Quantum logic gates operation using SQUID qubits in bimodal cavity

We present a scheme to realize the basic two-qubit logic gates such as the quantum phase gate and SWAP gate using a detuned microwave cavity interacting with three-level superconducting-quantum-interference-device （SQUID） qubit（s）, by placing SQUID（s） in a two-mode microwave cavity and using adiabatic passage methods. In this scheme, the two logical states of the qubit are represented by the two lowest levels of the SQUID, and the cavity fields are treated as quantized. Compared with the previous method, the complex procedures of adjusting tile level spacing of the SQUID and applying the resonant microwave pulse to the SQUID to create transformation are not required. Based on superconducting device with relatively long decoherence time and simplified operation procedure, the gates operate at a high speed, which is important in view of decoherence.

Conditional Entropy of Partitions on Quantum Logic

A construction of conditional entropy of partitions on quantum logic is given,and the properties ofconditional entropy are investigated.

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Quantum Logic Networks for Probabilistic Teleportation of an Arbitrary Three-Particle State

The scheme for probabilistic teleportation of an arbitrary three-particle state is proposed. By using single qubit gate and three two-qubit gates, efficient quantum logic networks for probabilistic teleportation of an arbitrary three-particle state are constructed.

Quantum logic operations on two distant atoms trapped in two optical-fibre-connected cavities

Based on the coupling of two distant three-level atoms in two separate optical cavities connected with two optical fibres, schemes on the generation of several two-qubit logic gates are discussed under the conditions of △ = δ- 2v cos πk/2 〉〉 g/2 and v-g. Discussion and analysis of the fidelity, gate time and experimental setups show that our schemes are feasible with current optical cavity, atomic trap and optical fibre techniques. Moreover, the atom-cavityfibre coupling can be used to generate an N-qubit nonlocal entanglement and transfer quantum information among N distant atoms by arranging N atom cavity assemblages in a line and connecting each two adjacent cavities with two optical fibres.

Scheme for implementing quantum logic gates for two atoms trapped in different cavities

A scheme is presented for realizing quantum logic gates for two atoms localized in two distant optical cavities. Our scheme works in a regime in which the atom-cavity coupling strength is smaller than the cavity decay rate. Thus the requirement on the quality factor of the cavities is greatly relaxed. Furthermore, the fidelity of our scheme is not affected by detection inefficiency and atomic decay. These advantages are important in view of experiment.

Entropy of Partitions on Quantum Logic

Partition and entropy of partitions in quantum logic are introduced and their properties are investigated.The results are generalized to the general case of T-norm and T-conorm.

Quantum Logic Network for Probabilistic Cloning Quantum States

We construct efficient quantum logic network for probabilistic cloning the quantum states used in imple mented tasks for which cloning provides some enhancement in performance.

Simple and Fast Scheme for Realizing Quantum Logic Gates in an Ion Trap

We propose a simple and fast scheme to realize a controlled-NOT gate between two trapped ions using a resonant laser pulse. Our scheme allows the Rabi frequency of the laser field to be of the order of the vibrational frequency and thus the time required to complete the operation is greatly shortened, which is of importance in view of decoherence.

Knotted Picture of Single Qubit Quantum Logic Gate

This paper briefly introduces the five types of the surgical operations in knot theory and obtains the expression of single qubit quantum logic gate in terms of these surgical operations.

Undulatory Theory with Paraconsistent Logic (Part I): Quantum Logical Model with Two Wave Functions

Paraconsistent logic (PL) is a non-classical logic that accepts contradiction in its foundations. It can be represented in the form of paraconsistent annotated logic with annotation of two values (PAL2v). When used to model quantum phenomena, PAL2v is called paraquantum logic (PQL). In this work, the concept of PQL is applied to create a logical model presenting the fundamental principles of quantum mechanics that support particle-wave theory. This study uses the well-known Young’s double-slit experiment, wherein quantum phenomena appear when a monochromatic light beam passes through the two slits. We focused on a reference point located between the slits, where we observed the effects of two types of wave interferences in a region defined as a two-wave region (2W region). Considering that the effect in this 2W region is very similar to that studied by Huygens, we adopt a paraquantum logical model in which a particle (or quantum) is represented by two wave functions. The two wave functions result in four State Vectors (Ket, Bra,,) in the PQL Lattice that express the symmetry and the entanglement of Quantum Mechanics. The constructed model adapts well to the quantum phenomena, is strongly consistent, and can be considered as an innovative form of analysis in the field of quantum mechanics. Based on this model, we present in two parts (Part I and Part II) the comparative analysis of values found in SchrÖdinger’s equation and probabilistic models of wave-particle theory using Bonferroni inequality.

