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Boson sampling is a specialised algorithm native to the quantum photonic platform developed for near-term demonstrations of quantum advantage over classical computers. While clear useful applications for such near-term pre-fault-tolerance devices are not currently known, reaching a quantum advantage regime serves as a useful benchmark for the hardware. Here, we analyse and detail hardware requirements needed to reach quantum advantage with deterministic quantum emitters, a promising platform for photonic quantum computing. We elucidate key steps that can be taken in experiments to overcome practical constraints and establish quantitative hardware-level requirements. We find that quantum advantage is within reach using quantum emitters with an efficiency of 60%-70% and interferometers constructed according to a hybrid-mode-encoding architecture, constituted of Mach-Zehnder interferometers with an insertion loss of 0.0035 (a transmittance of 99.92%) per component.

We experimentally investigate unusual light propagation inside a three-dimensional (3D) superlattice of resonant cavities that are confined within a 3D photonic band gap. Therefore, we fabricated 3D diamond-like photonic crystals from silicon with a broad 3D band gap in the near-infrared and doped them with a periodic array of point defects. In position-resolved reflectivity and scattering microscopy, we observe narrow spectral features that match well with superlattice bands in band structures computed with the plane wave expansion. The cavities are coupled in all three dimensions when they are closely spaced and uncoupled when they are further apart. The superlattice bands correspond to light that hops in high symmetry directions in 3D - so-called Cartesian Light - that opens applications in 3D photonic networks, 3D Anderson localization of light, and future 3D quantum photonic networks., Comment: Total 23 pages. 13 pages (main paper + references) and extra 10 pages for supplementary. 5 figures in the main text and 7 in supplementary (total 12 figures) The manuscript will be submitted to an APS journal shortly afterward

We analyse the entanglement properties of deterministic path-entangled photonic states generated by coupling the emission of a quantum-dot biexciton cascade to a chiral nanophotonic waveguide, as implemented by {\O}stfeldt et al. [PRX Quantum 3, 020363 (2022)]. We model the degree of entanglement through the concurrence of the two-photon entangled state in the presence of realistic experimental imperfections. The model accounts for imperfect chiral emitter-photon interactions in the waveguide and the asymmetric coupling of the exciton levels introduced by fine-structure splitting along with time-jitter in the detection of photons. The analysis shows that the approach offers a promising platform for deterministically generating entanglement in integrated nanophotonic systems in the presence of realistic experimental imperfections., Comment: 12 pages, 5 figures

We demonstrate the resonant excitation of two quantum dots in a photonic integrated circuit for on-chip single-photon generation in multiple spatial modes. The two quantum dots are electrically tuned to the same emission wavelength using a pair of isolated $p$-$i$-$n$ junctions and excited by a resonant pump laser via dual-mode waveguides. We demonstrate two-photon quantum interference visibility of $(79\pm2)\%$ under continuous-wave excitation of narrow-linewidth quantum dots. Our work solves an outstanding challenge in quantum photonics by realizing the key enabling functionality of how to scale-up deterministic single-photon sources., Comment: 7 pages 3 figures, Supplementary materials 7 pages 9 figures

On-demand single-photon sources emitting pure and indistinguishable photons at the telecommunication wavelength are a critical asset towards the deployment of fiber-based quantum networks. Indeed, single photons may serve as flying qubits, allowing communication of quantum information over long distances. Self-assembled InAs quantum dots embedded in GaAs constitute an excellent nearly deterministic source of high quality single photons, but the vast majority of sources operate in the 900-950 nm wavelength range, precluding their adoption in a quantum network. Here, we present a quantum frequency conversion scheme for converting single photons from quantum dots to the telecommunication C band, around 1550 nm, achieving 40.8% end-to-end efficiency, while maintaining both high purity and a high degree of indistinguishability during conversion with measured values of $g^{(2)}(0)=2.4\%$ and $V^{\text{corr}}=94.8\%$, respectively., Comment: 7 pages, 4 figures

