Quantum Logic Research Articles

Recurrence Resonance and 1/f Noise in Neurons Under Quantum Conditions and Their Manifestations in Proteinoid Microspheres

Recurrence resonance (RR), in which external noise is utilized to enhance the behaviour of hidden attractors in a system, is a phenomenon often observed in biological systems and is expected to adjust between chaos and order to increase computational power. It is known that connections of neurons that are relatively dense make it possible to achieve RR and can be measured by global mutual information. Here, we used a Boltzmann machine to investigate how the manifestation of RR changes when the connection pattern between neurons is changed. When the connection strength pattern between neurons forms a partially sparse cluster structure revealing Boolean algebra or Quantum logic, an increase in mutual information and the formation of a maximum value are observed not only in the entire network but also in the subsystems of the network, making recurrence resonance detectable. It is also found that in a clustered connection distribution, the state time series of a single neuron shows 1/f noise. In proteinoid microspheres, clusters of amino acid compounds, the time series of localized potential changes emit pulses like neurons and transmit and receive information. Indeed, it is found that these also exhibit 1/f noise, and the results here also suggest RR.

Achieving Pauli quantum logic gates with composite solitons of the Manakov system

Achieving Pauli quantum logic gates with composite solitons of the Manakov system

Correction: Birkhoff-von Neumann quantum logic enriched with entanglement quantifiers: coincidence theorem and semantic consequence

Correction: Birkhoff-von Neumann quantum logic enriched with entanglement quantifiers: coincidence theorem and semantic consequence

When implication algebras can be residuated lattices?

M. Ward and R.P. Dilworth were the first to describe the commutative residuated lattices as a generalization of ideal ring lattices. Complete studies on residuated lattices were developed by H. Ono, T. Kowalski, P. Jipsen and C. Tsinakis. Furthermore, Y. Xu is credited with the invention of lattice implication algebra. The aim of the paper was to link up the structures used in foundations of quantum logic and arising in many-valued reasoning. It is shown that implication algebra with unity can be described as residuated lattice.

Analysis of converting C0-circuit into C∗-circuit

A C∗-circuit, which was proposed in Asiacypt 2022 by Huang and Sun (Advances in cryptology – ASIACRYPT 2022, pp. 614–644, 2022), can directly perform calculations with the existing quantum states, thereby reducing the use of quantum resources in quantum logic synthesis. We theoretically prove how to convert a C0-circuit into the corresponding C∗-circuit through two lemmas and one theorem. The first lemma proves the interchangeability of CNOT gates and NOT gates by using the equivalence of quantum circuits. The second lemma proves that adding CNOT gates to the front of a quantum circuit whose initial states are all |0〉s will not change the output states of the circuit. The theorem is used to describe what kind of C0-circuit can be transformed into C∗-circuit, and the correctness of this transformation is proved. Our work will provide a theoretical basis for converting C0-circuit to C∗-circuit. Then applying the theoretical analysis results to the multiplication over GF(28), the constructed quantum circuit needs 27 Toffoli gates and 118 CNOT gates, which is 15 fewer Toffoli gates and 43 CNOT gates than the current best result. This shows that the method of constructing quantum circuits by using the conversion of C0-circuit to C∗-circuit is very efficient.

Ultra-stable transportable ultraviolet clock laser using cancellation between photo-thermal and photo-birefringence noise.

Optical clocks require an ultra-stable laser to probe and precisely measure the frequency of the narrow-linewidth clock transition. We introduce a portable ultraviolet (UV) laser system for use in an aluminum quantum logic clock, demonstrating a fractional frequency instability of approximately mod σ y = 2 × 10-16. The system is based on an ultra-stable cavity with crystalline AlGaAs/GaAs mirror coatings, with a frequency quadrupling system employing two single-pass second-harmonic generation (SHG) stages. Its acceleration sensitivity, measured in all three axes, does not exceed 4(2) × 10-12/(ms-2) and is among the lowest recorded for transportable systems to date. Additionally, partial cancellation between photo-thermal noise and photo-birefringence noise is used to effectively mitigate noise induced by intra-cavity optical power fluctuation at lower Fourier frequencies.

Problem of Existence of Joint Distribution on Quantum Logic.

This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitable for constructing virtual joint probabilities of even non-compatible propositions. The paper completes conclusions published in 2020 and extends the results for three or more random variables if the marginal distributions are known. The existence of a (n+1)-variate joint distribution is shown in special cases when the quantum logic consists of at most n blocks of Boolean algebras.

Birkhoff-von Neumann quantum logic as an assertion language for quantum programs

Birkhoff-von Neumann quantum logic as an assertion language for quantum programs

Automated Quantum Protocol Verification Based on Concurrent Dynamic Quantum Logic

Automated Quantum Protocol Verification Based on Concurrent Dynamic Quantum Logic

Two-step quantum dialogue protocols against collective noises

By designing two-step transmissions, this paper presents two quantum dialogue (QD) protocols that can resist different types of collective noise in the quantum channel. The message carrier of the proposed scheme utilizes decoherence-free subspaces to remain invariant under the impact of collective noise. We employ combinations of these quantum states to form decoy photon pairs, ensuring secure transmission and preventing message distortion. Based on the principle that a single photon in an EPR pair reveals no information about its actual state, an EPR pair requires only one photon for protection during transmission. This property effectively reduces the number of decoy photons needed to ensure the security of quantum transmission, which can also be applied to the logical EPR pair consisting of logical qubits. A quantum logic circuit is also designed to demonstrate the practical implementation of shuffling the logical qubits within each logical EPR pair. Therefore, the proposed two-step QD protocols require only half as many decoy photons to achieve the same security level as other state-of-the-art QD schemes. The significant reduction in the utilization of decoy photons improves the qubit efficiency of the proposed QD protocols compared to other existing works in the field. Additionally, the security analysis of the proposed QD schemes ensures the absence of information leakage and resistance to common quantum attacks.

