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We draw the current landscape of quantum algorithms, by classifying about 130 quantum algorithms, according to the fundamental mathematical problems they solve, their real-world applications, the main subroutines they employ, and several other relevant criteria. The primary objectives include revealing trends of algorithms, identifying promising fields for implementations in the NISQ era, and identifying the key algorithmic primitives that power quantum advantage.

In this work, we demonstrate that quantizing gravity on a null hypersurface leads to the emergence of a CFT associated with each null ray. This result stems from the ultralocal nature of null physics and is derived through a canonical analysis of the Raychaudhuri equation, interpreted as a constraint generating null time reparametrizations. The CFT exhibits a non-zero central charge, providing a mechanism for the quantum emergence of time in gravitational systems and an associated choice of vacuum state. Our analysis reveals that the central charge quantifies the degrees of freedom along each null ray. Throughout our investigation, the area element of a cut plays a crucial role, necessitating its treatment as a quantum operator due to its dynamic nature in phase space or because of quantum backreaction. Furthermore, we show that the total central charge diverges in a perturbative analysis due to the infinite number of null generators. This divergence is resolved if there is a discrete spectrum for the area form operator. We introduce the concept of `embadons’ to denote these localized geometric units of area, the fundamental building blocks of geometry at a mesoscopic quantum gravity scale.

This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader scientific community. Our approach seeks to integrate Quantum Field Theory on curved backgrounds and scenarios with indefinite causality. Building on concepts from the operational approach to Quantum Reference Frames, we extend these ideas significantly. Specifically, we initiate the development of a general integration theory for operator-valued functions (quantum fields) with respect to positive operator-valued measures (quantum frames). This allows us to define quantum frames within the context of arbitrary principal bundles, replacing group structures. By considering Lorentz principal bundles, we enable a relational treatment of quantum fields on arbitrarily curved spacetimes. A form of indefinite spatiotemporality arises from quantum states in the context of frame bundles. This offers novel perspectives on the problem of reconciling principles of generally relativistic and quantum physics and on modelling gravitational fields sourced by quantum systems.

Are you, with your perceptions, memories and observational data, a Boltzmann brain, namely a fleeting statistical fluctuation out of the thermal equilibrium of the universe? Arguments are given in the literature claiming that this bizarre hypothesis needs to be considered seriously, that all of our data about the past is actually a mirage. We point to a difficulty in these arguments. They are based on the dynamical laws and on statistical arguments, but they disregard the fact that we infer the dynamical laws presupposing the reliability of our data records about the past. Hence the reasoning in favor of the Boltzmann brain hypothesis contradicts itself, relying on the reliability of our data about the past to conclude that that data is wrong. More broadly, it is based on incomplete evidence. Incomplete evidence notoriously leads to false conclusions.

Recently, machine learning had a remarkable impact, from scientific to everyday-life applications. However, complex tasks often imply unfeasible energy and computational power consumption. Quantum computation might lower such requirements, although it is unclear whether enhancements are reachable by current technologies. Here, we demonstrate a kernel method on a photonic integrated processor to perform a binary classification. We show that our protocol outperforms state-of-the-art kernel methods including gaussian and neural tangent kernels, exploiting quantum interference, and brings a smaller improvement also by single photon coherence. Our scheme does not require entangling gates and can modify the system dimension through additional modes and injected photons. This result opens to more efficient algorithms and to formulating tasks where quantum effects improve standard methods.

