United Kingdom

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.

Bristol Quantum Information Technologies Workshop

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

track reconstruction

quantum algorithms

particle physics

**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

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.

Continuous-variable stochastic gradient descent methods applied for
a photonic variational quantum eigensolver

Entanglement creation using parametric down-conversion (PDC) sources has enabled pioneering studies of foundational physics and proof-of-principle demonstrations of quantum information processing techniques. However, typical PDC sources produce unwanted spectral correlations which degrade two-photon interference, introducing errors in the generation of multi-photon states.

Employing domain-engineering techniques to directly modify the non-linear PDC process to significantly suppress unwanted spectral correlation, we remove the need for spectral filtering. With this same technique, we have also demonstrated time-frequency mode entanglement and time-frequency hyper-entanglement.

For the generation of pure telecom photons, the optimisation of parameters that trade-off the non-trivial relationship between non-linearity and indistinguishability enabled us to improve upon previous crystal designs to operate on the achievable limits of domain-engineered PDC. We experimentally measured two-photon interference visibilities of up to 98.6 ± 1.1% between photons generated from two independent sources without filters. As a result, we obtain net heralding efficiencies up to 67.5%, corresponding to overall collection efficiencies exceeding 90%.

With the performance figures presented here, we can produce complex photonic graph states with high rates, allowing for experiments addressing realistic challenges prominent within prospective long-distance quantum networks.

Optimised parametric down-conversion sources for generating telecom graph states

Fibre lasers have become highly prevalent due to their cost, stability and practicality. However, they are inherently noisy and this is a severe limitation when using them for microscopy, spectroscopy or to generate quantum states of light. We have developed a “plug-and-play” module that can be retrofitted to fibre lasers that are already deployed in the field, reducing the optical noise at the laser output down to a fundamental limit of classical physics. 

The SLOW MO project is advancing the commercial readiness of this noise suppression module by identifying potential customers, engineering a robust demonstrator for deployment outside the optics laboratory and fostering relationships with end users willing to take part in trials. This poster will summarise the work done so far in identifying potential applications and suppressing noise in optical systems, bridging the gap between academic research and commercial exploitation of filter modules that allow lasers to operate at the fundamental shot noise limit.

A Shot-Noise Limited Optical Waveguide Module

The limited range of quantum key distribution (QKD) in fiber based systems led to several projects aiming for the development of a satellite based QKD infrastructure. Photonic integrated circuits (PICs) are a convenient way to implement all necessary optical functions necessary for QKD, while meeting the stringent demands on size, weight and power in satellite missions.

In this work, we present our payload intended for the demonstration of integrated quantum communication technology in space. It is based on two Indium-Phosphide PICs implementing a source for modulated weak coherent states as well as a quantum random number generator (QRNG) based on homodyne measurements of the quantum mechanical vacuum state. The whole system is implemented on a 10 cm x 10 cm PCB including electronics, making it compatible to the CubeSat standard. 

These developments will be tested as a part of the CubeSat mission QUBE, which is scheduled for launch in December 2021.

Integrated photonics for quantum communications on a CubeSat

High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables.
Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion.
Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed.
For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures.
We test the method numerically by analysing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test.
The method paves a road for unique experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.


Stroboscopic high-order nonlinearity for quantum optomechanics

The discrete time crystal (DTC) is a recently discovered out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Experimental observation has proven elusive due to the necessity of disorder-induced many-body localization to stabilize the DTC phase. Here, we observe the hallmark long-lived spatiotemporal order of the DTC phase using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. The observed subharmonic response is robust for states with different temperatures, distinguishing the DTC phase from the prethermal subharmonic responses attributed to previous experiments. Our results provide the experimental signatures of a new out-of-equilibrium phase of matter and introduce a programmable spin-based quantum simulator for many-body physics.

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

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Impact of Skipper-CCD technology on Quantum Microscopy

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