Entanglement is the fuel of advanced quantum technology. It is for instance consumed in measurement-based quantum computing and allows loss-tolerant encoding of quantum information. In photonics, entanglement has traditionally been generated probabilistically, requiring massive multiplexing for scaling up to many photons. An alternative approach utilizes quantum emitters in nanophotonic devices for deterministic generation of single photons, which an be extended to two- and multi-photon generation on demand. The proposed polarization-entanglement sources are, however, incompatible with spatial dual-rail qubit encoding, which is preferred in photonic quantum computing realized in scalable integrated photonic circuits. Here we propose and experimentally realize an on-demand source of dual-rail photon pairs using a quantum dot in a planar nanophotonic waveguide. The source exploits the cascaded decay of a biexciton state and chiral light-matter coupling to achieve deterministic generation of spatial dual-rail Bell pairs with the amount of entanglement determined by the chirality. The operational principle can readily be extended to multi-photon entanglement generation, and such sources may be interfaced with advanced photonic-integrated circuits, e.g., for efficient preparation of entanglement resource states for photonic quantum computing., Comment: 15 pages, 3 main figures and 8 supplementary figures

The scaling up of quantum hardware is the fundamental challenge ahead in order to realize the disruptive potential of quantum technology in information science. Among the plethora of hardware platforms, photonics stands out by offering a modular approach, where the main challenge is to construct sufficiently high-quality building blocks and develop methods to efficiently interface them. Importantly, the subsequent scaling-up will make full use of the mature integrated photonic technology provided by photonic foundry infrastructure to produce small foot-print quantum processors of immense complexity. A fully coherent and deterministic photon-emitter interface is a key enabler of quantum photonics, and can today be realized with solid-state quantum emitters with specifications reaching the quantitative benchmark referred to as Quantum Advantage. This light-matter interaction primer realizes a range of quantum photonic resources and functionalities, including on-demand single-photon and multi-photon entanglement sources, and photon-photon nonlinear quantum gates. We will present the current state-of-the-art in single-photon quantum hardware and the main photonic building blocks required in order to scale up. Furthermore, we will point out specific promising applications of the hardware building blocks within quantum communication and photonic quantum computing, laying out the road ahead for quantum photonics applications that could offer a genuine quantum advantage., Comment: 15 pages, 6 figures

We report on the analysis of electroabsorption in thin GaAs/Al$_{0.3}$Ga$_{0.7}$As nanophotonic waveguides with an embedded $p$-$i$-$n$ junction. By measuring the transmission through waveguides of different lengths, we derive the propagation loss as a function of electric field, wavelength, and temperature. The results are in good agreement with the Franz-Keldysh model of electroabsorption extending over 200 meV below the GaAs bandgap, i.e. in the 910--970 nm wavelength range. We find a pronounced residual absorption in forward bias, which we attribute to Fermi-level pinning at the waveguide surface, producing over 20 dB/mm loss at room temperature. These results are essential for understanding the origin of loss in nanophotonic devices operating in the emission range of self-assembled InAs semiconductor quantum dots, towards the realization of scalable quantum photonic integrated circuits., Comment: 6 pages, 3 figures

It is well known that waves incident upon a crystal are transported only over a limited distance - the Bragg length - before being reflected by Bragg interference. Here, we demonstrate how to send waves much deeper into crystals, by studying light in exemplary two-dimensional silicon photonic crystals. By spatially shaping the optical wavefronts, we observe that the intensity of laterally scattered light, that probes the internal energy density, is enhanced at a tunable distance away from the front surface. The intensity is up to $100 \times$ enhanced compared to random wavefronts and extends as far as $8 \times$ the Bragg length. Our novel steering of waves inside a forbidden gap exploits the transport channels induced by unavoidable deviations from perfect periodicity, here unavoidable fabrication deviations., Comment: 7 pages, 7 figures

Planar nanophotonic structures enable broadband, near-unity coupling of emission from quantum dots embedded within, thereby realizing ideal singe-photon sources. The efficiency and coherence of the single-photon source is limited by charge noise, which results in the broadening of the emission spectrum.We report suppression of the noise by fabricating photonic crystal waveguides in a gallium arsenide membrane containing quantum dots embedded in a $p$-$i$-$n$ diode. Local electrical contacts in the vicinity of the waveguides minimize the leakage current and allow fast electrical control ($\approx$4 MHz bandwidth) of the quantum dot resonances. Resonant linewidth measurements of $79$ quantum dots coupled to the photonic crystal waveguides exhibit near transform-limited emission over a 6 nm wide range of emission wavelengths. Importantly, the local electrical contacts allow independent tuning of multiple quantum dots on the same chip, which together with the transform-limited emission are key components in realizing multiemitter-based quantum information processing., Comment: 6 pages with 4 figures

