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Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain boost constraints on gravitons, QRFs and other fields. Here, we revisit the question of how these constraints should be understood through the lens of perturbation theory and particularly the study of linearization (in)stabilities, exploring when linearized solutions can be integrated to exact ones. Our aim is to provide some clarity about the status of justification, under various conditions, for imposing such constraints on the linearized theory in the $G_Nto0$ limit as they turn out to be of second-order. While for spatially compact spacetimes there is an essentially unambiguous justification, in the presence of boundaries or the absence of isometries this depends on whether one is also interested in second-order observables. Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations and to address this in a unified framework, we translate the subject from the usual canonical formulation into a systematic covariant phase space language. This overcomes theory-specific arguments, exhibiting the universal structure behind (in)stabilities, and permits us to cover arbitrary generally covariant theories. We comment on the relation to modular flow and illustrate our findings in several gravity and gauge theory examples.

One can theoretically conceive of processes where the causal order between quantum operations is no longer well-defined. Certain such causally indefinite processes have an operational interpretation in terms of quantum operations on time-delocalised subsystems — that is, they can take place as part of standard quantum mechanical evolutions on quantum systems that are delocalised in time. In this paper, we formalise the underlying idea that quantum evolutions can be represented with respect to different subsystem decompositions in a general way. We introduce a description of quantum circuits, including cyclic ones, in terms of an operator acting on the global Hilbert space of all systems in the circuit. This allows us to express in a concise form how a given circuit transforms under arbitrary changes of subsystem decompositions. We then explore the link between this framework and the concept of causal perspectives, which has been introduced to describe causally indefinite processes from the point of view of the different parties involved. Surprisingly, we show that the causal perspectives that one can associate to the different parties in the quantum switch, a paradigmatic example of a causally indefinite process, cannot be related by a change of subsystem decomposition, i.e., they cannot be seen as two equivalent descriptions of the same process.

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.

We present thought experiments to measure the Arnowitt-Deser-Misner and Bondi-Sachs energy of isolated systems in general relativity. The expression of the Bondi-Sachs energy used in the protocol is likely to have other applications. In particular, it is well-suited to to be promoted to an operator in non-perturbative loop quantum gravity.

We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of POVM decompositions. The latter arise from integrals over families of bounded positive operators. Crucially, these operators have the same locality properties as the underlying field operators. We use the decompositions to construct families of quantum operations implementing measurements of the field observables. Again, the quantum operations have the same locality properties as the field operators. What is more, we show that these quantum operations do not lead to superluminal signaling and are possible measurements on quantum fields in the sense of Sorkin.

We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number of events and spacetime configurations in superposition. By constructing diagrammatic and knot-theoretic representations of the causal order between events, we find that the definiteness or maximal indefiniteness of the causal order is topologically invariant. This reveals an intriguing connection between the field of quantum causality and knot theory. Furthermore, we provide an operational encoding of indefinite causal order and discuss how to incorporate a measure of quantum coherence into our classification.

In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S=mathbb{C}^*$ we recover the celebrated $Lw_{1+infty}$ algebra. For the 2-sphere $S^2$, the wedge algebra reduces to a central extension of the anti-self-dual projection of the Poincar’e algebra. We then extend $mathcal{W}(S)$ outside of the wedge space and build a new Lie algebra $mathcal{W}_sigma(S)$, which can be viewed as a deformation of the wedge algebra by a spin two field $sigma$ playing the role of the shear at a cut of $mathscr{I}$. This algebra represents the gravitational symmetry algebra in the presence of a non trivial shear and is characterized by a covariantized version of the wedge condition. Finally, we construct a dressing map that provides a Lie algebra isomorphism between the covariant and regular wedge algebras.