Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared with their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, researchers remain keen to develop novel designs and improve existing ones. In this review article, we aim to provide a systematically organized and easily comprehensible overview of the current state of the art in quantum arithmetic circuits. Specifically, this study covers fundamental operations such as addition, subtraction, multiplication, division and modular exponentiation. We delve into the detailed quantum implementations of these prominent designs and evaluate their efficiency considering various objectives. We also discuss potential applications of the presented arithmetic circuits and suggest future research directions.This article is part of the theme issue 'Emerging technologies for future secure computing platforms'.

Modern language models such as bidirectional encoder representations from transformers have revolutionized natural language processing (NLP) tasks but are computationally intensive, limiting their deployment on edge devices. This paper presents an energy-efficient accelerator design tailored for encoder-based language models, enabling their integration into mobile and edge computing environments. A data-flow-aware hardware accelerator design for language models inspired by Simba, makes use of approximate fixed-point POSIT-based multipliers and uses high bandwidth memory (HBM) in achieving significant improvements in computational efficiency, power consumption, area and latency compared to the hardware-realized scalable accelerator Simba. Compared to Simba, AxLaM achieves a ninefold energy reduction, 58% area reduction and 1.2 times improved latency, making it suitable for deployment in edge devices. The energy efficiency of AxLaN is 1.8 TOPS/W, 65% higher than FACT, which requires pre-processing of the language model before implementing it on the hardware.This article is part of the theme issue 'Emerging technologies for future secure computing platforms'.

The quantum interference effects of mixing the most non-classical states of light, number states, with the most classical-like of pure field states, the coherent state, are investigated. We demonstrate how the non-classicality of a single photon when mixed with a coherent field can transform the statistical properties of the output and further demonstrate that the entanglement of the output is independent of the coherent state amplitude.This article is part of the theme issue 'The quantum theory of light'.

Room-temperature cavity quantum electrodynamics with molecular materials in optical cavities offers exciting prospects for controlling electronic, nuclear and photonic degrees of freedom for applications in physics, chemistry and materials science. However, achieving strong coupling with molecular ensembles typically requires high molecular densities and substantial electromagnetic-field confinement. These conditions usually involve a significant degree of molecular disorder and a highly structured photonic density of states. It remains unclear to what extent these additional complexities modify the usual physical picture of strong coupling developed for atoms and inorganic semiconductors. Using a microscopic quantum description of molecular ensembles in realistic multimode optical resonators, we show that the emergence of vacuum Rabi splitting in linear spectroscopy is a necessary but not sufficient metric of coherent admixing between light and matter. In low-finesse multi-mode situations, we find that molecular dipoles can be partially hybridized with photonic dissipation channels associated with off-resonant cavity modes. These vacuum-induced dissipative processes ultimately limit the extent of light-matter coherence that the system can sustain.This article is part of the theme issue 'The quantum theory of light'.

This paper presents a short history of the discovery by Rodney Loudon and Heidi Fearn of the counter-intuitive destructive interference effect occurring when two indistinguishable photons meet at a beamsplitter. This effect, commonly known as the Hong Ou Mandel effect, underpins much of present day photonic quantum information processing. Here I try to review its development from inception to present day proposals of million qubit photonic quantum computers.This article is part of the theme issue 'The quantum theory of Light'.

Multipolar quantum optics deals with the interaction of light with matter as a many-body bound system of charged particles where the coupling to electromagnetic fields is in terms of the multipolar electric polarization and magnetization. We describe two transformations applied to the conventional non-relativistic formalism, namely a gauge transformation applied directly to the fields at the Lagrangian stage and a unitary transformation applied to the old Hamiltonian. We show how such transformations lead to the same Power-Zienau-Woolley (PZW) formulation of the quantum electrodynamics (QED) of an overall electrically neutral many-body bound system of charges, including the internal motion as well as the gross dynamics of the centre of mass. Besides highlighting the utility of the multipolar formalism as a reliable and convenient platform in dealing with optical processes in atomic and molecular physics, it is shown how the analysis can also lead to the identification of the Röntgen effect arising from the gross motion of an electric dipole moment in a magnetic field and the Aharonov-Casher effect due to the motion of a magnetic dipole moment in an electric field. The importance of the two effects is pointed out in both experimental and theoretical contexts.This article is part of the theme issue 'The quantum theory of light'.

Can a quantum advantage for imaging resolution be realized with the help of quantum estimation theory? We expect so, but we show that, presently, theoretical tools are insufficiently developed to answer this question for extended objects. Still, there is much to be learned from the current state of the art. In this review, we re-examine prominent results in the literature and probe the limits of quantum metrology in addressing imaging resolution. In particular, we show that under restrictive but well-defined conditions, any quantum advantage in one-dimensional phase imaging appears to diminish for increasingly detailed objects. We also show that a previous attempt at tackling this question, while incomplete, does predict an advantage for single-molecule localization microscopy, although this method may not be feasible in the near term. As for experimental claims of Heisenberg-limited imaging resolution, we briefly address the many inherent difficulties in demonstrating that such a thing has indeed been achieved.This article is part of the theme issue 'The quantum theory of light'.

We place Loudon's quantum treatment of optical phase in The quantum theory of light in its historical context, and outline research that it inspired. We show how it led Pegg and Barnett to their quantum phase formalism, explaining the challenges that they overcame to define phase operators and phase eigenstates rigorously. We show how the formalism essentially constructs an extended rigged Hilbert space that supports strong limits of the phase operators and includes their eigenstates. We identify the complementarity structure (consisting of mutually unbiased bases and generators of cyclical permutations) underpinning Pegg and Barnett's general approach that gives a quantum-classical correspondence free of the ambiguity of Dirac's commutator-Poisson bracket correspondence.This article is part of the theme issue 'The quantum theory of light'.

Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity dispersion are balanced by the nonlinear interaction with the medium while cavity losses balance the input energy. The history, properties, physical interpretation and wide application of cavity solitons are reviewed. Cavity solitons in the plane perpendicular to light propagation find application in optical information processing, while cavity solitons in the longitudinal direction produce high-quality frequency combs with applications in optical communications, frequency standards, optical clocks, future GPS, astronomy and quantum technologies.This article is part of the theme issue 'The quantum theory of light'.

The controlled SWAP test for detecting and quantifying entanglement applied to pure qubit states is robust to small errors in the states and efficient for large multi-qubit states (Foulds et al. 2021 Quantum Sci. Technol. 6, 035002 (doi:10.1088/2058-9565/abe458)). We extend this, and the related measure concentratable entanglement (CE), to enable important practical applications in quantum information processing. We investigate the lower bound of concentratable entanglement given in (Beckey et al. 2023 Phys. Rev. A 107, 062425 (doi:10.1103/physreva.107.062425)) and conjecture an upper bound of the mixed-state concentratable entanglement that is robust to c-SWAP test errors. Since experimental states are always slightly mixed, our work makes the c-SWAP test and CE measure suitable for application in experiments to characterize entanglement. We further present the CE of some key higher-dimensional states such as qudit states and entangled optical states to validate the CE as a higher-dimensional measure of entanglement.This article is part of the theme issue 'The quantum theory of light'.