Distributive Quantum Logic： Controlled-Error Approach

The idea that approximate exactness is the most we can and should expect scientific theories to yield underlies the formation and application of the multi-valued logic of approximation discussed in this paper. In this logic, inexactness （measured by truth values） is controlled and minimized by means of uniquely designed deductions. We show how the notion of equality （including substitution of equals） is handled within this logic and we apply it to certain principles and interpretations of quantum theory.

Quantum Logic and Geometric Quantization

We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all “experimental propositions” of M and we look for a model of quantum logic in relation to the quantization of the base manifold M. In particular we give a new interpretation about previous results of the author in order to build an “asymptotics quantum probability space” for the Hilbert lattice L(H).

Bipolar Quantum Logic Gates and Quantum Cellular Combinatorics—A Logical Extension to Quantum Entanglement

Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement;2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality.

Conditional Events and Quantum Logic

This paper begins with an overview of quantum mechanics, and then recounts a relatively recent algebraic extension of the Boolean algebra of probabilistic events to “conditional events” (order pairs of events). The main point is to show that a so-called “superposition” of two (or more) quantum events (usually with mutually inconsistent initial conditions) can be represented in this algebra of conditional events and assigned a consistent conditional probability. There is no need to imagine that a quantum particle can simultaneously straddle two inconsistent possibilities.

Buffer-atom-mediated quantum logic gates with off-resonant modulated driving

Connectivity of two-qubit logic gates plays a crucial and indispensable role in quantum computation research.For the cold atom qubit platform,while the two-qubit Rydberg blockade gate has recently made rapid experimental progress,a pressing challenge is to improve connectivity in pursuit of genuine scalability without sacrificing speed or fidelity.A significant advancement in this direction can be achieved by introducing an extra buffer atom to extend the two-qubit gate beyond purely nearest-neighbor two-body interactions.The buffer atom couples with the two qubit atoms through nearest-neighbor interactions,even though the qubit atoms do not directly exert any physical influence on each other.The established method of off-resonant modulated driving(ORMD)is not only convenient but also lays the groundwork for this latest development.Although the atomic linkage structure here exhibits more complex interactions compared to previous two-body systems,the population can satisfactorily return to the ground state after the ground-Rydberg transition with a properly designed modulation waveform.This can be achieved through one-photon and two-photon ground-Rydberg transitions in common practices.Furthermore,with buffer atom relay or similar structures,it is possible to realize a two-qubit entangling gate between two distant qubit atoms.In addition to demonstrating that such solutions are feasible,the representative modulation patterns are analyzed,showcasing the versatility of buffer-atom-mediated two-qubit gates.From a broader perspective,these efforts enhance the resemblance between the cold atom qubit platform and the superconducting qubit system,with the buffer atom functioning like wires and junctions.

History of Western Philosophy and Quantum Language (Including Quantum Mechanics, Statistics, Fuzzy Logic, etc.)

Although there are many different types of philosophy, many philosophers agree that the mainstream of Western philosophy (Socrates, Plato, Aristotle, Descartes, Kant, Wittgenstein) developed toward the perfection of Socrates’ absolutism. But can the absolutism maintain its central position after analytic philosophy? There are pessimistic views on this problem, such as that of R. Rorty, the standard-bearer of neo-pragmatism. Recently, I proposed quantum language (which is including quantum mechanics, statistics, fuzzy sets, etc.). I think that that this theory is not only one of the most fundamental scientific theories, but also the scientific final destination of Western philosophy. If so, Socrates’ dream has come true. The purpose of this paper is to discuss the above and to inform readers that quantum language has the power to create a paradigm shift from the classical mechanical world view to the quantum mechanical worldview.

Universal quantum logic gates in decoherence-free subspace with atoms trapped in distant cavities

We propose a scheme for implementation of a universal set of quantum logic gates in decoherence-free subspace with atoms trapped in distant cavities connected by optical fibers.The selective dispersive couplings between the ground states and the first-excited states of the atom-cavity-fiber system produce a state-dependent Stark shift,which can be used to implement nonlocal phase gates between two logic qubits.The single-logic-qubit quantum gates are achieved by the local two-atom collision and the Stark shift of a single atom.During all the logic operations,the logic qubits remain in decoherence-free subspace and thus the operation is immune to collective dephasing.

Notes on automata theory based on quantum logic

The main results are as follows： （1） it deals with a number of basic operations （concatenation, Kleene closure, homomorphism, complement）; （2） due to a condition imposed on the implication operator for discussing some basic issues in orthomodular lattice-valued automata, this condition is investigated in detail, and it is discovered that all the relatively reasonable five implication operators in quantum logic do not satisfy this condition, and that one of the five implications satisfies such a condition iff the truth-value lattice is indeed a Boolean algebra; （3） it deals further with orthomodular lattice-valued successor and source operators; （4） an example is provided, implying that some negative results obtained in the literature may still hold in some typical orthomodular lattice-valued automata.

Generalized Conditional Entropies of Partitions on Quantum Logic

For partitions on quantum logic, the Rdnyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.