Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon interactions, which limits their potential to explore strongly-correlated many-body physics of light. We propose a strongly interacting discrete-time photonic quantum walk using a network of single atom beamsplitters. We calculate output statistics of the quantum walk for the case of two photons, which reveals the strongly-correlated transport of photons. Particularly, the walk can exhibit either boson-like or fermion-like statistics which is tunable by post-selecting the two-photon detection time interval. Also, the walk can sort different types of two-photon bound states into distinct pairs of output ports under certain conditions. These unique phenomena show that our quantum walk is an intriguing platform to explore strongly-correlated quantum many-body states of light. Finally, we propose an experimental realization based on time-multiplexed synthetic dimensions.
We show that a beam splitter of reflectivity one-third can be used to realize a quantum phase gate operation if only the outputs conserving the number of photons on each side are post-selected.
We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility $χ^{(2)}$. Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method …
The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call "directionally-biased". Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recentl…
We demonstrate integrated photonic circuits for quantum devices using sputtered polycrystalline aluminum nitride (AlN) on insulator. The on-chip AlN waveguide directional couplers, which are one of the most important components in quantum photonics, are fabricated and show the output power splitting ratios from 50:50 to 99:1. The polarization beam splitters with an extinction ratio of more than 10 dB are also realized from the AlN directional couplers. Using the fabricated AlN waveguide beam splitters, we observe the Hong-Ou-Mandel interference with a visibility of 91.7 +(-) 5.66 %.
When two equal photon-number states are combined on a balanced beam splitter, both output ports of the beam splitter contain only even numbers of photons. Consider the time-reversal of this interference phenomenon: the probability that a pair of photon-number-resolving detectors at the output ports of a beam splitter both detect the same number of photons depends on the overlap between the input state of the beam splitter and a state containing only even photon numbers. Here, we propose using this even-parity detection to engineer quantum states containing only even photon-number terms. As an …
We demonstrate an atomic Faraday dichroic beam splitter suitable to spatially separate signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode $90^{\circ}$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of $(-26.3\pm0.1)$ and $(-21.2\pm0.1)$ dB in the two outputs, with a corresponding transmission of 97 and 99 %. This technique avoids the need to use spatial separation of four-wave mixing modes and thus opens the…
We numerically investigate the implementation of Haar-random unitarity transformations and Fourier transformations in photonic devices consisting of beam splitters and phase shifters, which are used for integrated photonics implementations of boson sampling. The distribution of reflectivities required to implement an arbitrary unitary transformation is skewed towards low values, and this skew becomes stronger the larger the number of modes. A realistic implementation using Mach-Zehnder interferometers is incapable of doing this perfectly and thus has limited fidelity. We show that numerical op…
We realize quantum gates for path qubits with a high-speed, polarization-independent and tunable beam splitter. Two electro-optical modulators act in a Mach-Zehnder interferometer as high-speed phase shifters and rapidly tune its splitting ratio. We test its performance with heralded single photons, observing a polarization-independent interference contrast above 95%. The switching time is about 5.6 ns, and a maximal repetition rate is 2.5 MHz. We demonstrate tunable feed-forward operations of a single-qubit gate of path-encoded qubits and a two-qubit gate via measurement-induced interaction b…
In quantum mechanics, photonic de Broglie waves have been understood as a unique property of quantum mechanics satisfying the complementarity between particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the heart of nonclassical feature of photon bunching on a beam splitter was newly interpreted using pure wave nature of coherence optics [arXiv:1911.07174v2], paving a road to unconditionally secured classical key distribution [arXiv:1807.04233v3]. Here, Mach-Zehnder in…
We simulated the radiative response of the cavity quantum electrodynamics (QED) coupled to the double quantum dot Cooper pair splitter and analyzed its spectral dependence to get insight into dynamics of the Cooper pair transfers. The model is confined to the energy subspace where two entangled electrons are transferred to two normal electrodes through the inter-dot singlet state on two proximitized quantum dots. Our research is focused on the Andreev scatterings in the subgap regime, for which the local charge susceptibility $Π(ω_p)$ is derived, by means of Keldysh Green functions, in a whole…
We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channe…
We perform generalized measurements of a qubit by realizing the qubit as a coin in a photonic quantum walk and subjecting the walker to projective measurements. Our experimental technique can be used to realize photonically any rank-1 single-qubit positive operator-valued measure via constructing an appropriate interferometric quantum-walk network and then projectively measuring the walker's position at the final step.