Quantum modal logic

Abstract 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 demonstrated. This framework is intended to serve as a basis for formalizing various modal logics over quantum logic, such as quantum alethic logic, quantum temporal logic, quantum epistemic logic, and quantum dynamic logic.

Exploring the interaction of design variability and stochastic operational uncertainties in software-intensive systems through the lens of modeling

AbstractIn software-intensive systems, navigating the complexities that emerge from the interaction of design variability and stochastic operational uncertainties presents a daunting challenge. This paper delves into the dynamics between these two dimensions of uncertainty, offering novel insights about how modeling can contribute to the analysis of their combined impact upon system properties. By elevating the abstraction level at which probabilistic models are conceptualized, our approach enables an integrated analysis framework that considers both structural and quantitative dimensions of design spaces. Through the introduction of novel language constructs, our methodology facilitates the direct referencing of structural relationships within probabilistic behavioral specifications. Furthermore, the adoption of novel quantifiers in probabilistic temporal logic enables evaluating complex properties across diverse design variants, thereby streamlining the assessment of guarantees within the solution space. We demonstrate the feasibility of this approach on four case studies, showcasing its potential to offer comprehensive insights into the trade-offs and decision-making processes inherent in managing different types of structural design variability and operational uncertainties in software-intensive systems.

Anti-Diodorean Quantum Logic of Observables

The conception of “Anti-Diodorean” logic is based on the reversal of the definitions of Diodorus Cronus, who proposed to define modal concepts in terms of temporal ones. In case of quantum logic this is done by using the semantic interpretation of anti-Diodorean definitions, i.e. semantically defining spatio-temporal concepts by means of a quantum accessibility relation. Since Quantum Logic of Observables could be treated as the many-valued extension of the usual Quantum Logic, we can consider the Anti-Diodorean Logic of Observables in the same way.

Quantifiers in connexive logic (in general and in particular)

Abstract Connexive logic has room for two pairs of universal and particular quantifiers: one pair, $\forall $ and $\exists $, are standard quantifiers; the other pair, $\mathbb{A}$ and $\mathbb{E}$, are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The results are logics that are negation inconsistent but non-trivial.

Entangling Four Logical Qubits beyond Break-Even in a Nonlocal Code.

Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable quantum computer is to reach the break-even point, where logical quantum circuits on error-corrected qubits achieve higher fidelity than equivalent circuits on uncorrected physical qubits. Using Quantinuum's H2 trapped-ion quantum processor, we encode the Greenberger-Horne-Zeilinger (GHZ) state in four logical qubits with fidelity 99.5±0.15%≤F≤99.7±0.1% (after postselecting on over 98% of outcomes). Using the same quantum processor, we can prepare an uncorrected GHZ state on four physical qubits with fidelity 97.8±0.2%≤F≤98.7±0.2%. The logical qubits are encoded in a ⟦25,4,3⟧ Tanner-transformed long-range-enhanced surface code. Logical entangling gates are implemented using simple swap operations. Our results are a first step toward realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.

Continuously tunable single-photon level nonlinearity with Rydberg state wave-function engineering

Extending optical nonlinearity into the extremely weak light regime is at the heart of quantum optics, since it enables the efficient generation of photonic entanglement and implementation of photonic quantum logic gate. Here, we demonstrate the capability for continuously tunable single-photon level nonlinearity, enabled by precise control of Rydberg interaction over two orders of magnitude, through the use of microwave-assisted wave-function engineering. To characterize this nonlinearity, light storage and retrieval protocol utilizing Rydberg electromagnetically induced transparency is employed, and the quantum statistics of the retrieved photons are analyzed. As a first application, we demonstrate our protocol can speed up the preparation of single photons in low-lying Rydberg states by a factor of up to∼40. Our work holds the potential to accelerate quantum operations and to improve the circuit depth and connectivity in Rydberg systems, representing a crucial step towards scalable quantum information processing with Rydberg atoms.

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

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

Quantum color image watermarking scheme based on quantum discrete cosine transform

Quantum watermarking is a technique that embeds specific information into a quantum carrier, used for digital copyright protection. This paper introduces a new quantum color image watermarking method that combines Quantum LOG (QLOG) edge detection with Quantum Discrete Cosine Transform (QDCT) technology. First, edge detection is used on the RGB channels of the quantum color image. This helps identify the best channel for embedding the watermark. Next, the image is decomposed using the quantum Haar wavelet transform (QHWT). The image is then processed with QDCT, selecting the mid-frequency parts for watermark embedding. Using QDCT improves the watermark’s resistance to JPEG compression. The invisibility of the watermark is verified by assessing its Peak Signal-to-Noise Ratio (PSNR) and histogram. Comparative analysis shows strong resistance to various noise attacks. Simulation results confirm that the watermarking technique maintains high visual quality and resists different adversarial attacks.

Harmonic flow-field representations of quantum bits and gates

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024

Optimization of Decoder Priors for Accurate Quantum Error Correction.

Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this information as a prior to the decoder. We introduce a reinforcement learning inspired method for calibrating these priors that aims to minimize the logical error rate. Our method significantly improves the decoding accuracy in repetition and surface code memory experiments executed on Google's Sycamore processor, outperforming the leading decoder-agnostic method by 16% and 3.3%, respectively. This calibration approach will serve as an important tool for maximizing the performance of both near-term and future error-corrected quantum devices.