Related papers: Nondeterministic testing of Sequential Quantum Log…
The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon…
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
Quantum-enhanced measurements use quantum mechanical effects in order to enhance the sensitivity of the measurement of classical quantities, such as the length of an optical cavity. The major goal is to beat the standard quantum limit…
Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation…
With the advent of delegated quantum computing as a service, verifying quantum computations is becoming a question of great importance. Existing information theoretically Secure Delegated Quantum Computing (SDQC) protocols require the…
We consider the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer. The result is…
The power of quantum computers relies on the capability of their components to maintain faithfully and process accurately quantum information. Since this property eludes classical certification methods, fundamentally new protocols are…
Besides their use for efficient computation, quantum computers are a base for studying quantum systems that create valid physical theories using mathematics and physics. An essential part of the validation process for quantum mechanics is…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
Scalable modern-time fault-tolerant quantum computation and quantum communication in a network employ a large number of physical qubits. For example, IBM is reported to have made a 127-qubit quantum computer. Unlike classical computation,…
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
SQL is the world's most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal…
As it is well known, quantum entanglement is one of the most important features of quantum computing, as it leads to massive quantum parallelism, hence to exponential computational speed-up. In a sense, quantum entanglement is considered as…
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…
One-way quantum computation, also known as Cluster State Quantum Computation, provides a robust and efficient tool to perform universal quantum computation using only single-qubit projective measurements, given a highly entangled cluster…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…