United Kingdom

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.

Bristol Quantum Information Technologies Workshop

Quantum simulation of a discrete time crystal using solid-state spins in diamond

**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 **


![](https://assets.underline.io/uploads/markdown_image/1/image/a12e0c1ad3410144cb48557690e4ecaf.png)
### 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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technical paper

Entanglement distribution is a fundamental component of quantum networks, often in the context of quantum key distribution. It is less well known that entanglement distribution can help with a very different problem: time distribution. In this talk I will describe a protocol for time distribution and clock synchronization that allows synchronization on the order of ps, is extremely robust against losses and is resilient against spoofing attacks, which are problematic in, for example, time distribution via GPS satellites.

Right in time: Entanglement distribution for accurate and safe clock synchronization

Quantum key distribution (QKD) protocols based on high-dimensional quantum states have shown the route to increase the key rate generation while benefiting from enhanced error tolerance, thus overcoming the limitations of two-dimensional QKD protocols. Nonetheless, the reliable transmission through fiber links of high-dimensional quantum states remains an open challenge that must be addressed to boost their application. In this talk, I will present our recent demonstration of the reliable transmission, over a 2 km long multicore fiber, of path-encoded high-dimensional quantum states. Leveraging on a phase-locked loop system, stable interferometric detection is guaranteed, allowing for low error rates and the generation of 6.3 Mbit/s of secret key rate.

Path-encoded high-dimensional quantum states distribution towards QKD applications

The global interest in quantum networks stems from the security guaranteed by the laws of physics. Deploying quantum networks means facing the challenges of scaling up the physical hardware and, more importantly, of scaling up all other network layers and optimally utilising network resources. Here we consider two related protocols, their experimental demonstrations on an 8-user quantum network test-bed, and discuss their usefulness with the aid of example use cases. First, an authentication transfer protocol to manage a fundamental limitation of quantum communication -- the need for a pre-shared key between every pair of users linked together on the quantum network. By temporarily trusting some intermediary nodes for a short period of time (<35 min in our network), we can generate and distribute these initial authentication keys with a very high level of security. Second, when end users quantify their trust in intermediary nodes, our flooding protocol can be used to improve both end-to-end communication speeds and increase security against malicious nodes.

Scalable authentication and optimal flooding in a quantum network

Satellite-based quantum key distribution enables quantum-secured communication on a global scale. There are international efforts underway to build and launch satellites capable of Quantum Key Distribution (‘QKD’) e.g. the QUARC, QEYSSat, Micius and SpooQy-1 missions. 
These QKD satellites work with a network of Optical Ground Stations (OGSs) to receive optical signals and distribute cryptographic keys to end users. However, OGSs near metropolitan centres are often subject to high levels of light pollution and suffer from restricted clear lines of sight to the satellite. Further, static ground stations are severely limited by local meteorological conditions. A mobile OGS is not subject to these restrictions and can be used to distribute keys flexibly. This may be useful when performing site surveys in order to derive realistic data on expected key rates and meteorological/geographic conditions. We present our progress towards field-demonstrations of QKD using our mobile OGS to receive both a beacon signal and quantum signal. This OGS is designed to work with our industry lead 6U and research focused 12 U QKD CubeSats.

Field Demonstration Of A Mobile Optical Ground Station For CubeSat Quantum Key Distribution

Jonathan Dowling was a driving force in the optical quantum information community. His work introduced new fundamental concepts and helped experimentalists implement the abstract ideas from quantum information theory. In this commemorative talk I will use Jon’s work over the past two-and-a-bit decades to give a highly subjective sketch of the history of the field and Jon’s role in it. I will conclude with Jon’s most recent work on photonic quantum data locking. Due to the nature of the anecdotes about Jon, this talk has a PG-13 rating.

From High Noon to Boson Sampling — Commemorative Talk for Jon Dowling

Quantum computing is a promised method to solve some computational tasks that are intractable for classical computing. Boson Sampling is one of the candidates to demonstrate quantum computational advantage. In our recent experiment, we realize quantum computational advantage in a Gaussian Boson Sampling (GBS) experiment. We inject 25 two-mode squeezed states into a 100-mode ultralow-loss interferometer with full connectivity and random matrix, and sample the output distribution using 100 single photon detectors. We have ruled out some plausible hypotheses, including thermal states, distinguishable photons, and uniform distribution. We observe coincidence event with up to 76 clicks. This GBS machine can sample 14 orders of magnitude faster than classical supercomputer.