We theoretically analyze the dynamical evolution of photonic quantum walks on Möbius strips and other exotic structures in 3D integrated photonics. Our flexible design allows discrete observations of continuous time quantum walks of photons in a variety of waveguide arrays. Furthermore, our design allows one to inject photons during the evolution, allowing the possibility of interacting with the photons as they are 'walking'. We find that non-trivial array topologies introduce novel time-dependent symmetries of the two-photon correlations. These properties allow a large degree of control for q…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze quantum random walks implemented by coherent light propagation in series-coupled photonic ring resonators. We propose a family of graphs modeling these devices and compare quantum and classical random walks on these structures, calculating steady-state and time-dependent solutions. We obtain conditions for quantum advantage in this setting and show how to recover …
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW …
We demonstrate an implementation of unambiguous state discrimination of two equally probable single-qubit states via a one-dimensional photonic quantum walk experimentally. Furthermore we experimentally realize a quantum walk algorithm for implementing a generalized measurement in terms of positive operator value measurement on a single qubit. The measurement of the single-photons' positions corresponds to a measurement of an element of the positive operator value measurement on the polarizations of the single-photons.
University of the Basque Country UPV/EHU（巴斯克大学（UPV/EHU））；IKERBASQUE, Basque Foundation for Science（巴斯克科学基金会IKERBASQUE）；Shanghai University（上海大学）
We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that this tunable beam splitter, when equipped with weak measurements and classical feedback, behaves as a quantum memristor. Indeed, in order to prove its quantumness, we show how to codify quantum information in the coherent beams. Moreover, we estimate the memory capability of the qu…
Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically implemented. To this end we design, model and experimentally fabricate, using the femtosecond laser direct-write technique, a 3D tubular waveguide array within glass to implement a photonic quantum walk on a circle. The boundary conditions of a QRW on a circle naturally suggests a 3D waveguide implementation - allowing much simpler device design than what could be achieved using a 2D waveguide archi…
We study the generation of intensity quantum correlations using four-wave mixing in a rubidium vapor. The absence of cavity in these experiments allows to deal with several spatial modes simultaneously. In the standard, amplifying, configuration, we measure relative intensity squeezing up to 9.2 dB below the standard quantum limit. We also theoretically identify and experimentally demonstrate an original regime where, despite no overall amplification, quantum correlations are generated. In this regime a four-wave mixing set-up can therefore play the role of a photonic beam splitter with non--c…
Manipulation of qudits in optical tables is a difficult and nonscalable task. The use of integrated optical circuits opens new possibilities for the generation, manipulation, and characterization of high dimensional states besides the ease of transmission of these states through an optical fiber. In this work we propose photonic circuits to perform minimum quantum state tomography of path qudits and show how to determine all the constituents parameters of these circuits (beam splitters and phase shifters). Our strategies were based on the symmetries of the involved POVMs (positive operator-val…
We study quantum walks of many non-interacting particles on a beam splitter array, as a paradigmatic testing ground for the competition of single- and many-particle interference in a multi-mode system. We derive a general expression for multi-mode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an unbiased estimator for quantum states with the minimal number of outcomes needed for full tomography. We present an experimental approach on a photonic quantum walk which can be used to implement SIC-POVMs on a single-qbubit. The projection measurements of single-photons' positions correspond to elements of SIC-POVM on the polarization of single-photons.
The properties of an entangled two-photon state antisymmetric in frequencies are studied. At a beam-splitter, two entangled photons are perfectly anti-correlated. In addition, they cannot be detected at the same time instant despite the fact that their detection times are confined to a narrow time window, i.e. they are temporally anti-bunched. Using nonlinear photonic-band-gap structures made of GaN/AlN, two schemes for generating such states are described.
