Hard limits on the postselectability of optical graph states

Coherent control of large entangled graph states enables a wide variety of quantum information processing tasks, including error-corrected quantum computation. The linear optical approach offers excellent control and coherence, but today most photon sources and entangling gates---required for the construction of large graph states---are probabilistic and rely on postselection. In this work, we provide proofs and heuristics to aid experimental design using postselection. We derive a fundamental limitation on the generation of photonic qubit states using postselected entangling gates: experiments which contain a cycle of postselected gates cannot be postselected. Further, we analyse experiments that use photons from postselected photon pair sources, and lower bound the number of classes of graph state entanglement that are accessible in the non-degenerate case---graph state entanglement classes that contain a tree are are always accessible. Numerical investigation up to 9-qubits shows that the proportion of graph states that are accessible using postselection diminishes rapidly. We provide tables showing which classes are accessible for a variety of up to nine qubit resource states and sources. We also use our methods to evaluate near-term multi-photon experiments, and provide our algorithms for doing so.Comment: Our manuscript comprises 4843 words, 6 figures, 1 table, 47 references, and a supplementary material of 1741 words, 2 figures, 1 table, and a Mathematica code listin

Mid-infrared quantum optics in silicon

Applied quantum optics stands to revolutionise many aspects of information technology, provided performance can be maintained when scaled up. Silicon quantum photonics satisfies the scaling requirements of miniaturisation and manufacturability, but at 1.55 $\mu$m it suffers from unacceptable linear and nonlinear loss. Here we show that, by translating silicon quantum photonics to the mid-infrared, a new quantum optics platform is created which can simultaneously maximise manufacturability and miniaturisation, while minimising loss. We demonstrate the necessary platform components: photon-pair generation, single-photon detection, and high-visibility quantum interference, all at wavelengths beyond 2 $\mu$m. Across various regimes, we observe a maximum net coincidence rate of 448 $\pm$ 12 Hz, a coincidence-to-accidental ratio of 25.7 $\pm$ 1.1, and, a net two photon quantum interference visibility of 0.993 $\pm$ 0.017. Mid-infrared silicon quantum photonics will bring new quantum applications within reach.Comment: 8 pages, 4 figures; revised figures, updated discussion in section 3, typos corrected, added referenc

Mapping graph state orbits under local complementation

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay---our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement

Maximizing precision in saturation-limited absorption measurements

Quantum fluctuations in the intensity of an optical probe is noise which limits measurement precision in absorption spectroscopy. Increased probe power can offer greater precision, however, this strategy is often constrained by sample saturation. Here, we analyse measurement precision for a generalised absorption model in which we account for saturation and explore its effect on both classical and quantum probe performance. We present a classical probe-sample optimisation strategy to maximise precision and find that optimal probe powers always fall within the saturation regime. We apply our optimisation strategy to two examples, high-precision Doppler broadened thermometry and an absorption spectroscopy measurement of Chlorophyll A. We derive a limit on the maximum precision gained from using a non-classical probe and find a strategy capable of saturating this bound. We evaluate amplitude-squeezed light as a viable experimental probe state and find it capable of providing precision that reaches to within > 85% of the ultimate quantum limit with currently available technology.Comment: 12 pages and 5 figure

Relative multiplexing for minimizing switching in linear-optical quantum computing

Many existing schemes for linear-optical quantum computing (LOQC) depend on multiplexing (MUX), which uses dynamic routing to enable near-deterministic gates and sources to be constructed using heralded, probabilistic primitives. MUXing accounts for the overwhelming majority of active switching demands in current LOQC architectures. In this manuscript, we introduce relative multiplexing (RMUX), a general-purpose optimization which can dramatically reduce the active switching requirements for MUX in LOQC, and thereby reduce hardware complexity and energy consumption, as well as relaxing demands on performance for various photonic components. We discuss the application of RMUX to the generation of entangled states from probabilistic single-photon sources, and argue that an order of magnitude improvement in the rate of generation of Bell states can be achieved. In addition, we apply RMUX to the proposal for percolation of a 3D cluster state in [PRL 115, 020502 (2015)], and we find that RMUX allows a 2.4x increase in loss tolerance for this architecture.Comment: Published version, New Journal of Physics, Volume 19, June 201

High-performance, adiabatically nanotapered fibre-chip couplers in silicon at 2 microns wavelength

Fibre optic technology connects the world through the Internet, enables remote sensing, and connects disparate functional optical devices. Highly confined silicon photonics promises extreme scale and functional integration. However, the optical modes of silicon nanowire waveguides and optical fibres are very different, making efficient fibre-chip coupling a challenge. Vertical grating couplers, the dominant coupling method today, have limited optical bandwidth and are naturally out-of-plane. Here we demonstrate a new method that is low-loss, broadband, easily manufacturable, and naturally planar. We adiabatically couple a tapering silicon nanowire waveguide to a conic nanotapered optical fibre, measuring transmission between 2.0 and 2.2 micron wavelength. The silicon chip is fabricated at a commercial foundry and then post-processed to release the tapering nanowires. We estimate an optimal per-coupler transmission of -0.48 dB (maximum; 95% confidence interval [+0.46, -1.68] dB) and a 1-dB bandwidth of 295 nm . With automated measurements, we quantify the device tolerance to lateral misalignment, measuring a flat response within +/- 0.968 micron. This design can enable low-loss modular systems of integrated photonics irrespective of material and waveband.Comment: 6 pages, 3 figure

Gallium Arsenide (GaAs) Quantum Photonic Waveguide Circuits

Integrated quantum photonics is a promising approach for future practical and large-scale quantum information processing technologies, with the prospect of on-chip generation, manipulation and measurement of complex quantum states of light. The gallium arsenide (GaAs) material system is a promising technology platform, and has already successfully demonstrated key components including waveguide integrated single-photon sources and integrated single-photon detectors. However, quantum circuits capable of manipulating quantum states of light have so far not been investigated in this material system. Here, we report GaAs photonic circuits for the manipulation of single-photon and two-photon states. Two-photon quantum interference with a visibility of 94.9 +/- 1.3% was observed in GaAs directional couplers. Classical and quantum interference fringes with visibilities of 98.6 +/- 1.3% and 84.4 +/- 1.5% respectively were demonstrated in Mach-Zehnder interferometers exploiting the electro-optic Pockels effect. This work paves the way for a fully integrated quantum technology platform based on the GaAs material system.Comment: 10 pages, 4 figure

Multidimensional quantum entanglement with large-scale integrated optics

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to $15 \times 15$ on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies.Comment: Science, (2018

Programmable four-photon graph states on a silicon chip

Future quantum computers require a scalable architecture on a scalable technology---one that supports millions of high-performance components. Measurement-based protocols, based on graph states, represent the state of the art in architectures for optical quantum computing. Silicon photonics offers enormous scale and proven quantum optical functionality. Here we report the first demonstration of photonic graph states on a mass-manufactured chip using four on-chip generated photons. We generate both star- and line-type graph states, implementing a basic measurement-based protocol, and measure heralded interference of the chip's four photons. We develop a model of the device and bound the dominant sources of error using Bayesian inference. The two-photon barrier, which has constrained chip-scale quantum optics, is now broken; future increases in on-chip photon number now depend solely on reducing loss, and increasing rates. This experiment, combining silicon technology with a graph-based architecture, illuminates one path to a large-scale quantum future