Photon-based quantum advantage

Continuous variable measurement-based quantum computation (MBQC) shows great potential for scalable quantum information processing. It has in recent years witnessed an increasing interest due to the simplicity in generating the foundational states – the cluster states – deterministically and in a scalable manner (1,2). There are still numerous steps to be taken towards realizing universal quantum computation but one of the critical steps is the realization of single and two-mode gates. 

In MBQC, quantum gates are implemented through simple Gaussian measurements of the cluster state: High-efficiency homodyne detection suffices to realize a complete gate set in the two-dimensional sub-space of the Gottesman-Kitaev-Preskill (GKP) qubits. GKP qubits are of particular interest as they allow for the implementation of non-Clifford gates via Gaussian transformation and they are error-correctable by Gaussian transformations (3). 

Here we present the execution of a complete set of measurement-based Gaussian single- and two-mode gates in a large two-dimensional cluster state (4). The fully programmable gates are also combined into a small-scaled circuit, demonstrating the programmability and flexibility of the setup. These demonstrations are critical steps towards realizing a universal quantum processor based on continuous variables. 

(1) Larsen et al, Science 366, 369 (2019) 
(2) Warit et al, Science 366, 373 (2019)
(3) Larsen et al, arxiv:2101.03014
(4) Larsen et al, arxiv:2010.14422 


Implementing gates in a continuous variable optical cluster state

Large multipartite Continuous Variables (CV) quantum states are easy to characterize as far as the measurement statistics of quadratures is Gaussian. Although they are essential resources for CV quantum technologies, non-Gaussian statistics is required for reaching a quantum computational advantage. Non Gaussianity can be induced via local operations. When the number of involved optical mode and non-Gaussian operations are large enough, these systems are hard to benchmark in theory, to test experimentally, and they can even be hard to sample. I will speak about experimental challenges on producing such states, theoretical benchmarks based on complex network theory [1] and machine learning technique for experimental detection of Wigner negativity[2].
[1]Emergent complex quantum networks in continuous-variables non-Gaussian states M .Walschaers, N. Treps, B. Sundar, L.D. Carr, V. Parigi, arXiv:2012.15608
[2]Neural networks for detecting multimode wigner negativity V. Cimini, M. Barbieri, N. Treps, M. Walschaers, V. Parigi , Physical Review Letters 125, 160504 (2020)


Non-Gaussian Continuous Variables quantum networks

The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involves maximising the interference visibility whilst maintaining an acceptable photon generation rate [1]. By developing a general theoretical framework that allows us to include large numbers of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong--Ou--Mandel interference visibility of parametric photon sources, considering both threshold and number resolving detectors, together with the effects of spectral filtering. We find that for any degree of spectral impurity, increasing the photon generation rate necessarily decreases the interference visibility, even when using number resolving detection. While tight spectral filtering can be used to enforce spectral purity and increased interference visibility at low powers, we find that the induced photon number impurity results in a decreasing interference visibility and heralding efficiency with pump power, while the maximum generation rate is also reduced [2]. More generally this formalism could be readily applied to investigations into larger scale Gaussian boson sampling protocols [3] for which the effects of source errors is yet to be fully understood.

References
[1] S. Slussarenko, and G. J. Pryde. “Photonic quantum information processing: A concise review.” Applied Physics Reviews 6.4 (2019).
[2] O. F. Thomas, W. McCutcheon, and D. P. S. McCutcheon, “A general framework for multimode Gaussian quantum optics and photo-detection: application to Hong-Ou-Mandel interference with filtered heralded single photon sources.” arXiv:2012.05991 (2020).
[3] H. S. Zhong, et al. ”Quantum computational advantage using photons.” Science 370.6523 (2020): 1460-1463.

A General Framework for Multimode Gaussian Quantum Optics and Photo-detection

Photonics is a promising platform for demonstrating quantum computational supremacy (QCS) by convincingly outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.

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Quantum simulation of a discrete time crystal using solid-state spins in diamond

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