Photonic qubits are key enablers for quantum-information processing deployable across a distributed quantum network. An on-demand and truly scalable source of indistinguishable single photons is the essential component enabling high-fidelity photonic quantum operations. A main challenge is to overcome noise and decoherence processes in order to reach the steep benchmarks on generation efficiency and photon indistinguishability required for scaling up the source. We report on the realization of a deterministic single-photon source featuring near-unity indistinguishability using a quantum dot in an 'on-chip' planar nanophotonic waveguide circuit. The device produces long strings of $>100$ single photons without any observable decrease in the mutual indistinguishability between photons. A total generation rate of $122$ million photons per second is achieved corresponding to an 'on-chip' source efficiency of $84 \%$. These specifications of the single-photon source are benchmarked for boson sampling and found to enable scaling into the regime of quantum advantage., Comment: 17 pages, 12 figures

A deterministic source of coherent single photons is an enabling device of quantum-information processing for quantum simulators, and ultimately a full-fledged quantum internet. Quantum dots (QDs) in nanophotonic structures have been employed as excellent sources of single photons, and planar waveguides are well suited for scaling up to multiple photons and emitters exploring near-unity photon-emitter coupling and advanced active on-chip functionalities. An ideal single-photon source requires suppressing noise and decoherence, which notably has been demonstrated in electrically-contacted heterostructures. It remains a challenge to implement deterministic resonant excitation of the QD required for generating coherent single photons, since residual light from the excitation laser should be suppressed without compromising source efficiency and scalability. Here, we present the design and realization of a novel planar nanophotonic device that enables deterministic pulsed resonant excitation of QDs through the waveguide. Through nanostructure engineering, the excitation light and collected photons are guided in two orthogonal waveguide modes enabling deterministic operation. We demonstrate a coherent single-photon source that simultaneously achieves high-purity ($g^{(2)}(0)$ = 0.020 $\pm$ 0.005), high-indistinguishability ($V$ = 96 $\pm$ 2 %), and $>$80 % coupling efficiency into the waveguide. The novel `plug-and-play' coherent single-photon source could be operated unmanned for several days and will find immediate applications, e.g., for constructing heralded multi-photon entanglement sources for photonic quantum computing or sensing., Comment: 12 pages, 10 figures

Semiconductor quantum dots in photonic integrated circuits enable scaling quantum-information processing to many single photons and quantum-optical gates. On-chip spectral filters are essential to achieve high-purity and coherent photon emission from quantum dots embedded in waveguides, without resorting to free-space optics. Such spectral filters should be tunable, to compensate for the inhomogeneous spectral distribution of the quantum dots transitions. Here, we report an on-chip filter monolithically integrated with quantum dots, that uses nanomechanical motion for tuning its resonant wavelength over 10 nm, enabling operation at cryogenic temperatures and avoiding cross-talk with the emitter. We demonstrate single-photon emission from a quantum dot under non-resonant excitation by employing only the on-chip filter. These results are key for the development of fully-integrated de-multiplexing, multi-path photon encoding schemes, and multi-emitter circuits.

The identification of a complete three-dimensional (3D) photonic band gap in real crystals always employs theoretical or numerical models that invoke idealized crystal structures. Thus, this approach is prone to false positives (gap wrongly assigned) or false negatives (gap missed). Therefore, we propose a purely experimental probe of the 3D photonic band gap that pertains to many different classes of photonic materials. We study position and polarization-resolved reflectivity spectra of 3D inverse woodpile structures that consist of two perpendicular nanopore arrays etched in silicon. We observe intense reflectivity peaks $(R > 90\%)$ typical of high-quality crystals with broad stopbands. We track the stopband width versus pore radius, which agrees much better with the predicted 3D photonic band gap than with a directional stop gap on account of the large numerical aperture used. A parametric plot of s-polarized versus p-polarized stopband width agrees very well with the 3D band gap and is model-free. This practical probe provides fast feedback on the advanced nanofabrication needed for 3D photonic crystals and stimulates practical applications of band gaps in 3D silicon nanophotonics and photonic integrated circuits, photovoltaics, cavity QED, and quantum information processing., Comment: 11 pages, 12 figures

We report on the realization of a highly efficient optical spot-size converter for the end-face coupling of single photons from GaAs-based nanophotonic waveguides with embedded quantum dots. The converter is realized using an inverted taper and an epoxy polymer overlay providing a 1.3~$\mu$m output mode field diameter. We demonstrate the collection of single photons from a quantum dot into a lensed fiber with a rate of 5.84$\pm0.01$~MHz and estimate a chip-to-fiber coupling efficiency of $\sim48$~\%. The stability and compatibility with cryogenic temperatures make the epoxy waveguides a promising material to realize efficient and scalable interconnects between heterogeneous quantum photonic integrated circuits., Comment: 16 pages, 5 figures, 1 table

The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity has never been established. Therefore we present precise, universal limits on the scattering properties, beyond which diffusion theory yields unphysical negative energy density and negative incident flux. When applying diffusion theory to samples outside validity ranges to {\it infer} scattering properties from transmission and reflection, the resulting transport parameters deviate by up to an order of magnitude compared to the true ones. These discrepancies are relevant to atmospheric and climate sciences, biophysics and health sciences, white LEDs and lighting, and Anderson localization of waves.

