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Feb 14 2022 quant-ph arXiv:2202.05741v1
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the classical electronic back-end. Decoders employing neural networks (NN) are well-suited for this task but their hardware implementation has not been presented yet. This work presents a space exploration of fully-connected feed-forward NN decoders for small distance surface codes. The goal is to optimize the neural network for high decoding performance, while keeping a minimalistic hardware implementation. This is needed to meet the tight delay constraints of real-time surface code decoding. We demonstrate that hardware based NN-decoders can achieve high decoding performance comparable to other state-of-the-art decoding algorithms whilst being well below the tight delay requirements (≈440 ns)(≈440 ns) of current solid-state qubit technologies for both ASIC designs (<30 ns)(<30 ns) and FPGA implementations (<90 ns)(<90 ns). These results designates NN-decoders as fitting candidates for an integrated hardware implementation in future large-scale quantum computers.
Feb 16 2022 quant-ph arXiv:2202.06979v1
Variational algorithms have received significant attention in recent years due to their potential to solve practical problems in noisy intermediate-scale quantum (NISQ) devices. A fundamental step of these algorithms is the evaluation of the expected value of Hamiltonians. Efficient schemes to perform this task are required to speed up these algorithm. The standard approach employs local measurements of Pauli operators, which requires a large number of circuits. An alternative is to make use of entangled measurements, which significantly reduce the number of circuits but involve entangling gates between non-physically connected qubits, introducing intermediate entangling operations that increase the depth of the circuits. As a solution to this problem we propose hardware-efficient entangled measurements (HEEM), that is, measurements that only permit entanglement between physically connected qubits. We show that this strategy enhances the evaluation of molecular Hamiltonians in NISQ devices because it reduces the number of circuits required without increasing their depth. We provide quantitative metrics of how this approach offers better results than only local measurements and arbitrarily entangled ones. We estimate with classical simulators and quantum hardware the ground state energy of the H22O molecule by the variational quantum eigensolver using HEEM.
Feb 15 2022 quant-ph arXiv:2202.06804v1
Deep neural networks are a powerful tool for characterizing quantum states. In this task, neural networks are typically trained with measurement data gathered from the quantum state to be characterized. But is it possible to train a neural network in a general-purpose way, which makes it applicable to multiple unknown quantum states? Here we show that learning across multiple quantum states and different measurement settings can be achieved by a generative query neural network, a type of neural network originally used in the classical domain for learning 3D scenes from 2D pictures. Our network can be trained offline with classically simulated data, and later be used to characterize unknown quantum states from real experimental data. With little guidance of quantum physics, the network builds its own data-driven representation of quantum states, and then uses it to predict the outcome probabilities of requested quantum measurements on the states of interest. This approach can be applied to state learning scenarios where quantum measurement settings are not informationally complete and predictions must be given in real time, as experimental data become available, as well as to adversarial scenarios where measurement choices and prediction requests are designed to expose learning inaccuracies. The internal representation produced by the network can be used for other tasks beyond state characterization, including clustering of states and prediction of physical properties. The features of our method are illustrated on many-qubit ground states of Ising model and continuous-variable non-Gaussian states.
Feb 18 2022 quant-ph arXiv:2202.08473v1
Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. Variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state of a quantum system and expected to work on even such a device. The deep VQE [K. Fujii, et al., arXiv:2007.10917] is an extension of the original VQE algorithm, which takes a divide-and-conquer approach to relax the hardware requirement. While the deep VQE is successfully applied for spin models and periodic material, its validity on a molecule, where the Hamiltonian is highly non-local in the qubit basis, is still unexplored. Here, we discuss the performance of the deep VQE algorithm applied to quantum chemistry problems. Specifically, we examine different subspace forming methods and compare their accuracy and complexity on a ten H-atom tree-like molecule as well as a 13 H-atom version. Additionally, we propose multiple methods to lower the number of qubits required to calculate the ground state of a molecule. We find that the deep VQE can simulate the electron-correlation energy of the ground-state to an error of below 1%, thus helping us to reach chemical accuracy in some cases. The accuracy differences and qubits reduction highlights the basis creation method’s impact on the deep VQE.
In the training of over-parameterized model functions via gradient descent, sometimes the parameters do not change significantly and remain close to their initial values. This phenomenon is called lazy training, and motivates consideration of the linear approximation of the model function around the initial parameters. In the lazy regime, this linear approximation imitates the behavior of the parameterized function whose associated kernel, called the tangent kernel, specifies the training performance of the model. Lazy training is known to occur in the case of (classical) neural networks with large widths. In this paper, we show that the training of geometrically local parameterized quantum circuits enters the lazy regime for large numbers of qubits. More precisely, we prove bounds on the rate of changes of the parameters of such a geometrically local parameterized quantum circuit in the training process, and on the precision of the linear approximation of the associated quantum model function; both of these bounds tend to zero as the number of qubits grows. We support our analytic results with numerical simulations.
Feb 18 2022 quant-ph arXiv:2202.08306v1
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we propose a quantum perceptron (QP) model that uses a reduced number of multi-qubit gates and is therefore less susceptible to quantum errors in current actual quantum computers with limited tolerance. The proposed quantum algorithm is superior to its classical counterpart, although since it does not take full advantage of quantum entanglement, it provides a lower encoding power than other quantum algorithms using multiple qubit entanglement. However, the use of separable-sate encoding allows for testing the algorithm and different training schemes at a large scale in currently available non-fault tolerant quantum computers. We demonstrate the performance of the proposed model by implementing a few qubits version of the QP in a simulated quantum computer. The proposed QP uses an N-ary encoding of the binary input data characterizing the patterns. We develop a hybrid (quantum-classical) training procedure for simulating the learning process of the QP and test their efficiency.
The learning process of classical machine learning algorithms is tuned by hyperparameters that need to be customized to best learn and generalize from an input dataset. In recent years, Quantum Machine Learning (QML) has been gaining traction as a possible application of quantum computing which may provide quantum advantage in the future. However, quantum versions of classical machine learning algorithms introduce a plethora of additional parameters and circuit variations that have their own intricacies in being tuned. In this work, we take the first steps towards Automated Quantum Machine Learning (AutoQML). We propose a concrete description of the problem, and then develop a classical-quantum hybrid cloud architecture that allows for parallelized hyperparameter exploration and model training. As an application use-case, we train a quantum Generative Adversarial neural Network (qGAN) to generate energy prices that follow a known historic data distribution. Such a QML model can be used for various applications in the energy economics sector.