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Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these algorithms to be as efficient as possible it is important that we use the fewest number of parameters. We show that, while the general problem of minimising the number of parameters is NP-hard, when we restrict to circuits that are Clifford apart from parametrised phase gates and where each parameter is used just once, we can efficiently find the optimal parameter count. We show that when parameter transformations are required to be sufficiently well-behaved that the only rewrites that reduce parameters correspond to simple ‘fusions’. Using this we find that a previous circuit optimisation strategy by some of the authors [Kissinger, van de Wetering. PRA (2019)] finds the optimal number of parameters. Our proof uses the ZX-calculus. We also prove that the standard rewrite rules of the ZX-calculus suffice to prove any equality between parametrised Clifford circuits.

A black hole evaporates by Hawking radiation. Each mode of that radiation is thermal. If the total state is nevertheless to be pure, modes must be entangled. Estimating the minimum size of this entanglement has been an important outstanding issue. We develop a new theory of constrained random symplectic transformations, based on that the total state is pure, Gaussian and random, and every mode thermal as in Hawking theory. From this theory we compute the distribution of mode-mode correlations, from which we bound mode-mode entanglement. We find that correlations between thinly populated modes (early-time high-frequency modes and/or late modes of any frequency) are strongly suppressed. Such modes are hence very weakly entangled. Highly populated modes (early-time low-frequency modes) can on the other hand be strongly correlated, but a detailed analysis reveals that they are nevertheless also weakly entangled. Our analysis hence establishes that restoring unitarity after a complete evaporation of a black hole does not require strong quantum entanglement between any pair of Hawking modes. Our analysis further gives exact general expressions for the distribution of mode-mode correlations in random, pure, Gaussian states with given marginals, which may have applications beyond black hole physics.

Networks of quantum devices with coherent control over their configuration offer promising advantages in quantum information processing. So far, the investigation of these advantages assumed that the control system was initially uncorrelated with the data processed by the network. Here, we explore the power of quantum correlations between data and control, showing two communication tasks that can be accomplished with information-erasing channels if and only if the sender shares prior entanglement with a third party (the “controller”) controlling the network configuration. The first task is to transmit classical messages without leaking information to the controller. The second task is to establish bipartite entanglement with a receiver, or, more generally, to establish multipartite entanglement with a number of spatially separated receivers.

Motivated by issues in the context of asymptotically flat spacetimes at null infinity, we discuss in the simplest example of a massless scalar field in two dimensions several subtleties that arise when setting up the canonical formulation on a single or on two intersecting null hyperplanes with a special emphasis on the infinite-dimensional global and conformal symmetries and their canonical generators, the free data, a consistent treatment of zero modes, matching conditions, and implications for quantization of massless versus massive fields.

This volume contains the proceedings of the 19th International Conference on Quantum Physics and Logic (QPL 2022), which was held June 27-July 1, 2022 at Wolfson College, University of Oxford, UK. QPL is an annual conference that brings together academic and industry researchers working on mathematical foundations of quantum computation, quantum physics, and related areas. The main focus is on the use of algebraic and categorical structures, formal languages, semantic methods, as well as other mathematical and computer scientific techniques applicable to the study of physical systems, physical processes, and their composition.

Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations of indefinite causal order conditioned on assumptions on the devices used in the laboratory. But is a device-independent certification possible, similar to the certification of Bell nonlocality through the violation of Bell inequalities? Previous results have shown that the answer is negative if the switch is considered in isolation. Here, however, we present an inequality that can be used to device-independently certify indefinite causal order in the quantum switch in the presence of an additional spacelike-separated observer under an assumption asserting the impossibility of superluminal and retrocausal influences.

We introduce the task of shadow process simulation, where the goal is to reproduce the expectation values of arbitrary quantum observables at the output of a target physical process. When the sender and receiver share classical random bits, we show that the performance of shadow process simulation exceeds that of conventional process simulation protocols in a variety of scenarios including communication, noise simulation, and data compression. Remarkably, shadow simulation provides increased accuracy without any increase in the sampling cost. Overall, shadow simulation provides a unified framework for a variety of quantum protocols, including probabilistic error cancellation and circuit knitting in quantum computing.

In the model of quantum cloud computing, the server executes a computation on the quantum data provided by the client. In this scenario, it is important to reduce the amount of quantum communication between the client and the server. A possible approach is to transform the desired computation into a compressed version that acts on a smaller number of qubits, thereby reducing the amount of data exchanged between the client and the server. Here we propose quantum autoencoders for quantum gates (QAEGate) as a method for compressing quantum computations. We illustrate it in concrete scenarios of single-round and multi-round communication and validate it through numerical experiments. A bonus of our method is it does not reveal any information about the server’s computation other than the information present in the output.

We construct an explicit realization of the action of the $Lw_{1+infty}$ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of $Lw_{1+infty}$ symmetries in twistor space, ensuring that it forms a representation of the algebra. Finally, we show that this action coincides with the canonical action of $Lw_{1+infty}$ Noether charges on the asymptotic phase space.

There is a significant disconnect between linguistic theory and modern NLP practice, which relies heavily on inscrutable black-box architectures. DisCoCirc is a newly proposed model for meaning that aims to bridge this divide, by providing neuro-symbolic models that incorporate linguistic structure. DisCoCirc represents natural language text as a `circuit’ that captures the core semantic information of the text. These circuits can then be interpreted as modular machine learning models. Additionally, DisCoCirc fulfils another major aim of providing an NLP model that can be implemented on near-term quantum computers. In this paper we describe a software pipeline that converts English text to its DisCoCirc representation. The pipeline achieves coverage over a large fragment of the English language. It relies on Combinatory Categorial Grammar (CCG) parses of the input text as well as coreference resolution information. This semantic and syntactic information is used in several steps to convert the text into a simply-typed $lambda$-calculus term, and then into a circuit diagram. This pipeline will enable the application of the DisCoCirc framework to NLP tasks, using both classical and quantum approaches.