Planar nanostructures allow near-ideal extraction of emission from a quantum emitter embedded within, thereby realizing deterministic single-photon sources. Such a source can be transformed into M single-photon sources by implementing active temporal-to-spatial mode demultiplexing. We report on the realization of such a demultiplexed source based on a quantum dot embedded in a nanophotonic waveguide. Efficient outcoupling (>60%) from the waveguide into a single mode optical fiber is obtained with high-efficiency grating couplers. As a proof-of-concept, active demultiplexing into M=4 spatial channels is demonstrated by the use of electro-optic modulators with an end-to-end efficiency of >81% into single-mode fibers. Overall we demonstrate four-photon coincidence rates of >1 Hz even under non-resonant excitation of the quantum dot. The main limitation of the current source is the residual population of other exciton transitions that corresponds to a finite preparation efficiency of the desired transition. We quantitatively extract a preparation efficiency of 15% using the second-order correlation function measurements. The experiment highlights the applicability of planar nanostructures as efficient multiphoton sources through temporal-to-spatial demultiplexing and lays out a clear path way of how to scale up towards demonstrating quantum advantages with the quantum dot sources., Comment: 5 pages, 3 figures

Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes' solution by the principle of maximum ignorance. We analyse the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions of the space in between the chords by determining the largest enclosed circles and balls in this pore space, finding a lognormal distribution of the pore sizes. We apply the algorithm to the direct-laser-writing fabrication design of optical multiple-scattering samples as three-dimensional cubes of random but homogeneously positioned and oriented chords., Comment: 10 pages, 12 figures; v3: restructured paper, more references, more graphs

Secure communication is of paramount importance in modern society. Asymmetric cryptography methods such as the widely used RSA method allow secure exchange of information between parties who have not shared secret keys. However, the existing asymmetric cryptographic schemes rely on unproven mathematical assumptions for security. Further, the digital keys used in their implementation are susceptible to copying that might remain unnoticed. Here we introduce a secure communication method that overcomes these two limitations by employing Physical Unclonable Keys (PUKs). Using optical PUKs realized in opaque scattering materials and employing off-the-shelf equipment, we transmit messages in an error-corrected way. Information is transmitted as patterned wavefronts of few-photon wavepackets which can be successfully decrypted only with the receiver's PUK. The security of PUK-Enabled Asymmetric Communication (PEAC) is not based on any stored secret but on the hardness of distinguishing between different few-photon wavefronts., Comment: 20 pages, 8 figures

We theoretically investigate quantum interference of two single photons at a lossy asymmetric beam splitter, the most general passive 2$\times$2 optical circuit. The losses in the circuit result in a non-unitary scattering matrix with a non-trivial set of constraints on the elements of the scattering matrix. Our analysis using the noise operator formalism shows that the loss allows tunability of quantum interference to an extent not possible with a lossless beam splitter. Our theoretical studies support the experimental demonstrations of programmable quantum interference in highly multimodal systems such as opaque scattering media and multimode fibers.

We investigate two-photon quantum interference in an opaque scattering medium that intrinsically supports $10^6$ transmission channels. By adaptive spatial phase-modulation of the incident wavefronts, the photons are directed at targeted speckle spots or output channels. From $10^3$ experimentally available coupled channels, we select two channels and enhance their transmission, to realize the equivalent of a fully programmable $2\times2$ beam splitter. By sending pairs of single photons from a parametric down-conversion source through the opaque scattering medium, we observe two-photon quantum interference. The programmed beam splitter need not fulfill energy conservation over the two selected output channels and hence could be non-unitary. Consequently, we have the freedom to tune the quantum interference from bunching (Hong-Ou-Mandel-like) to antibunching. Our results establish opaque scattering media as a platform for high-dimensional quantum interference that is notably relevant for boson sampling and physical-key-based authentication.