Quantum computing and AI have found a fruitful intersection in the field of natural language processing. We focus on the recently proposed DisCoCirc framework for natural language, and propose a quantum adaptation, QDisCoCirc. This is motivated by a compositional approach to rendering AI interpretable: the behavior of the whole can be understood in terms of the behavior of parts, and the way they are put together. For the model-native primitive operation of text similarity, we derive quantum algorithms for fault-tolerant quantum computers to solve the task of question-answering within QDisCoCirc, and show that this is BQP-hard; note that we do not consider the complexity of question-answering in other natural language processing models. Assuming widely-held conjectures, implementing the proposed model classically would require super-polynomial resources. Therefore, it could provide a meaningful demonstration of the power of practical quantum processors. The model construction builds on previous work in compositional quantum natural language processing. Word embeddings are encoded as parameterized quantum circuits, and compositionality here means that the quantum circuits compose according to the linguistic structure of the text. We outline a method for evaluating the model on near-term quantum processors, and elsewhere we report on a recent implementation of this on quantum hardware. In addition, we adapt a quantum algorithm for the closest vector problem to obtain a Grover-like speedup in the fault-tolerant regime for our model. This provides an unconditional quadratic speedup over any classical algorithm in certain circumstances, which we will verify empirically in future work.

We develop a feedback strategy based on optimal quantum feedback control for Gaussian systems to maximise the likelihood of steady-state entanglement detection between two directly interacting masses. We employ linear quadratic Gaussian (LQG) control to engineer the phase space dynamics of the two masses and propose Einstein-Podolsky-Rosen (EPR)-type variance minimisation constraints for the feedback to facilitate unconditional entanglement generation. This scheme allows for stationary entanglement in parameter regimes where strategies based on total energy minimisation ($cooling$) would fail. This feedback strategy, applied to the system of two masses driven out-of-thermal equilibrium [arXiv:2408.06251] enables unconditional entanglement generation under realistic experimental conditions.

We present a protocol that maximizes unconditional entanglement generation between two masses interacting directly through $1/r^{n}$ potential. The protocol combines optimal quantum control of continuously measured masses with their non-equilibrium dynamics, driven by a time-dependent interaction strength. Applied to a pair of optically trapped sub-micron particles coupled via electrostatic interaction, our protocol enables unconditional entanglement generation at the fundamental limit of the conditional state and with an order of magnitude smaller interaction between the masses compared to the existing steady-state approaches.

We present the first implementation of text-level quantum natural language processing, a field where quantum computing and AI have found a fruitful intersection. We focus on the QDisCoCirc model, which is underpinned by a compositional approach to rendering AI interpretable: the behaviour of the whole can be understood in terms of the behaviour of parts, and the way they are put together. Interpretability is crucial for understanding the unwanted behaviours of AI. By leveraging the compositional structure in the model’s architecture, we introduce a novel setup which enables ‘compositional generalisation’: we classically train components which are then composed to generate larger test instances, the evaluation of which asymptotically requires a quantum computer. Another key advantage of our approach is that it bypasses the trainability challenges arising in quantum machine learning. The main task that we consider is the model-native task of question-answering, and we handcraft toy scale data that serves as a proving ground. We demonstrate an experiment on Quantinuum’s H1-1 trapped-ion quantum processor, which constitutes the first proof of concept implementation of scalable compositional QNLP. We also provide resource estimates for classically simulating the model. The compositional structure allows us to inspect and interpret the word embeddings the model learns for each word, as well as the way in which they interact. This improves our understanding of how it tackles the question-answering task. As an initial comparison with classical baselines, we considered transformer and LSTM models, as well as GPT-4, none of which succeeded at compositional generalisation.

Pointlike systems coupled to quantum fields are often employed as toy models for measurements in quantum field theory. In this paper, we identify the field observables recorded by such models. We show that in models that work in the strong coupling regime, the apparatus is correlated with smeared field amplitudes, while in models that work in weak coupling the apparatus records particle aspects of the field, such as the existence of a particle-like time of arrival and resonant absorption. Then, we develop an improved field-detector interaction model, adapting the formalism of Quantum Brownian motion, that is exactly solvable. This model confirms the association of field and particle properties in the strong and weak coupling regimes, respectively. Further, it can also describe the intermediate regime, in which the field-particle characteristics `merge’. In contrast to standard perturbation techniques, this model also recovers the relativistic Breit-Wigner resonant behavior in the weak coupling regime. The modulation of field-particle-duality by a single tunable parameter is a novel feature that is, in principle, experimentally accessible.