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Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds., Comment: 50 pages (including Appendix), many figures, accepted as a poster on QTML2024. Code available at https://github.com/peiyong-addwater/Let-The-Quantum-Creep-In

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the ``quantisation" of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning [1]. Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models [2]. In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit [3] with the quantum Hamiltonian data embedding unitary [4]. Through numerical experiments on images datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN)[5] by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks., Comment: 11 figures, 31 pages. Code available on https://github.com/peiyong-addwater/HamEmbedding. Author affiliation updated for v2. Acknowledgements and funding information added for v2

Spin qubits in silicon are strong contenders for realizing a practical quantum computer. This technology has made remarkable progress with the demonstration of single and two-qubit gates above the fault-tolerant threshold and entanglement of up to three qubits. However, maintaining high fidelity operations while executing multi-qubit algorithms has remained elusive, only being achieved for two spin qubits to date due to the small qubit size, which makes it difficult to control qubits without creating crosstalk errors. Here, we use a four-qubit silicon processor with every operation above the fault tolerant limit and demonstrate Grover's algorithm with a ~95% probability of finding the marked state, one of the most successful implementations to date. Our four-qubit processor is made of three phosphorus atoms and one electron spin precision-patterned into 1.5 nm${}^2$ isotopically pure silicon. The strong resulting confinement potential, without additional confinement gates that can increase cross-talk, leverages the benefits of having both electron and phosphorus nuclear spins. Significantly, the all-to-all connectivity of the nuclear spins provided by the hyperfine interaction not only allows for efficient multi-qubit operations, but also provides individual qubit addressability. Together with the long coherence times of the nuclear and electron spins, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity. The high control fidelities, combined with >99% fidelity readout of all nuclear spins, allows for the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with 96.2% fidelity, the highest reported for semiconductor spin qubits so far. Such nuclear spin registers can be coupled via electron exchange, establishing a path for larger scale fault-tolerant quantum processors., Comment: 16 pages, 9 figures, 3 tables. Updated following peer review

The reliable, deterministic production of trustworthy high-quality single photons is a critical component of discrete variable, optical quantum technology. For single-photon based fully error-corrected quantum computing systems, it is estimated that photon sources will be required to produce a reliable stream of photons at rates exceeding 1 GHz [1]. Photon multiplexing, where low probability sources are combined with switching networks to route successful production events to an output, are a potential solution but requires extremely fast single photon switching with ultra-low loss rates. In this paper we examine the specific properties of the switching elements and present a new design that exploits the general one-way properties of common switching elements such as thermal pads. By introducing multiple switches to a basic, temporal multiplexing device, we are able to use slow switching elements in a multiplexed source being pumped at much faster rates. We model this design under multiple error channels and show that anticipated performance is now limited by the intrinsic loss rate of the optical waveguides within integrated photonic chipsets.

We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli measurements on this graph state. By compiling the graph state directly instead of starting with a standard lattice cluster state and preparing it over the course of the computation, we are able to better understand the resource costs involved and eliminate wasteful Pauli measurements on the actual quantum device. Access to this algorithm-specific graph state also allows for optimisation over locally equivalent graph states to implement the same quantum circuit. The compiler presented here finds ready application in measurement based quantum computing, NISQ devices and logical level compilation for fault tolereant implementations.

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability., Comment: 32 pages, 24 figures

We present a detailed analytic framework for studying multimode non-Gaussian states that are conditionally generated when few modes of a multimode Gaussian state are subject to photon-number-resolving detectors. From the output state Wigner function, we deduce that the state factorizes into a Gaussian gate applied to a finite Fock-superposition non-Gaussian state. The framework provides an approach to find the optimal strategy to generate a given target non-Gaussian state. We explore examples, such as the generation of cat states, weak cubic phase states, and bosonic code states, and achieve improvements of success probability over other schemes. Our framework also applies to the case in which the measured Gaussian state is mixed which is very important for the analysis of experimental imperfections such as photon loss. The framework has potential far-reaching implications to the generation of bosonic error-correcting codes and for the implementation of non-Gaussian gates using resource states, among other applications requiring non-Gaussianity, Comment: 5 pages, 2 figures. See also related long paper arXiv:1902.02323 uploaded concurrently. Added references and corrected typos

