We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part of a broader research program aiming to define a logic with a proof language that forms a quantum programming language.

Development of large-scale quantum computing systems will require radio frequency (RF) and microwave technologies operating reliably at cryogenic temperatures down to tens of milli-Kelvin (mK). The quantum bits in the most promising quantum computing technologies such as the superconducting quantum computing are designed using principles of microwave engineering and operated using microwave signals. The control, readout, and coupling of qubits are implemented using a network of microwave components operating at various temperature stages. To ensure reliable operation of quantum computing systems, it is critical to ensure optimal performance of these microwave components and qubits at their respective operating temperatures, which can be as low as mK temperatures. It is, therefore, critical to understand the microwave characteristics of waveforms, components, circuits, networks, and systems at cryogenic temperatures. The UK’s National Physical Laboratory (NPL) is focussed on developing new microwave measurement capabilities through the UK’s National Quantum Technologies Programme to address various microwave test and measurement challenges in quantum computing. This includes the development of various measurement capabilities to characterize the microwave performance of quantum and microwave devices and substrate materials at cryogenic temperatures. This paper summarizes the roadmap of activities at NPL to address these microwave metrology challenges in quantum computing.

Quantum computers hold significant promise for peaceful applications, but one of the more immediate potential applications is breaking of public key encryption technologies. This poses significant risks to the information security of global digital infrastructure in a broader sense. At the same time, the development of quantum computing is a quintessentially scientific undertaking. There is a tension in the scientific freedom required to develop these technologies, and the measures to mitigate the risks associated with quantum computers. Policy for resolving this tension must be in line with the human right to science, read together with the right to privacy and the right to freedom of expression. In this article, I apply these rights to the development of quantum computing to provide guidance for government policy on quantum computing. I conclude that states must create the conditions for scientific research to flourish, even if this research may carry significant societal risks. This applies also to research and development of quantum technologies. In the context of quantum computing, this primarily means investing in the development and uptake of alternative encryption technologies which are resistant to attacks by quantum computers. It also means regulating the use of these technologies for applications which are undesirable.

Learning finite automata (termed as model learning) has become an important field in machine learning and has been useful realistic applications. Quantum finite automata (QFA) are simple models of quantum computers with finite memory. Due to their simplicity, QFA have well physical realizability, but one-way QFA still have essential advantages over classical finite automata with regard to state complexity (two-way QFA are more powerful than classical finite automata in computation ability as well). As a different problem in quantum learning theory and quantum machine learning, in this paper, our purpose is to initiate the study of learning QFA with queries (naturally it may be termed as quantum model learning), and the main results are regarding learning two basic one-way QFA (1QFA): (1) we propose a learning algorithm for measure-once 1QFA (MO-1QFA) with query complexity of polynomial time and (2) we propose a learning algorithm for measure-many 1QFA (MM-1QFA) with query complexity of polynomial time, as well.

We give an adequate, concrete, categorical-based model for Lambda-${\mathcal S}$, which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda-${\mathcal S}$ is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi: to forbid duplication of variables and to consider all lambda-terms as algebraic linear functions. The type system of Lambda-${\mathcal S}$ has a superposition constructor S such that a type A is considered as the base of a vector space, while SA is its span. Our model considers S as the composition of two functors in an adjunction relation between the category of sets and the category of vector spaces over $\mathbb C$. The right adjoint is a forgetful functor U, which is hidden in the language, and plays a central role in the computational reasoning.

