Quantum Logic Research Articles

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.

Universal quantum operations and ancilla-based read-out for tweezer clocks

Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology1,2. Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and read-out strategies3–7. Neutral-atom optical clocks8, which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation9–11 but at present lack the control capabilities for realizing such schemes. Here we show universal quantum operations and ancilla-based read-out for ultranarrow optical transitions of neutral atoms. Our demonstration in a tweezer clock platform9,12–16 enables a circuit-based approach to quantum metrology with neutral-atom optical clocks. To this end, we demonstrate two-qubit entangling gates with 99.62(3)% fidelity—averaged over symmetric input states—through Rydberg interactions15,17,18 and dynamical connectivity19 for optical clock qubits, which we combine with local addressing16 to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state1,4, a cascade of Greenberger–Horne–Zeilinger states of different sizes, and perform a dual-quadrature5 Greenberger–Horne–Zeilinger read-out. We also show repeated fast phase detection with non-destructive conditional reset of clock qubits and minimal dead time between repetitions by implementing ancilla-based quantum logic spectroscopy20 for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell-state preparation21–24. Our work lays the foundation for hybrid processor–clock devices with neutral atoms and more generally points to a future of practical applications for quantum processors linked with quantum sensors25.

Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers.

Direct pulse-level compilation of arbitrary quantum logic gates on superconducting qutrits

Direct pulse-level compilation of arbitrary quantum logic gates on superconducting qutrits

Alternative fast quantum logic gates using nonadiabatic Landau-Zener-Stückelberg-Majorana transitions

A conventional realization of quantum logic gates and control is based on resonant Rabi oscillations of the occupation probability of the system. This approach has certain limitations and complications, like counter-rotating terms. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry with nonresonant driving and the alternation of adiabatic evolution and nonadiabatic transitions. Compared to Rabi oscillations, the main differences are a nonresonant driving frequency and a small number of periods in the external driving. We explore the dynamics of a multilevel quantum system under LZSM drives and optimize the parameters for increasing the gate speed. We define the parameters of the external driving required for implementing a specific quantum logic gate using the adiabatic-impulse model. In particular, we demonstrate the implementations of single-qubit X, Y, Hadamard gates, and two-qubit i and gates using the LZSM transitions. The considered LZSM approach for implementing arbitrary quantum logic gates can be applied to a large variety of multilevel quantum systems and external driving. Published by the American Physical Society 2024

Propositional logic and modal logic—A connection via relational semantics

Abstract In this paper, by slightly generalizing an observation of Dalla Chiara and Giuntini in their chapter on quantum logic in Handbook of Philosophical Logic, we propose a relational semantics for propositional language with negation and conjunction, which unifies the relational semantics of intuitionistic logic and that of ortho-logic. We study the semantic and syntactic consequence relations and prove the soundness and completeness theorems for five propositional logics: $\textbf{BL}$, $\textbf{PL}$, $\textbf{IL}$, $\textbf{OL}$ and $\textbf{CL}$. Moreover, we prove that they can be translated into the modal logics $\textbf{K}$, $\textbf{T}$, $\textbf{S4}$, $\textbf{KTB}$ and $\textbf{S5}$, respectively, and thus establish a systematic connection between propositional logics and modal logics. The paper ends with a discussion about the possibility and difficulty of incorporating disjunction into our framework.

Reducing Leakage of Single-Qubit Gates for Superconducting Quantum Processors Using Analytical Control Pulse Envelopes

Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the ef transition of a transmon qubit with an anharmonicity of −212 MHz, we implement RX(π/2) gates achieving a leakage error below 3.0×10−5 down to a gate duration of 6.25 ns without the need for iterative closed-loop optimization. The obtained leakage error represents a 20-fold reduction in leakage compared to a conventional cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of (1.56±0.07)×10−4 at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control-pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion. Published by the American Physical Society 2024

Quantum logic automata generate class IV-like patterns and [formula omitted] noise

Owing to recent advancements in brain science and AI, researchers tend to focus on the concept of self-organized criticality or the edge of chaos. On the other hand, quantum cognition, which is rooted in quantum mechanics, is promising for resolving various cognitive illusions. However, until recently, no connection between criticality and quantum mechanics was proposed. Gunji et al. (2024) recently introduced a linkage termed quantum logic automata, which encompasses not only quantum logic but also criticality characterized by power-law distributions. While quantum logic automata can be derived from various structures, only one of them has been proposed and discussed. Here, we define another type of quantum logic automata involving quantum logic and demonstrate that symmetric quantum logic automata lead to complex Class IV-like patterns and power-law distributions. Our findings support the association between criticality and quantum theory.

Automatic Test Pattern Generation for Robust Quantum Circuit Testing

Quantum circuit testing is essential for detecting potential faults in realistic quantum devices, while the testing process itself also suffers from the inexactness and unreliability of quantum operations. This article alleviates the issue by proposing a novel framework of automatic test pattern generation (ATPG) for robust testing of logical quantum circuits. We introduce the stabilizer projector decomposition (SPD) for representing the quantum test pattern and construct the test application (i.e., state preparation and measurement) using Clifford-only circuits, which are rather robust and efficient as evidenced in the fault-tolerant quantum computation. However, it is generally hard to generate SPDs due to the exponentially growing number of the stabilizer projectors. To circumvent this difficulty, we develop an SPD generation algorithm, as well as several acceleration techniques that can exploit both locality and sparsity in generating SPDs. The effectiveness of our algorithms are validated by (1) theoretical guarantees under reasonable conditions and (2) experimental results on commonly used benchmark circuits, such as Quantum Fourier Transform (QFT), Quantum Volume (QV), and Bernstein-Vazirani (BV) in IBM Qiskit.

Efficient Characterization of Qudit Logical Gates with Gate Set Tomography Using an Error-Free Virtual Z Gate Model.

Gate set tomography (GST) characterizes the process matrix of quantum logic gates, along with measurement and state preparation errors in quantum processors. GST typically requires extensive data collection and significant computational resources for model estimation. We propose a more efficient GST approach for qudits, utilizing the qudit Hadamard and virtual Z gates to construct fiducials while assuming virtual Z gates are error-free. Our method reduces the computational costs of estimating characterization results, making GST more practical at scale. We experimentally demonstrate the applicability of this approach on a superconducting transmon qutrit.

Astrophotonics: recent and future developments

Astrophotonics is a burgeoning field that lies at the interface of photonics and modern astronomical instrumentation. Here we provide a pedagogical review of basic photonic functions that enable modern instruments, and give an overview of recent and future applications. Traditionally, optical fibres have been used in innovative ways to vastly increase the multiplex advantage of an astronomical instrument, e.g. the ability to observe hundreds or thousands of stars simultaneously. But modern instruments are using many new photonic functions, some emerging from the telecom industry, and others specific to the demands of adaptive optics systems on modern telescopes. As telescopes continue to increase in size, we look to a future where instruments exploit the properties of individual photons. In particular, we envisage telescopes and interferometers that build on international developments in quantum networks, the so-called quantum internet. With the aid of entangled photons and quantum logic gates, the new infrastructures seek to preserve the photonic state and timing of individual photons over a coherent network.