arXiv subjects

Jacob F. F. Bulmer

Publications and source records attributed to Jacob F. F. Bulmer.

8 recordsLinked to original sources

arXiv2025

Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation

To understand quantum optics experiments, we must perform calculations that consider the principal sources of noise, such as losses, spectral impurity and partial distinguishability. In both discrete and continuous variable systems, these can be modeled as mixed Gaussian states over multiple modes. The modes are not all resolved by photon-number measurements and so require calculations on coarse-grained photon-number distribution. Existing methods can lead to a combinatorial explosion in the time complexity, making this task unfeasible for even moderate sized experiments of interest. In this work, we prove that the computation of this type of distributions can be done in exponential time, providing a combinatorial speedup. We develop numerical techniques that allow us to determine coarse-grained photon number distributions of Gaussian states, as well as density matrix elements of heralded non-Gaussian states prepared in the presence of spectral impurity and partial distinguishability. These results offer significant speed-up and accuracy improvements to validation tests of both Fock and Gaussian boson samplers that rely on binned probability distributions. Moreover, they pave the way to a more efficient simulation of realistic photonic circuits, unlocking the ability to perform exact calculations at scales which were previously out of reach. In addition to this, our results, including loop Hafnian master theorems, may be of interest to the fields of combinatorics and graph theory.

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arXiv2022

Threshold detection statistics of bosonic states

In quantum photonics, threshold detectors, distinguishing between vacuum and one or more photons, such as superconducting nanowires and avalanche photodiodes, are routinely used to measure Fock and Gaussian states of light. Despite being the standard measurement scheme, there is no general closed form expression for measurement probabilities with threshold detectors, unless accepting coarse approximations or combinatorially scaling summations. Here, we present new matrix functions to fill this gap. We develop the Bristolian and the loop Torontonian functions for threshold detection of Fock and displaced Gaussian states, respectively, and connect them to each other and to existing matrix functions. By providing a unified picture of bosonic statistics for most quantum states of light, we provide novel tools for the design and analysis of photonic quantum technologies.

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arXiv2022

On-chip quantum information processing with distinguishable photons

Multi-photon interference is at the heart of photonic quantum technologies. Arrays of integrated cavities can support bright sources of single-photons with high purity and small footprint, but the inevitable spectral distinguishability between photons generated from non-identical cavities is an obstacle to scaling. In principle, this problem can be alleviated by measuring photons with high timing resolution, which erases spectral information through the time-energy uncertainty relation. Here, we experimentally demonstrate that detection can be implemented with a temporal resolution sufficient to interfere photons detuned on the scales necessary for cavity-based integrated photon sources. By increasing the effective timing resolution of the system from 200ps to 20ps, we observe a 20% increase in the visibility of quantum interference between independent photons from integrated micro-ring resonator sources that are detuned by 6.8GHz. We go on to show how time-resolved detection of non-ideal photons can be used to improve the fidelity of an entangling operation and to mitigate the reduction of computational complexity in boson sampling experiments. These results pave the way for photonic quantum information processing with many photon sources without the need for active alignment.

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arXiv2022

Making Music Using Two Quantum Algorithms

This document explores how to make music using quantum computing algorithms. The text is an unedited pre-publication chapter which will appear in the book "Quantum Computer Music", Miranda, E. R. (Editor). This chapters provides the background and specific details of a collaboration formed in 2021 between the Quantum Engineering Technology Labs - a quantum computing and technology research group at the University of Bristol - and music artist, producer and audio engineer Simon Small. The goal of the collaboration was to explore how the data and concepts used in the research at the university could be `sonified' to create sounds or even make music.

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arXiv2022

Protocol for generation of high-dimensional entanglement from an array of non-interacting photon emitters

Encoding high-dimensional quantum information into single photons can provide a variety of benefits for quantum technologies, such as improved noise resilience. However, the efficient generation of on-demand, high-dimensional entanglement was thought to be out of reach for current and near-future photonic quantum technologies. We present a protocol for the near-deterministic generation of $N$-photon, $d$-dimensional photonic Greenberger-Horne-Zeilinger (GHZ) states using an array of $d$ non-interacting single-photon emitters. We analyse the impact on performance of common sources of error for quantum emitters, such as photon spectral distinguishability and temporal mismatch, and find they are readily correctable with time-resolved detection to yield high fidelity GHZ states of multiple qudits. When applied to a quantum key distribution scenario, our protocol exhibits improved loss tolerance and key rates when increasing the dimensionality beyond binary encodings.

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arXiv2021

The Boundary for Quantum Advantage in Gaussian Boson Sampling

Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian Boson Sampling (GBS), in which photons are measured from a highly entangled Gaussian state, is a leading approach in pursuing quantum advantage. State-of-the-art quantum photonics experiments that, once programmed, run in minutes, would require 600 million years to simulate using the best pre-existing classical algorithms. Here, we present substantially faster classical GBS simulation methods, including speed and accuracy improvements to the calculation of loop hafnians, the matrix function at the heart of GBS. We test these on a $\sim \! 100,000$ core supercomputer to emulate a range of different GBS experiments with up to 100 modes and up to 92 photons. This reduces the run-time of classically simulating state-of-the-art GBS experiments to several months -- a nine orders of magnitude improvement over previous estimates. Finally, we introduce a distribution that is efficient to sample from classically and that passes a variety of GBS validation methods, providing an important adversary for future experiments to test against.

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arXiv2021

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

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise-resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.

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arXiv2021

A proposal for practical multidimensional quantum networks

A Quantum Internet, i.e., a global interconnection of quantum devices, is the long term goal of quantum communications, and has so far been based on two-dimensional systems (qubits). Recent years have seen a significant development of high-dimensional quantum systems (qudits). While qudits present higher photon information efficiency and robustness to noise, their use in quantum networks present experimental challenges due to the impractical resources required in high-dimensional quantum repeaters. Here, we show that such challenges can be met via the use of standard quantum optical resources, such as weak coherent states or weak squeezed states, and linear optics. We report a concrete design and simulations of an entanglement swapping scheme for three and four dimensional systems, showing how the network parameters can be tuned to optimize secret key rates and analysing the enhanced noise robustness at different dimensions. Our work significantly simplifies the implementation of high-dimensional quantum networks, fostering their development with current technology.

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