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Frequency-encoded quantum multi-photon interference devices

Periodic Reporting for period 1 - FrEQuMP (Frequency-encoded quantum multi-photon interference devices)

Période du rapport: 2019-12-01 au 2021-11-30

Advances in computing have revolutionised many aspects of our lives. However, increasingly new models of computation are required, as shrinking feature sizes in processors approach the limit where quantum effects become relevant, and some important problems remain intractable to solve. In this context, quantum computing has far-reaching implications – it holds the promise of exponentially greater computing power for particular tasks, such as optimization of a quantity depending on many variables or simulation of molecules to enable the design of new drugs and materials. Optical quantum computing with single photons is a good candidate for demonstrating a near-term computational speed-up. Photons are well isolated from thermal noise and maintain their quantum coherence even at room temperature, avoiding the cost and complexity of cryogenic or vacuum conditions. The propagation of single photons in a linear optical circuit is inefficient to simulate using classical methods (so-called Boson Sampling), so by extension this experimentally accessible architecture can provide a quantum advantage for specific problems.

Gaussian boson sampling is a variant on Boson Sampling which replaces the single photon inputs with 'squeezed' light - highly non-classical states which are readily generated using nonlinear optics. Gaussian boson sampling exhibits a quantum advantage, and has a variety of useful applications - these include calculating the vibronic spectra of molecules, and identifying densely connected sub-graphs in networks. Hence Gaussian boson sampling is a practical and useful model for near-term quantum computation. However, current implementations based on free-space optics are bulky, labour-intensive to align, and lack programmability. Approaches based on integrated photonics offer compactness and the potential for programmability, but they are currently limited by lossy components.

This project aims to develop compact and programmable approaches which can quickly and practically be scaled to a useful size - with a focus on frequency-encoding of information onto photons, to reduce the number of separate components required. By leveraging the frequency entanglement generated by a single squeezed-light source powered by a short pump laser, complex multi-mode states can be generated without the need for a large optical circuit. Further, applying pulse-shaping techniques to the pump pulse adds control over the generated state without the need to manipulate the actual quantum light - and hence avoids introducing loss and other imperfections. An experimental demonstration verified the quantum interference between 8 photons distributed across 16 frequency channels - the largest such experiment to be performed in frequency-encoding. The use of commercially available components in a compact setup will make this scheme convenient to scale to still larger experiments.

Another focus has been understanding the classical complexity of Gaussian boson sampling - when assessing the advantage achieved by quantum devices, they are often compared to a simulation on classical hardware, so it is important to have an accurate idea of the classical runtime. New classical algorithms were developed for the simulation of Gaussian boson sampling outperforming previous efforts by nine orders of magnitude, which were benchmarked on high-performance computing hardware up to a scale of 100 modes - comparable to the largest experiments. This will be valuable in assessing and verifying future experiments.
Using a squeezed-light source and a time-of-flight spectrometer to measure the generated photons' frequencies, it was demonstrated that the joint spectral state of the photons could be shaped by pulse-shaping of the pump laser. Applying a chirp to the pump laser, an interference landscape was created in the four photon events generated from the source. Results were published in Optics Express 28, 34246-34254 (2020). A further scheme to characterise joint spectra using multi-photon interference was conceived and demonstrated, using interference with a weak coherent reference pulse. This result was recently published in Physical Review Letters 128, 023601 (2022). Shaping the pump into a comb of discrete components and separating the photons into 16 discrete channels using a wavelength multiplexer, a Gaussian boson sampling experiment was demonstrated. With a source chosen for brightness and a wideband emission, up to 9-photon events were detected. An article based on these results is in preparation.

Gaussian boson sampling experiments were performed combining squeezed quantum light with a classical coherent state for the first time, a necessary step for some applications, and new methods of characterising the resulting state were developed. The experiment made use of a 15-mode interferometer on a silicon photonic chip, developed with researchers at Sun Yat-sen University. An article based on these results is in preparation.

An algorithm was developed for classical simulation of Gaussian boson sampling with a run-time scaling quadratically faster than previous algorithms. This was published in PRX Quantum 3, 010306 (2022). Further advances were made speeding up calculations when multiple photons arrive at the same detector, a characteristic of current large-scale experiments. In collaboration with researchers at the University of Bristol and Hewlett Packard Enterprise, this algorithm was benchmarked on a high-performance computer, generating samples as large as 92 photons across 100 modes. This work has been accepted for publication in Science Advances.
Gaussian boson sampling is a form of photonic quantum computing which is practical to realise in the near-term and which can deliver societal impacts through applications such as molecular simulations and graph-based optimisation tasks. This project has focused on achieving practical, compact, and programmable implementations of Gaussian boson sampling which will aid scaling to useful sizes and applications to useful tasks. Leveraging frequency-time entanglement generated by quantum light sources pumped by femtosecond laser pulses, complex multi-mode Gaussian states are generated without requiring a bulky circuit.

To date this has reached a scale of 16 frequency channels. While smaller than the 100 modes achieved by free-space optics, the experimental setup is far more compact and less labour intensive to align, consisting entirely of commercially available components. This will make it easier to reproduce and accelerate scaling. Work on Gaussian boson sampling in silicon photonic circuits has also pushed the state of the art by combining quantum and classical light for the first in such an experiment, which is a requirement in the simulation of molecular vibronic spectra.

This project has progressed beyond the state of the art in the classical simulation of Gaussian boson sampling. Classical simulations are needed to assess the advantage achieved by quantum experiments, and to verify their results. We have developed dramatically faster classical algorithms, improving the runtime of simulating the largest experiments by nine orders of magnitude. This has advanced the understanding of computational complexity in such experiments, and will guide further experimental efforts towards increasing quantum advantage.
Four photon interference in the frequency domain (a) Experiment and (b) Simulation
Measured distribution of six photon counts across 16 frequency channels
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