Related papers: Quantum Alternation: Prospects and Problems
The word \textit{proposition} is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages $\mathcal{L}^{\ast}(x)$ and $\mathcal{L}(x)$ with classical set-theoretical…
In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum…
This paper gives an introduction to and overview of the functional quantum programming language QML. The syntax of this language is defined and explained, along with a new QML definition of the quantum teleport algorithm. The categorical…
Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential…
Quantum information processing shows advantages in many tasks, including quantum communication and computation, comparing to its classical counterpart. The essence of quantum processing lies on the fundamental difference between classical…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…
We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…
We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given…
Unlike the standard Quantum Computational Logic (QCL), where the carrier of information (target) is conventionally assumed to be only the last qubit over a sequence of many qubits, here we propose an extended version of the QCL (we call…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…
As it is known, neither classical logical conjunction "and" nor classical logical alternative "either...or" can replace "+" representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Imagine a lock with two states, "locked" and "unlocked", which may be manipulated using two operations, called 0 and 1. Moreover, the only way to (with certainty) unlock using four operations is to do them in the sequence 0011, i.e.,…
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…
Controlled operations allow for the entanglement of quantum registers. In particular, a controlled-$U$ gate allows an operation, $U$, to be applied to the target register and entangle the results to certain values in the control register.…
Quantum computing is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for quantum computing were designed with fault-tolerant hardware in…