United Kingdom

Photons are natural carriers of high-dimensional quantum information, and the encoded qudits can benefit from higher quantum information capacity and noise-resilience. However, schemes to generate the resources needed for high-dimensional quantum computing have so far not been demonstrated for linear optics. Here, we show how to generate GHZ states of arbitrary numbers of photons in arbitrary dimensions using destructive interference in linear optical circuits described by Fourier matrices. We combine our results with recent schemes for qudit Bell measurements to show that universal linear optical quantum computing can be performed in arbitrary dimensions.

Bristol Quantum Information Technologies Workshop

A scheme for universal high-dimensional quantum computation with linear optics

interference

single photons

quantum computing

**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

Natural language processing (NLP) problems are ubiquitous in classical computing, where they often require millions of dollars on computational resources and billions of parameters to infer sentence meanings. It is not efficient classically to improve these state-of-the-art language models and this means that the required computational resources are expected to scale exponentially with the increase in parameters. With the appearance of quantum computing hardware and simulators, it is worth developing methods to examine such problems on these platforms. 

Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware.

We are introducing a version of the popular transformer model in which by the application quantum phenomena we are trying to find a way to bring down the training cost in NISQ computers. We are using the DisCoCat language modeling framework to encode text into quantum gates. The quantum transformer algorithm is created in Qiskit by adding variational quantum circuit layers to the classical transformer. We are also experimenting with different ansatz and cost functions to prevent the barren plateau issue. We will evaluate the model on NLP tasks like classification, machine translation, and next-word prediction.

Quantum Transformer

Entanglement between remote matter systems is the cornerstone of quantum information transfer, crucial for establishing quantum secure communication between distant parties as well as for distributed quantum information processing architectures. This can be done via the implementation of cooperative light-matter coupling between coherently controllable matter qubits. This can manifest in collective rate enhancements, such as those at the heart of super radiance [1], but also includes effects such as measurement-induced remote entanglement via path erasure [2]. Here, we report coherent control of cooperative emission from two indistinguishable solid-state emitters, brought into resonance via Stark tuning. We characterize the indistinguishability of the emitters and the degree of correlation in the initial state of the joint system by observing the emergence of the bunched correlation peak in the intensity correlation experiment [3], the primary signature of cooperative emission. We find that due to the substantial spatial separation between the emitters, the cooperative emission lifetime is unchanged from the spontaneous emission lifetimes of the uncorrelated emitters. This highlights the fact that the bunched correlation peak in the intensity correlation is not a sufficient witness of superradiant behavior. Finally, in a stark departure from a pair of uncorrelated emitters, we observe photon statistics resembling that of a weak coherent state in Hong-Ou-Mandel type two-photon interference measurements. These experiments establish a new way to control and characterize cooperative behavior between distant matter qubits using the full quantum optics toolbox, a key stepping stone on the route to realizing large-scale quantum photonic network.

[1] R. H. Dicke, Phys. Rev. 93, 99 (1954). [2] S. Wolf et. Al., Phys. Rev. Lett. 124, 063603 (2020). [3] A. Sipahigil et. al., Science 354, 847-850 (2016).

Coherent Control of Cooperative Photon Emission from Indistinguishable Quantum Emitters

Energy-based neural networks adopt the principles of statistical physics to guarantee their self-regulation. Contrary to probabilistic models, they do not need labels to train and normalization efforts to compute their scores. Shaping the energy function brings substantial power and flexibility to a learning process, which is normally framed as an optimization problem. 

The energy landscape for the modern neural network architectures comprises high but thin barriers surrounding shallow local minima. While there is no clear understanding of convergence dynamics produced by classical optimization techniques, quantum annealing which allows tuning the underlying quantum dynamics and has a hardware implementation looks promising.

To deepen the understanding of the potential of quantum tunnelling in energy-based optimization, this study suggests adopting a new paradigm of simulation or "gamification". We analyse the convergence dynamics through building a real (classical) and the alternate (quantum) world, where we can model, observe, and control the behaviour of neurons, communities of neurons, and different types of interactions between them facing open challenges in AI.

Classical versus quantum convergence dynamics in energy-based neural networks

In this presentation, we introduce and study the Quantum Measurement Detection Algorithms (QMDA), whose objective is to detect weather unwanted measurements are being made in a quantum circuit or not. A QMDA is a quantum circuit that includes three unitary matrices, one of them being applied numerous times consecutively, and whose initial state is fixed when no foreign measurements occur. One of the most basic yet effective examples is the Elitzur-Vaidman bomb-tester, which is generalized, among other similar circuits, in the QMDA definition; however, the algorithms studied in this work must be prepared for detecting measurements that are made in an unknown basis. We will show some key properties and limitations of these algorithms, as well as studying the performance of the Elitzur-Vaidman bomb-tester. We finish the presentation suggesting different extensions of the definition that may lead to more effective algorithms and that englobe other existing ones like the counterfactual communication algorithm.

Quantum Measurement Detection Algorithms

To investigate the fundamental nature of matter and its interactions, particles are accelerated to very high energies and collided within detectors, producing a multitude of other particles that are scattered in all directions. These particles leave signals of their passage while transversing the detector. The problem of track reconstruction is to recover the original trajectories from these signals. This represents a very demanding data analysis problem, and it will become even more so as the luminosity of the next generation accelerators keeps increasing.
Approaches to track reconstruction based on quantum information technologies have recently been put forward. In order to access the potential for a quantum speedup for this problem, we start by elaborating a computational complexity analysis of a standard tracking algorithm, the Combinatorial Track Finder. First, we find that it is possible to improve the classical complexity of the original algorithm.
We further show that we can use quantum search algorithms to reach a lower quantum computational complexity. To the best of our knowledge, this is the first computational complexity-level demonstration of a quantum advantage for a state-of-the-art track reconstruction method.
Work developed in collaboration with A.Ambainis, P.Bargassa, M.Dimitrijevs, A.Glos, M.Kālis, A.Kumar, A.Locāns, Y.Omar, S.Pratapsi, G.Quinta, A.Rivošs, J.Seixas.

