Qiss

Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum optics and condensed matter theory to quantum information and quantum field theory in curved spacetime. They are known to form a representation of the metaplectic and spin group for bosons and fermions, respectively. These groups are the double covers of the symplectic and special orthogonal group, respectively, and our goal is to analyze the behavior of the sign ambiguity that one needs to deal with when moving between these groups and their double cover. We relate this sign ambiguity to expectation values of the form $langle 0|exp{(-ihat{H})}|0rangle$, where $|0rangle$ is a Gaussian state and $hat{H}$ an arbitrary quadratic Hamiltonian. We provide closed formulas for $langle 0|exp{(-ihat{H})}|0rangle$ and show how we can efficiently describe group multiplications in the double cover without the need of going to a faithful representation on an exponentially large or even infinite-dimensional space. Our construction relies on an explicit parametrization of these two groups (metaplectic, spin) in terms of symplectic and orthogonal group elements together with a twisted U(1) group.

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.

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.

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 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 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 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 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.

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.

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.