Generation of high fidelity photonic non-Gaussian states is a crucial ingredient for universal quantum computation using continous-variable platforms, yet it remains a challenge to do so efficiently. We present a general framework for a probabilistic production of multimode non-Gaussian states by measuring few modes of multimode Gaussian states via photon-number-resolving detectors. We use Gaussian elements consisting of squeezed displaced vacuum states and interferometers, the only non-Gaussian elements consisting of photon-number-resolving detectors. We derive analytic expressions for the output Wigner function, and the probability of generating the states in terms of the mean and the covariance matrix of the Gaussian state and the photon detection pattern. We find that the output states can be written as a Fock basis superposition state followed by a Gaussian gate, and we derive explicit expressions for these parameters. These analytic expressions show exactly what non-Gaussian states can be generated by this probabilistic scheme. Further, it provides a method to search for the Gaussian circuit and measurement pattern that produces a target non-Gaussian state with optimal fidelity and success probability. We present specific examples such as the generation of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON states and bosonic code states. The proposed framework has potential far-reaching implications for the generation of bosonic error-correction codes that require non-Gaussian states, resource states for the implementation of non-Gaussian gates needed for universal quantum computation, among other applications requiring non-Gaussianity. The tools developed here could also prove useful for the quantum resource theory of non-Gaussianity., Comment: 37 pages, 15 figures. See also related short paper arXiv:1902.02331 uploaded concurrently. Added references and corrected typos

We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state, our method discovers circuits for preparing a desired quantum state. In the more general case of several input and output relations, our method obtains circuits that reproduce the action of a target unitary transformation. We use a continuous-variable quantum neural network as the circuit architecture. The network is composed of several layers of optical gates with variable parameters that are optimized by applying automatic differentiation using the TensorFlow backend of the Strawberry Fields photonic quantum computer simulator. We demonstrate the power and versatility of our methods by learning how to use short-depth circuits to synthesize single photons, Gottesman-Kitaev-Preskill states, NOON states, cubic phase gates, random unitaries, cross-Kerr interactions, as well as several other states and gates. We routinely obtain high fidelities above 99\% using short-depth circuits, typically consisting of a few hundred gates. The circuits are obtained automatically by simply specifying the target state or gate and running the optimization algorithm., Comment: 13 pages, 14 figures. Source code for the algorithms employed in this paper is available at https://github.com/XanaduAI/quantum-learning

Implementing quantum algorithms is essential for quantum computation. We study the implementation of three quantum algorithms by performing homodyne measurements on a two-dimensional temporal continuous-variable cluster state. We first review the generation of temporal cluster states and the implementation of gates using the measurement-based model. Alongside this we discuss methods to introduce non-Gaussianity into the cluster states. The first algorithm we consider is Gaussian Boson Sampling in which only Gaussian unitaries need to be implemented. Taking into account the fact that input states are also Gaussian, the errors due to the effect of finite squeezing can be corrected, provided a moderate amount of online squeezing is available. This helps to construct a large Gaussian Boson Sampling machine. The second algorithm is the continuous-variable Instantaneous Quantum Polynomial circuit in which one needs to implement non-Gaussian gates, such as the cubic phase gate. We discuss several methods of implementing the cubic phase gate and fit them into the temporal cluster state architecture. The third algorithm is the continuous-variable version of Grover's search algorithm, the main challenge of which is the implementation of the inversion operator. We propose a method to implement the inversion operator by injecting a resource state into a teleportation circuit. The resource state is simulated using the Strawberry Fields quantum software package., Comment: 22 pages, 29 figures, comments are welcome

Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-photon interference via a classically controlled beam splitter. The visibility of the two-photon interference is particularly sensitive to coherent excitations in the mechanical resonator and this could form the basis of an optically transduced weak-force sensor., Comment: 39 pages, 11 figures