Investigating Quantum Speedup for Track Reconstruction: Classical and Quantum Computational Complexity Analysis

The field of Quantum Microscopy (QM) promises highly efficient imaging for low absorption samples and microscopy at the single photon level. The recently developed Skipper-CCD detector technology is able to measure the charge in each pixel, repeatedly, in a non-destructive way. As a result, the readout noise can be reduced as much as desired [Tiffenberg et al, 2017]. It allows the precise counting of the number of electrons in each pixel ranging from empty pixel to more than 1900 electrons [Rodrigues et al. 2021]. In addition, they account for very high quantum efficiency (above 90% in the visible range), extremely low dark current (less than 1 electron per pixel per day), and high resolution (pixel size of 15 microns by 15 microns). The use of Skipper-CCD detectors opens the possibilities for multiple applications within this field. In particular, they are expected to provide comparable resolution and Noise Reduction Factor to state-of-the-art setups for QM, with a dramatically/drastically reduced photon count per pixel. The same advantage can be expressed as an order of magnitude increase in resolution for the same number of photons per pixel. This presents a valuable impact of QM applications in biology and chemistry, when avoiding damage of the sample is required [Taylor et al, 2012]. The status and plans for the implementation of Skipper-CCD in this field will be presented.

[Tiffenberg et al.] Single-Electron and Single-Photon Sensitivity with a Silicon Skipper CCD. Phys. Rev. Lett.,119,13,131802,2017,10.1103/PhysRevLett.119.131802
[Rodrigues et al.] Absolute measurement of the Fano factor using a Skipper-CCD. arXiv:2004.11499v3
[Taylor et al.] Biological measurement beyond the quantum limit. Nature Photon 7, 229–233 (2013). https://doi.org/10.1038/nphoton.2012.346


Impact of Skipper-CCD technology on Quantum Microscopy

Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as Quantum Approximate Optimization Algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quantifying the efficiency of QAOA in general classes of models has been lacking. Here, we propose that the success of QAOA in preparing ordered states is related to the interaction distance of the target state, which measures how close that state is to the manifold of all Gaussian states in an arbitrary basis of single-particle modes. 
We numerically verify this for several examples of non-integrable quantum models, including Ising models with two- and three-spin interactions and the cluster model in an external field.
Our results suggest that the structure of the entanglement spectrum, as witnessed by the interaction distance, correlates with the success of QAOA state preparation, and that this correlation also contains information about different phases present in the model. We conclude that QAOA typically finds a solution that perturbs around the closest free-fermion state.

Quantifying the efficiency of state preparation via quantum variational eigensolvers

Twin-field (TF) quantum key distribution (QKD) is the only currently implementable protocol able to beat point-to-point QKD and behave similarly to a single repeater system. Exploiting this behaviour, recent experiments have increased the record distance of QKD to 500 km. Nevertheless, the full potential of TF-QKD is yet to be exploited as such results suffered by the stringent requirement on phase coherence posed by the protocol. Their performance is limited in both, distance and secret key rate, by the methods implemented to satisfy this requirement, which include the generation of bright phase reference signals at the same wavelength as the quantum channel, thereby generating noise due to Rayleigh scattering. Here, we demonstrate a new technique for phase stabilisation, based on the wavelength separation of bright phase reference light and dim signal pulses, robust against past limitations. This dual-band phase correction scheme allows us to realise a low noise system, able to perform all proposed TF-QKD protocols, with results limited solely by the protocol’s theory and the usual experimental restrictions, such as detector performance. We show repeater-like key rates over record communication distances up to 605 km, and a secure key rate increase of two orders of magnitude at long distance.

Twin-field quantum key distribution over 600 km of fibre

Mechanical quantum systems embedded in an external nonlinear potential currently offer the first deep excursion into non-Gaussian quantum motion. The Gaussian statistics of the motion of a linear mechanical quantum system, characterised by its mass and a linear-and-quadratic potential, possess a limited capacity to reduce noise in nonlinear variables. This limitation induces thresholds for noise reduction in nonlinear variables beyond which linear mechanical oscillators cannot pass. Squeezing below these thresholds is relevant for the implementation of nonlinear mechanical devices, such as sensors, processors or engines. First however, quantum non-Gaussian motion must be identified in experiments with diverse nonlinear potentials. For this purpose, we provide sufficient criteria for quantum non-Gaussian motion based on the observation of mechanical squeezing in nonlinear variables. We further extend these criteria to a hierarchy able to recognise the quantum non-Gaussian motion induced via diverse nonlinear potentials through their capacity to produce nonlinear squeezing. 


Criteria for Quantum Non-Gaussian Motion

Variational Quantum Eigensolvers are subject to active research as applications of near-term quantum computers. Recent work introduced stochastic gradient descent methods for such parametric quantum circuits, but studied their efficiency only on qubit-based architectures.
In this work we present the application of different variants of the stochastic gradient descent method in the continuous-variable framework. In particular, we use stochastic and doubly stochastic gradient descent to find the ground state of a Bose-Hubbard model. We achieve acceptable convergence even with a relatively low number of shots, and sampling about half of the terms of the original Hamiltonian.

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