Abstract 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.
Abstract 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.
A limiting factor to the exploitation of continuous variables in quantum computing, in particular in the field of quantum machine learning, has been the hindrances of computing the derivatives of a model. The constraint occurs when applying the parameter-shift rule to a photonic circuit, and the number of non-Gaussian gates exceeds a logarithmic trend with respect to the length of the circuit. This condition occurs when dealing with most nonlinear functions. Indeed, it hampers subroutines, such as backpropagation, which are paramount for machine learning and, most significantly, the computation of the derivatives of the model itself. To overcome this hurdle, we propose a method to compute derivatives of functions, implemented by continuous variable circuits, directly through photonic quantum circuits. Unlike the parameter-shift rule, this method does not fail when the number of non-Gaussian gates scales more than logarithmically against the depth of the circuit. We exploit the fact that computing the derivative of a wave function is equivalent to applying the momentum operator, which in the position basis acts as its derivative. The action of this operator is physically embodied by photon-added coherent states. We prove that, up to the second order of derivation, the number of operations does not scale with the depth of the circuit, but only with the order of derivation. We showcase numerical examples of derivatives of elementary functions parametrized on simulated photonic quantum circuits. Thanks to this method, we unleash an embodiment of quantum neural networks on photonic quantum computing platforms.
A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent 2n-dimensional data using only n qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.
With recent advancements in quantum computing technology, optimizing quantum circuits and ensuring reliable quantum state preparation have become increasingly vital. Traditional methods often demand extensive expertise and manual calculations, posing challenges as quantum circuits grow in qubit- and gate-count. Therefore, harnessing machine learning techniques to handle the growing variety of gate-to-qubit combinations is a promising approach. In this work, we introduce a comprehensive reinforcement learning environment for quantum circuit synthesis, where circuits are constructed utilizing gates from the the Clifford+T gate set to prepare specific target states. Our experiments focus on exploring the relationship between the depth of synthesized quantum circuits and the circuit depths used for target initialization, as well as qubit count. We organize the environment configurations into multiple evaluation levels and include a range of well-known quantum states for benchmarking purposes. We also lay baselines for evaluating the environment using Proximal Policy Optimization. By applying the trained agents to benchmark tests, we demonstrated their ability to reliably design minimal quantum circuits for a selection of 2-qubit Bell states.
Recent reports of large photonic nonlinearities in integrated photonic devices, using the strong excitonic light-matter coupling in semiconductors, necessitate a tailored design framework for quantum processing in the limit of low photon occupation. We present a gradient-based optimization method for quantum photonic integrated circuits, which are composed of nonlinear unitary coupling gates and stochastic, nonunitary components for sampling the photonic losses. As core of our method, differentiable tensor-networks are leveraged, which are accurate in the regime of low photonic occupation and modest intermode entanglement. After characterizing the circuit gate architecture with field simulations of GaAs-based samples, we demonstrate the applicability of our method by optimizing quantum photonic circuits for two key use cases: integrated designs for quantum optical state preparation and tailored optimal readout for quantum phase sensing.
A possible approach to tackling computationally demanding issues beyond the capabilities of conventional algorithms is the use of quantum circuits, which provide a fundamental foundation for utilizing the power of quantum computation. This abstract examines how quantum circuits are implemented, emphasizing important topics such as circuit optimization, gate operations, and qubit manipulation. We explore different methods of encoding quantum information into topological qubits, trapped ions, and superconducting circuits, among other physical qubit formats. Furthermore, we go over the function of gate operations in quantum circuits, emphasizing crucial gates like phase, Hadamard, and CNOT gates, which serve as the foundation for quantum algorithms. Additionally, we look at methods for maximizing the efficiency and dependability of quantum processing by designing quantum circuits to minimize gate counts, depth, and error rates. To enhance the capabilities of quantum computing, this abstract presents a novel synthesis of quantum neural networks (QNNs) and quantum parameterized circuits. Through the use of parameterized quantum circuits' inherent flexibility, our approach makes it easier to design and optimize quantum circuits with flexible parameters, providing a flexible foundation for a variety of quantum algorithms. Using this amalgamation, we unleash the capacity of quantum computers to address intricate optimization and machine learning assignments with unparalleled effectiveness and expandability. Our solution bridges the gap between traditional machine learning approaches and quantum computing paradigms by enabling the smooth integration of classical data processing techniques with quantum computation. We use quantum states as data representations in our implementation of quantum neural networks, and we optimize trainable parameters to meet predetermined goals. This new paradigm opens up the investigation of the inherent features of quantum states and provides new perspectives on their processing power compared to their classical counterparts. We show, by thorough testing and analysis, how effective quantum parameterized circuits and QNNs are at solving practical problems in a variety of fields. Our work sets the ground for revolutionary breakthroughs in quantum information processing by pushing the boundaries of quantum computation and machine learning integration, offering hitherto unseen insights and solutions to challenging challenges in science, engineering, and beyond.
Near-term quantum computers have significant error rates and short coherence times, so compilation of circuits to be as short as possible is essential. Two types of compilation problems are typically considered: circuits to prepare a given state from a fixed input state, called “state preparation”; and circuits to implement a given unitary operation, for example by “unitary synthesis”. In this paper we solve a more general problem: the transformation of a set of m states to another set ofmstates, which we call “multi-state preparation”. State preparation and unitary synthesis are special cases; for state preparation, m=1, while for unitary synthesis, m is the dimension of the full Hilbert space. We generate and optimize circuits for multi-state preparation numerically. In cases where a top-down approach based on matrix decompositions is also possible, our method finds circuits with substantially (up to 40 %) fewer two-qubit gates. We discuss possible applications, including efficient preparation of macroscopic superposition (“cat”) states and synthesis of quantum channels.