We show a simulation of quantum random walks with multiple photons using a staggered array of 50/50 beam splitters with a bank of detectors at any desired level. We discuss the multiphoton interference effects that are inherent to this setup, and introduce one, two, and threefold coincidence detection schemes. The use of Feynman diagrams are used to intuitively explain the unique multiphoton interference effects of these quantum random walks.
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one dimensional graphs, and several experimental demonstrations have been performed. In this paper we discuss generalizing the model of discrete time quantum walks to the case of an arbitrary number of walkers acting on arbit…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and measurements of non-classical multi-particle correlations is likely to reveal the quantum nature. The number of elements $O(n)$ in a setup realizing walks grows with their length or spread $n$. We introduce the concept of a quantum leap, a process which can be achieved with fewer or complementary resources and which in a single step simulates another long proc…
We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters and photodetectors. Our model enables us to simulate a quantum random walk with use of the wave nature of classical light fields. Furthermore, the proposed set-up allows the analysis of the effects of decoherence. The transition from a pure mean photon-number distribution to a classical one is studied varying the decoherence parameters.
One of the greatest difficulties in the applications of single photon polarization states as qubits is the realization of controlled interactions between two photons. Recently, it has been shown that such interactions can be realized using only beam splitters and high efficiency photon detection by post-selecting a well defined part of the results in the output. We analyze these interactions and discuss schemes for qubit operations based on this mechanism.
In the quantum world, a single particle can have various degrees of freedom to encode quantum information. Controlling multiple degrees of freedom simultaneously is necessary to describe a particle fully and, therefore, to use it more efficiently. Here we introduce the transverse waveguide-mode degree of freedom to quantum photonic integrated circuits, and demonstrate the coherent conversion of a photonic quantum state between path, polarization and transverse waveguide-mode degrees of freedom on a single chip. The preservation of quantum coherence in these conversion processes is proven by si…
Entanglement generation in discrete time quantum walks is deemed to be another key property beyond the transport behaviors. The latter has been widely used in investigating the localization or topology in quantum walks. However, there are few experiments involving the former for the challenges in full reconstruction of the final wave function. Here, we report an experiment demonstrating the enhancement of the entanglement in quantum walks using dynamic disorder. Through reconstructing the local spinor state for each site, von Neumann entropy can be obtained and used to quantify the coin-positi…
Quantum anomalies lead to finite expectation values that defy the apparent symmetries of a system. These anomalies are at the heart of topological effects in fundamental, electronic, photonic and ultracold atomic systems, where they result in a unique response to external fields but generally escape a more direct observation. Here, we implement an optical-network realization of a topological discrete-time quantum walk (DTQW), which we design so that such an anomaly can be observed directly in the unique circular polarization of a topological midgap state. This feature arises in a single-step p…
Adiabatic techniques have much potential to realise practical and robust optical waveguide devices. Traditionally photonic elements are limited to coupling schemes that rely on proximity to nearest neighbour elements. We combine adiabatic passage with a continuum based long-range optical bus to break free from such topological restraints and thereby outline a new approach to photonic quantum gate design. We explicitly show designs for adiabatic quantum gates that produce a Hadamard, 50:50 and 1/3:2/3 beam splitter, and non-deterministic CNOT gate based on planar thin, shallow ridge waveguides.…
Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain range of dynamics on complex graphs, higher dimensional coins are necessary to unleash the full potential of discrete-time quantum walks. In this work we present an experimental realization of a discrete-time quantum walk on a line graph that, instead of two-dimensional, exhibits a four-dimensional coin space. Making use of the extra degree of freedom we observe…
A heterogeneously integrated coupled-cavity frequency beam splitter
Sandia National Laboratories（桑迪亚国家实验室）；Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories（量子算法与应用合作实验室，桑迪亚国家实验室）；Photonic and Phononic Microsystems, Sandia National Laboratories（光子和声子微系统实验室，桑迪亚国家实验室）；Quantinuum；Manzano Systems
