Related papers: Quantum Synchronizing Words: Resetting and Prepari…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…
Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy…
The manipulation of quantum many-body systems is a frontier challenge in quantum science. Entangled quantum states that are symmetric to permutation between qubits are of growing interest. Yet, the creation and control of symmetric states…
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…
The paper develops a methodology for the design of coherent equalizing filters for quantum communication channels. Given a linear quantum system model of a quantum communication channel, the aim is to obtain another quantum system which,…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
The set of synchronizing words of a given $n$-state automaton forms a regular language recognizable by an automaton with $2^n - n$ states. The size of a recognizing automaton for the set of synchronizing words is linked to computational…
Quantum computers process information with the laws of quantum mechanics. Current quantum hardware is noisy, can only store information for a short time, and is limited to a few quantum bits, i.e., qubits, typically arranged in a planar…
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,…
Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…
We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of non-deterministic quantum…
Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state,…
Recent advances in quantum technology facilitate the realization of information processing using quantum computers at least on the small and intermediate scales of up to several dozens of qubits. We investigate entanglement cost required…
Dynamic quantum circuits generate states that depend on the measurement results obtained during circuit execution. To date such a quantum computing model has mainly been implemented with qubit-based superconducting hardware utilizing reset…
Uncomputation is a feature in quantum programming that allows the programmer to discard a value without losing quantum information, and that allows the compiler to reuse resources. Whereas quantum information has to be treated linearly by…
Probabilistic quantum filtering is proposed to properly adapt sequential independent quantum channels in order to stop sudden death of entanglement. In the adaptation, the quantum filtering does not distill or purify more entanglement, it…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term…
Quantum computing and AI have found a fruitful intersection in the field of natural language processing. We focus on the recently proposed DisCoCirc framework for natural language, and propose a quantum adaptation, QDisCoCirc. This is…
Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can…
In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing…