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A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.

Bristol Quantum Information Technologies Workshop

Distributing Multipartite Entanglement over Noisy Quantum Networks

multi-objective routing

quantum networks

entanglement distribution

**BQIT is a three day annual workshop** aimed at enabling leading UK and international academics and industrial partners to come together; to explore and discuss future ambitions and challenges in the field of **Quantum Information Technologies.** Since our conception in 2014 we have had 230 speakers and panellists who have presented their work and opinions on a range of topics, from quantum theory to innovation in industry.


### Welcome Message
The BQIT:21 team welcomes you to the eighth Bristol Quantum Information Technologies workshop! 

Last year was the first time in our workshop's history that we had gone fully virtual. The global circumstances that continue to impact us all professionally and personally have forced BQIT once again to be delivered as an all-virtual workshop for 2021. The access this creates to colleagues across the world who would otherwise be unable to join us, as well as being able to make the workshop free for all attendees due to the lower costs involved in delivering an online workshop, are just a couple of the extraordinary benefits of meeting online. This also means that we can welcome three times as many attendees to BQIT than previous years.   

We take this opportunity to thank each of our speakers and poster presenters for contributing their technical content, this year's sponsors, whose support this year enabled BQIT:21 to be free to all attendees, and to all of our attendees for joining us online this year. We recognise the extra energy required to stay connected and motivated during these difficult times, and are hugely encouraged to see so many of you willing to continue to connect with us on an online platform. 

It is our hope that you have a productive and enjoyable time while you engage and interact with BQIT:21, and to everyone that has helped take BQIT:21 online, thank you! 

**The BQIT board and organisation team **


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### This year's workshop agenda is available here: [Virtual BQIT:21](https://drive.google.com/file/d/1QwsSM0ztnxC_lgUKf3TbO3GvnI44AQkY/view?usp=sharing)
For further information, please contact us at: **bqit-admin@bristol.ac.uk**

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poster

We demonstrate a method to create maximal entanglement between two qubits encoded in two spectrally distinct solid-state emitters embedded in a waveguide interferometer. The qubits are repeatedly probed using readily accessible squeezed light, generated by parametric down-conversion, and the photon scattering process results in a build-up of entanglement between the two qubits. The method accommodates spectral variations that arise due to the fabrication process and therefore relaxes the requirement of perfectly identical emitters.

Maximal entanglement of spectrally distinct solid-state qubits by iteration

Small, controllable quantum systems, known as quantum probes, have been proposed to estimate various parameters characterizing complex systems such as the environments of quantum systems. These probes, prepared in some initial state, are allowed to interact with their environment, and subsequent measurements reveal information about different quantities characterizing the environment such as the system-environment coupling strength, the cutoff frequency, and the temperature. These estimates have generally been made by considering only the way that the probe undergoes decoherence. However, we show that information about the environment is also imprinted on the probe via the probe and environment correlations that exist before the probe state preparation. This information can then be used to improve our estimates for any environment. We apply this general result to the particular case of a two-level system probe undergoing pure dephasing, due to a harmonic oscillator environment, to show that a drastic increase in the quantum Fisher information, and hence the precision of our estimates, can indeed be obtained. We also consider applying periodic control pulses to the probe to show that with a combination of the two - the effect of the control pulses as well as the initial correlations - the quantum Fisher information can be increased by orders of magnitude.

Improving the estimation of environment parameters via initial probe-environment correlations

Multilayer polymer photonic crystals, with a bandgap in the near-infrared (~1.3um), can be easily fabricated using two-photon lithography [1]. To achieve shorter period structures, we explore thermal decomposition to eliminate unpolymerized material and reduce the oxygen content of exposed polymer structures using heat [2]. This method has been shown to shrink polymer structures by a factor of 4 [2,3]. The current challenge is about conserving symmetry and geometry. Those two factors play a significant role in the resulting optical properties. The material strongly adheres to the substrate and requires a deformable/elastic anchoring to enable isotropic (shape-conserving) shrinking of the main photonic crystal structure. After shrinkage, the relative rod diameter appears larger, and we are investigating isotropic oxygen plasma etching to remove some material [2]. Finally, we use Fourier-Image spectroscopy to characterize the bandgaps of fabricated structures (before & after thermal post-processing), comparing results with various simulation tools (Plane-Wave Expansion and finite-difference time-domain). We plan to extend this technique to 3D photonic crystal defect cavities [4,5], in order to facilitate the creation of future quantum devices using quantum emitters in the visible wavelength region.


Shrinking of direct laser written polymeric structures by thermal annealing to move the bandgap into the visible range

We have developed two quantum classifier models for the $t\bar{t}H$ classification problem, both of which fall into the category of hybrid quantum-classical algorithms for Noisy Intermediate Scale Quantum devices (NISQ). Our results, along with other studies, serve as a proof of concept that Quantum Machine Learning (QML) methods can have similar or better performance, in specific cases of low number of training samples, with respect to conventional ML methods even with a limited number of qubits available in current hardware. To utilise algorithms with a low number of qubits --- to accommodate for limitations in both simulation hardware and real quantum hardware --- we investigated different feature reduction methods. Their impact on the performance of both the classical and quantum models was assessed. We addressed different implementations of two QML models, representative of the two main approaches to supervised quantum machine learning today: a Quantum Support Vector Machine (QSVM), a kernel-based method, and a Variational Quantum Circuit (VQC), a variational approach.

Higgs analysis with quantum support vector machines and variational quantum classifiers

Quantum networks are a new paradigm of complex networks, allowing us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that quantum networks based on typical noisy quantum-repeater nodes are prone to discontinuous phase transitions with respect to the random loss of operating links and nodes, abruptly compromising the connectivity of the network, and thus significantly limiting the reach of its operation. Furthermore, we determine the critical quantum-repeater efficiency necessary to avoid this catastrophic loss of connectivity as a function of the network topology, the network size, and the distribution of entanglement in the network. In particular, our results indicate that a scale-free topology is a crucial design principle to establish a robust large-scale quantum internet.

Robustness of Noisy Quantum Networks

The premise for this study is that quantum computing/simulation techniques can be integrated with the latest artificial intelligence (AI)/machine learning (ML) methods to deliver hybrid quantum/classical solutions for global crisis response management and war-gaming tasks. This capability would enable not only unparalleled fidelity in characterising global crisis response scenarios, but also the ability to 'war-game' vast numbers of scenarios, to find optimum responses to rapidly changing crisis situations. By exploiting these quantum techniques, we believe that these hybrid solutions could eventually help crisis responders/managers to refine optimised response plans dynamically, not just for the current crisis (e.g. global pandemic), but also for subsequent global economic and security crises that might result; enabling critical resources to be deployed more effectively to maximise operational benefits. They could also help crisis policy makers to refine policy to better prepare for global crises by war-gaming huge numbers of crisis response scenarios, and to help them determine how best to prevent and mitigate future global crises (e.g. public health, economic, security).

This feasibility study will explore which parts of the complex crisis management process could benefit from quantum algorithms, especially in representing the space of possible response plans to global crisis scenarios, and wargaming which responses deliver the most optimum response to diverse global scenarios. The premise is that quantum computers could deliver orders of magnitude improvement in processing power, that could enable global crises to be managed more effectively, before they happen!

Global crisis response management and wargaming using quantum computing/simulation techniques

We present the simulations of optical waveguide arrays used as photonic quantum simulators of a Heisenberg spin-chain in a silicon nitride photonic chip. The photonic lattices were manufactured using electron beam lithography and reactive ion etching process to obtain ridge waveguides. The photonic devices are currently in process of characterization with a CW laser of 780 nm, where the light is coupled vertically with a single mode fiber into Bragg gratings optimized for a wavelength of 800 nm. Finally, the dynamics of the system can be determined by measuring the output of the lattice and choosing the initial state with the input port of the array of waveguides.

Integrated Nanophotonic Waveguide Lattices as Photonic Quantum Simulators

We proposed a new constrained quantum optimization algorithm (CQOA) inspired by the quantum extreme value Searching algorithm (QEVSA) [1]. The QEVSA finds the extreme value (minimum or maximum) of an unconstraint goal function. It combines the well-known binary searching algorithm and the quantum existence testing [QET] which is a special case of a quantum counting algorithm. if one is interested in finding the extreme value of a constraint goal function, an extension of the functionalities of the QEVSA is required, in other words, a new extended version of the QET is needed, we name it constraint quantum relation testing (CQRT). The QET exploits the power of the quantum phase estimation (QPE) [2] for computing the necessary qubits for classical and quantum certainty of the physical implementation. Therefore, involving the constraint and the index relation which determines the type of optimization (minimum or maximum) in the QET does not modify the working mechanism of the QPE. Consequently, the optimum number of qubits necessary for the CQRT is similar to the QET function i.e., the computational complexities of QET and CQRT are equal. The CQOA merges the binary search algorithm and the CQRT function.

[1] S. Imre, ”Quantum Existence Testing and Its Application for Finding Extreme Values in Unsorted Databases” IEEE Transactions on Computers, Vol: 56, Issue: 5, May 2007.
[2] Imre, S.; Balázs, F.: Quantum computing and communications: An engineering approach (Wiley, Chichester, UK) 2005 ISBN 0-470-86902-X, DOI: 10.1002/9780470869048.


Constrained Quantum Optimization Strategy

Quantum machine learning is a research subject that is becoming increasingly relevant within the near-term quantum computation. Quantum neural networks are a well-known example for learning tasks in both qubit and qumode-based systems. Stochastic Gradient Descent (SGD) methods have been introduced in recent work for various variational quantum circuits but only in qubit-based architectures. In this work, we present different variants of the SGD method in the continuous-variable framework via the example application of photonic quantum neural networks for regression models. Using only a low number of shots, we see a nicely converging training process using simulated circuits on StrawberryFields [3] photonic simulator and its GPU enabled TensorFlow backend. Regression results are found best on 2-qumode circuits for the presented test function approximations and the effect of further stochastically sampling with mini-batches during the training process.​

Continuous-variable stochastic gradient descent methods applied for
a photonic quantum neural network

Delivering quantum optical technologies at scale will also require the scaling and integration of classical readout and control hardware. To date, silicon quantum photonics has not fully harnessed the performance of the complimentary metal-oxide-semiconductor (CMOS) electronics industry and typically relies on discrete, PCB scale, packaged hardware. We report an integrated homodyne detector consisting of a silicon photonic integrated circuit wirebonded directly to a dedicated silicon-germanium transimpedance amplifier die. We measure a bandwidth of 1.7 GHz, 84% efficiency for on-chip states, shot noise clearance across 9 GHz with a device footprint of 0.84 mm2. Using a fibre coupled PPLN source, we measure up to 0.89 dB of quadrature squeezing on-chip and characterise the squeezing across the entire 9 GHz bandwidth available. In addition, we present some new results further demonstrating the performance advances available from photonic-electronic integration.

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