该研究展示异质集成薄膜铌酸锂-硅耦合腔调制器，可实现可调双向频率模式变换，还验证材料灵活性，为可扩展集成频率 bin 量子光子电路提供方案。
Phases of matter with non-trivial topological order are predicted to exhibit a variety of exotic phenomena, such as the existence robust localized bound states in 1D systems, and edge states in 2D systems, which are expected to display spin-helicity, immunity to back-scattering, and weak anti-localization. In this Letter, we present an experimental observation of topological structures generated via the controlled implementation of two consecutive non-commuting rotations in photonic discrete-time quantum walks. The second rotation introduces valley-like Dirac points in the system, allowing to …
Integrated optics is an engineering solution proposed for exquisite control of photonic quantum information. Here we use silicon photonics and the linear combination of quantum operators scheme to realise a fully programmable two-qubit quantum processor. The device is fabricated with readily available CMOS based processing and comprises four nonlinear photon-sources, four filters, eighty-two beam splitters and fifty-eight individually addressable phase shifters. To demonstrate performance, we programmed the device to implement ninety-eight various two-qubit unitary operations (with average qua…
Discrete-time photonic quantum walks on a synthetic lattice, where both spatial and temporal evolution of light is discretized, have provided recently a fascinating platform for the observation of a wealth of non-Hermitian physical phenomena and for the control of light scattering in complex media. A rather open question is whether invisible potentials, analogous to the ones known for continuous optical media, do exist in such discretized systems. Here it is shown that, under certain conditions, slowly-drifting Kramers-Kronig potentials behave as invisible potentials in discrete-time photonic …
We present the novel embodiment of a photonic qubit that makes use of one continuous spatial degree of freedom of a single photon and relies on the the parity of the photon's transverse spatial distribution. Using optical spontaneous parametric downconversion to produce photon pairs, we demonstrate the controlled generation of entangled-photon states in this new space. Specifically, two Bell states, and a continuum of their superpositions, are generated by simple manipulation of a classical parameter, the optical-pump spatial parity, and not by manipulation of the entangled photons themselves.…
Integrated quantum photonic circuits (IQPCs) with deterministically integrated quantum emitters are critical elements for scalable quantum information applications and have attracted significant attention in recent years. However, scaling up them towards fully functional photonic circuits with multiple deterministically integrated quantum emitters to generate photonic input states remains a great challenge. In this work, we report on a monolithic prototype IQPC consisting of two pre-selected quantum dots deterministically integrated into nanobeam cavities at the input ports of a 2x2 multimode …
This note reviews the model of computation generated by photonic circuits, comprising edges that are traversed by photons in a single time-bin and vertices given by idealised lossless beam splitters and phase shifters. The circuit model is abstracted as a representation of the symmetric monoidal category of unitary matrices on the bosonic Fock space of multimode photons. A diagrammatic language, designed to aid with the understanding and development of photonic algorithms, is presented that encapsulates the category properties of this representation. As demonstrations of the formalism, the bos…
A quantum memristor is a resistive passive circuit element with memory engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and …
Photonic-crystal-based integrated optical systems have been used for a broad range of sensing applications with great success. This has been motivated by several advantages such as high sensitivity, miniaturization, remote sensing, selectivity and stability. Many photonic crystal sensors have been proposed with various fabrication designs that result in improved optical properties. In parallel, integrated optical systems are being pursued as a platform for photonic quantum information processing using linear optics and Fock states. Here we propose a novel integrated Fock state optical sensor a…
We demonstrate a coherent and dynamic beam splitter based on light storage in cold atoms. An input weak laser pulse is first stored in a cold atom ensemble via electromagnetically-induced transparency (EIT). A set of counter-propagating control fields, applied at a later time, retrieves the stored pulse into two output spatial modes. The high visibility interference between the two output pulses clearly demonstrates that the beam splitting process is coherent. Furthermore, by manipulating the control lasers, it is possible to dynamically control the storage time, the power splitting ratio, the…