Until robots and humans mostly worked in fast-paced and yet separate environments, occupational health and safety (OHS) rules could address workers’ safety largely independently from robotic conduct. This is no longer the case: collaborative robots (cobots) working alongside humans warrant the design of policies ensuring the safety of both humans and robots at once, within shared spaces and upon delivery of cooperative workflows. Within the European Union (EU), the applicable regulatory framework stands at the intersection between international industry standards and legislation at the EU as well as Member State level. Not only do current standards and laws fail to satisfactorily attend to the physical and mental health challenges prompted by human–robot interaction (HRI), but they exhibit important gaps in relation to smart cobots (“SmaCobs”) more specifically. In fact, SmaCobs combine the black-box unforeseeability afforded by machine learning with more general HRI-associated risks, towards increasingly complex, mobile and interconnected operational interfaces and production chains. Against this backdrop, based on productivity and health motivations, we urge the encoding of the enforcement of OHS policies directly into SmaCobs. First, SmaCobs could harness the sophistication of quantum computing to adapt a tangled normative architecture in a responsive manner to the contingent needs of each situation. Second, entrusting them with OHS enforcement vis-à-vis both themselves and humans may paradoxically prove safer as well as more cost-effective than for humans to do so. This scenario raises profound legal, ethical and somewhat philosophical concerns around SmaCobs’ legal personality, the apportionment of liability and algorithmic explainability. The first systematic proposal to tackle such questions is henceforth formulated. For the EU, we propose that this is achieved through a new binding OHS Regulation aimed at the SmaCobs age.

Medicine, including fields in healthcare and life sciences, has seen a flurry of quantum-related activities and experiments in the last few years (although biology and quantum theory have arguably been entangled ever since Schrödinger's cat). The initial focus was on biochemical and computational biology problems; recently, however, clinical and medical quantum solutions have drawn increasing interest. The rapid emergence of quantum computing in health and medicine necessitates a mapping of the landscape. In this review, clinical and medical proof-of-concept quantum computing applications are outlined and put into perspective. These consist of over 40 experimental and theoretical studies. The use case areas span genomics, clinical research and discovery, diagnostics, and treatments and interventions. Quantum machine learning (QML) in particular has rapidly evolved and shown to be competitive with classical benchmarks in recent medical research. Near-term QML algorithms have been trained with diverse clinical and real-world data sets. This includes studies in generating new molecular entities as drug candidates, diagnosing based on medical image classification, predicting patient persistence, forecasting treatment effectiveness, and tailoring radiotherapy. The use cases and algorithms are summarized and an outlook on medicine in the quantum era, including technical and ethical challenges, is provided.

Quantum computing research and development efforts have grown dramatically over the past decades, led in part by initiatives from governments around the world. Government quantum computing investments are often driven by national security or digital sovereignty concerns, with the language used depending on the geography involved. For example, a focus on “national security” and quantum computing is prominent in the USA, while European countries regularly focus on “digital sovereignty”. These phrases are often loosely defined and open to interpretation, and they share some common motivations and characteristics (but also have important differences). This paper identifies specific governmental entities typifying the national security/digital sovereignty perspectives, along with these organisations’ respective roles within national and international policy engagement in quantum computing. It analyses governmental structures, historical developments and cultural characteristics that contributed to this national security–digital sovereignty divide. Building on this analysis, we use the history of other technologies to illustrate how we might adapt tested policy approaches to modern political dynamics and to quantum computing specifically. We frame these policy approaches so that they do not overemphasise “digital sovereignty” or “national security”, but rather address interests shared across both concepts, with a view to facilitating international collaboration.

The classic game of Battleship involves two players taking turns attempting to guess the positions of a fleet of vertically or horizontally positioned enemy ships hidden on a $10\times 10$ grid. One variant of this game, also referred to as Battleship Solitaire, Bimaru or Yubotu, considers the game with the inclusion of X-ray data, represented by knowledge of how many spots are occupied in each row and column in the enemy board. This paper considers the Battleship puzzle problem: the problem of reconstructing an enemy fleet from its X-ray data. We generate non-unique solutions to Battleship puzzles via certain reflection transformations akin to Ryser interchanges. Furthermore, we demonstrate that solutions of Battleship puzzles may be reliably obtained by searching for solutions of the associated classical binary discrete tomography problem which minimise the discrete Laplacian. We reformulate this optimisation problem as a quadratic unconstrained binary optimisation problem and approximate solutions via a simulated annealer, emphasising the future practical applicability of quantum annealers to solving discrete tomography problems with predefined structure.

In this perspective, I give my answer to the question of how quantum computing will impact on data-intensive applications in engineering and science. I focus on quantum Monte Carlo integration as a likely source of (relatively) near-term quantum advantage, but also discuss some other ideas that have garnered widespread interest.