFA). We demonstrate that computing the state complexity of an NFA within polynomial precision is…
We are studying long term sequence prediction (forecasting). We approach this by investigating criteria for choosing a compact useful state representation. The state is supposed to summarize useful information from the history. We want a…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and…
State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a…
A connection between fractional supersymmetric quantum mechanics and ordinary supersymmetric quantum mechanics is established in this Letter.
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
Work in progress concerning alternative formalizations of arithmetic.
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
We give a generating function for the number of unimodal permutations with a given cycle structure.
The paper introduce a new type of partitions where the largest part appears exactly once, and the remaining parts constitute a partition of that largest part. We derive the generating function associated with these partitions and…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…