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 architecture that can be used for force, refractive index and possibly local temperature detection. In this scheme, two coupled cavities behave as an "effective beam splitter". The sensor works based on fourth order interference (the Hong-Ou-Mandel effect) and requires a sequence of single photon pulses and consequently has low pulse power. Changes in the parameter to be measured induce variations in the effective beam splitter reflectivity and result in changes to the visibility of interference. We demonstrate this generic scheme in coupled L3 photonic crystal cavities as an example and find that this system, which only relies on photon coincidence detection and does not need any spectral resolution, can estimate forces as small as $10^{-7}$ Newtons and can measure one part per million change in refractive index using a very low input power of $10^{-10}$W. Thus linear optical quantum photonic architectures can achieve comparable sensor performance to semiclassical devices., Comment: 24 pages, 7 figures

Closed timelike curves are among the most controversial features of modern physics. As legitimate solutions to Einstein's field equations, they allow for time travel, which instinctively seems paradoxical. However, in the quantum regime these paradoxes can be resolved leaving closed timelike curves consistent with relativity. The study of these systems therefore provides valuable insight into non-linearities and the emergence of causal structures in quantum mechanics-essential for any formulation of a quantum theory of gravity. Here we experimentally simulate the non-linear behaviour of a qubit interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve. These include perfect discrimination of non-orthogonal states and, most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states. Finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction, and the influence of decoherence., Comment: 9 pages, 8 figures

In this paper we present results illustrating the power and flexibility of one-bit teleportations in quantum bus computation. We first show a scheme to perform a universal set of gates on continuous variable modes, which we call a quantum bus or qubus, using controlled phase-space rotations, homodyne detection, ancilla qubits and single qubit measurement. The resource usage for this scheme is lower than any previous scheme to date. We then illustrate how one-bit teleportations into a qubus can be used to encode qubit states into a quantum repetition code, which in turn can be used as an efficient method for producing GHZ states that can be used to create large cluster states. Each of these schemes can be modified so that teleportation measurements are post-selected to yield outputs with higher fidelity, without changing the physical parameters of the system., Comment: 10 pages, 12 figures

We model an optical implementation of a CSIGN gate that makes use of the Quantum Zeno effect [1,2] in the presence of photon loss. The raw operation of the gate is severely affected by this type of loss. However, we show that by using the same photon loss codes that have been proposed for linear optical quantum computation (LOQC), the performance is greatly enhanced and such gates can outperform LOQC equivalents. The technique can be applied to other types of nonlinearities, making the implementation of nonlinear optical gates much more attractive.

In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group of a quantum code. First, we show how to measure a Pauli operator acting on physical qubits using a single coherent state with large average photon number, displacement operations, and photon detection. Second, we show how to measure the stabilizer operators fault-tolerantly by the deterministic preparation of coherent cat states along with one-bit teleportations between a qubit-like encoding of coherent states and physical qubits., Comment: 4 pages, 5 figures

Quantum information processing using photons has recently been stimulated by the suggestion to use linear optics, single photon sources and detectors. The recent work by Knill has also shown that errors in photon detectors leads to a high error rate threshold (around 29%). An important missing element are good single photon sources. In this paper we show how to make a single photon source using squeezed states, linear optics and conditional measurement. We use degenerate squeezed vacuum states, in contrast to the normal non-degenerate squeezed vacuum states used for single photon production. We show that we can get a photon with certainty when detectors click appropriately, the last event happening up to around 25% of the time. We also show the robustness of this method with respect to a variety of potential imperfections., Comment: 5 pages, 7 figures

Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states. We show that it is impossible to increase the probability for a single photon using linear optics and photodetection on fewer than four modes. This impossibility is due to the incoherence of the inputs; if the inputs were pure-state superpositions, it would be possible to obtain a perfect single-photon output. In the more general case, a chain of beam splitters can be used to increase the probability for a single photon, but at the expense of adding an additional multiphoton component. This improvement is robust against detector inefficiencies, but is degraded by dark counts or multiphoton components in the input., Comment: 17 pages, 5 figures