6,048 research outputs found
Quantum Uncertainties and Holism Seem to Render Irrelevant Qudit-Semantics
No full textWe consider a semantics based on the peculiar holistic features of the quantum formalism. Any formula of the language gives rise to a quantum circuit that transforms the density operator associated to the formula into the density operator associated to the atomic subformulas in a reversible way. The procedure goes from the whole to the parts against the compositionality-principle and gives rise to a semantic characterization for a new form of quantum logic that has been called “Łukasiewicz quantum computational logic”. It is interesting to compare the logic based on qubit-semantics with that on qudit-semantics. Having in mind the relationships between classical logic and Łukasiewicz-many valued logics, one could expect that the former is stronger than the fragment of the latter. However, this is not the case. From an intuitive point of view, this can be explained by recalling that the former is a very weak form of logic. Many important logical arguments, which are valid either in Birkhoff and von Neumann’s quantum logic or in classical logic, are generally violated
Extending a Model Language to Handle Entangled Concepts in Artificial Intelligence
No full textIn quantum information and computation, entanglement is a resource. When combining concepts, the application of entanglement outside of micro-physical systems is an useful tool. We suggest new cognitive image-based tests that do not need to be translated. No prior knowledge of terms related to the concepts is required, therefore the choice is more intuitive. We examine the merging of two concepts that establish non-classical statistical correlation and present an entanglement-aware vector encoding algorithm. This research’s
added value results in an automated system that teaches artificial intelligence to identify and handle entangled concepts
Holistic and Compositional Logics Based on the Bertini Gate
No full textThe theory of logical gates in quantum computation has inspired the development of new forms of quantum logic where the meaning of a formula is identified with a density operator and the logical connectives are interpreted as operations defined in terms of quantum gates. We show some relations between the Bertini gate and many valued connectives by probability values. On this basis, one can deal with quantum circuits as expressions in an algebraic environment such as product many valued algebra for combinational circuits. As can be expected, we show that the compositional logic characterized by the qubit semantics is stronger than the compositional Lukasiewicz quantum computational logic by a counterexample. But, in the holistic case, we conjecture that they can characterize the same logic
Logics from Quantum Information
No full textIn the first chapter we introduce new forms of quantum logic suggested by quantum computation, 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 possible pure state of a compound quantum system. The generalization to mixed states might be useful to analyse entanglement-phenomena. We study structural properties of density operators systems, where some basic quantum logical gate are defined. We introduce the notions of standard reversible and standard irreversible quantum computational structure. Quantum computational logics represent non standard examples of unsharp quantum logic, where the non-contradiction principle is violated, while conjunctions and disjunctions are strongly non-idempotent. In this framework, any sentence of the language gives rise to a quantum tree: a kind of quantum circuit that transforms the quregister associated to the atomic subformulas of the formula into the quregister associated to the formula. We generalize the quantum computational semantics in order to represent some typical quantum holistic situations where the meaning of the whole determines the contextual meanings of the parts, but not vice versa. We describe some holistic models in the framework of Mach-Zehnder interferometers.
In the second chapter we extend the basic principles and results of conservative logic to include the main features of many-valued logics with a finite number of truth values. Different approaches to many-valued logics are examined in order to determine some possible functionally complete sets of logic connectives. In particular, we consider the typical connectives of Lukasiewicz and Gödel logics, as well as Zawirski/Chang's MV-algebras. As a result, we describe some possible three-valued and finite-valued universal gates which realize a functionally complete set of fundamental connectives. One of the purposes of this work is to show that the framework of reversible and conservative computation can be extended toward some non classical "reasoning environments", originally proposed to deal with propositions which embed imprecise and uncertain information, that are usually based upon many-valued and modal logics.
We also describe a possible quantum realization of the proposed gates, using creation and annihilation operators. These formulas are obtained using three techniques: a "brute force" technique, an extension of the Conditional Quantum Control method introduced by Barenco, Deutsch, Ekert and Jozsa in 1995, and a new technique that we call the Constants method. The formulas obtained with these techniques are sums of local operators. In the brute force technique, each local operator corresponds to a single row of the truth table of the implemented gate. In the Conditional Quantum Control method, an assumption is made on the behavior of the gate: this assumption usually leads to much shorter formulas, but on the other hand the method cannot be applied to the gates that do not satisfy it. Our Constants method is a general technique, since we do not impose any constraint on the structure or on the behavior of the gate; the length of the corresponding formula is minimized by looking at all possible realizations of the desired connectives, obtained by setting some input lines of the gate to appropriate constant values.
In the third chapter we discuss a model to realize the Petri-Fredkin gate by a Mach-Zehnder like optical device with a non-linear component. The device uses optical nonlinear Kerr effect generated into a substance with an intensity dependent refractive index: the intensity dependence of the refractive index is the source of nonlinearity
Quantum logics with bounded additive operators
No full textThe theory of gates in quantum computation has suggested new forms of quantum logic,
called quantum computational logics, where the meaning of a sentence is identi ed with a
system of qubits in a pure or, more generally, mixed state. In this framework, any formula
of the language gives rise to a quantum circuit that transforms the state associated to
the atomic subformulas into the state associated to the formula and vice versa. On this
bases, some holistic semantic situations can be described, where the meaning of whole
determine the meaning of the parts, by non-linear and anti-unitary operators. We prove
that the semantics with such operators and the semantics with unitary operators turn
out to characterize the same logic
An efficient geometric approach to quantum-inspired classifications
No full textOptimal measurements for the discrimination of quantum states are useful tools for classification problems. In order to exploit the potential of quantum computers, feature vectors have to be encoded into quantum states represented by density operators. However, quantum-inspired classifiers based on nearest mean and on Helstrom state discrimination are implemented on classical computers. We show a geometric approach that improves the efficiency of quantum-inspired classification in terms of space and time acting on quantum encoding and allows one to compare classifiers correctly in the presence of multiple preparations of the same quantum state as input. We also introduce the nearest mean classification based on Bures distance, Hellinger distance and Jensen–Shannon distance comparing the performance with respect to well-known classifiers applied to benchmark datasets
Quantum approach to epistemic semantics
No full textQuantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can be stored and transmitted by means of quantum particles. This approach can be applied to a semantic characterization of epistemic logical operations, which may occur in sentences like “At time t' Bob knows that at time t Alice knows that the spin-value is up”. Each epistemic agent (say, Alice, Bob,...) has a characteristic truth perspective, corresponding to a particular orthonormal basis of the Hilbert space C^2. From a physical point of view, a truth perspective can be associated with an apparatus that allows one to measure a given observable. An important feature that characterizes the knowledge of any agent is the amount of information that is accessible to him/her (technically, a special set of density operators, which also represents the internal memory of the agent in question). One can prove that interesting epistemic operations are special examples of quantum channels, which generally are not unitary. The act of knowing may involve some intrinsic irreversibility due to possible measurement procedures or to a loss of information about the environment. We also illustrate some relativistic-like effects that arise in the behavior of epistemic agents
Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements
No full textIn quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination
Support Vector Machines with Quantum State Discrimination
No full textWe analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification
Quantum-Inspired Applications for Classification Problems
No full textIn the context of quantum-inspired machine learning, quantum state discrimination is a useful tool for classification problems. We implement a local approach combining the k-nearest neighbors algorithm with some quantum-inspired classifiers. We compare the performance with respect to well-known classifiers applied to benchmark datasets
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