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Register a new userGradient-free quantum optimization on NISQ devices
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Variational Quantum Eigensolvers (VQEs) have recently attracted considerable attention. Yet, in practice, they still suffer from the efforts for estimating cost function gradients for large parameter sets or resource-demanding reinforcement strategies. Here, we therefore consider recent advances in weight-agnostic learning and propose a strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We investigate the use of NEAT-inspired algorithms which evaluate circuits via genetic competition and thus circumvent issues due to exceeding numbers of parameters. Our methods are tested both via simulation and on real quantum hardware and are used to solve the transverse Ising Hamiltonian and the Sherrington-Kirkpatrick spin model.
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Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.
Quantum machine learning is one of the most promising applications of quantum computing in the Noisy Intermediate-Scale Quantum(NISQ) era. Here we propose a quantum convolutional neural network(QCNN) inspired by convolutional neural networks(CNN), which greatly reduces the computing complexity compared with its classical counterparts, with $O((log_{2}M)^6) $ basic gates and $O(m^2+e)$ variational parameters, where $M$ is the input data size, $m$ is the filter mask size and $e$ is the number of parameters in a Hamiltonian. Our model is robust to certain noise for image recognition tasks and the parameters are independent on the input sizes, making it friendly to near-term quantum devices. We demonstrate QCNN with two explicit examples. First, QCNN is applied to image processing and numerical simulation of three types of spatial filtering, image smoothing, sharpening, and edge detection are performed. Secondly, we demonstrate QCNN in recognizing image, namely, the recognition of handwritten numbers. Compared with previous work, this machine learning model can provide implementable quantum circuits that accurately corresponds to a specific classical convolutional kernel. It provides an efficient avenue to transform CNN to QCNN directly and opens up the prospect of exploiting quantum power to process information in the era of big data.
In the era of noisy intermediate-scale quantum (NISQ), executing quantum algorithms on actual quantum devices faces unique challenges. One such challenge is that quantum devices in this era have restricted connectivity: quantum gates are allowed to act only on specific pairs of physical qubits. For this reason, a quantum circuit needs to go through a compiling process called qubit routing before it can be executed on a quantum computer. In this study, we propose a CNOT synthesis method called the token reduction method to solve this problem. The token reduction method works for all quantum computers whose architecture is represented by connected graphs. A major difference between our method and the existing ones is that our method synthesizes a circuit to an output qubit mapping that might be different from the input qubit mapping. The final mapping for the synthesis is determined dynamically during the synthesis process. Results showed that our algorithm consistently outperforms the best publicly accessible algorithm for all of the tested quantum architectures.
In this study, we focus on the question of stability of NISQ devices. The parameters that define the device stability profile are motivated by the work of DiVincenzo where the requirements for physical implementation of quantum computing are discussed. We develop the metrics and theoretical framework to quantify the DiVincenzo requirements and study the stability of those key metrics. The basis of our assessment is histogram similarity (in time and space). For identical experiments, devices which produce reproducible histograms in time, and similar histograms in space, are considered more reliable. To investigate such reliability concerns robustly, we propose a moment-based distance (MBD) metric. We illustrate our methodology using data collected from IBMs Yorktown device. Two types of assessments are discussed: spatial stability and temporal stability.
A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.
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