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Register a new userHybrid quantum-classical classifier based on tensor network and variational quantum circuit
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One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available.
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We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for both the energy and correlation functions of the 1D Heisenberg and Fermi-Hubbard models in the gapless regime. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of quantum advantage with respect to expressiveness in the representation of physical ground-states.
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as the quantum variational eigensolver was developed with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
We introduce a new open-source software library Jet, which uses task-based parallelism to obtain speed-ups in classical tensor-network simulations of quantum circuits. These speed-ups result from i) the increased parallelism introduced by mapping the tensor-network simulation to a task-based framework, ii) a novel method of reusing shared work between tensor-network contraction tasks, and iii) the concurrent contraction of tensor networks on all available hardware. We demonstrate the advantages of our method by benchmarking our code on several Sycamore-53 and Gaussian boson sampling (GBS) supremacy circuits against other simulators. We also provide and compare theoretical performance estimates for tensor-network simulations of Sycamore-53 and GBS supremacy circuits for the first time.
Quantum error mitigation techniques are at the heart of quantum hardware implementation, and are the key to performance improvement of the variational quantum learning scheme (VQLS). Although VQLS is partially robust to noise, both empirical and theoretical results exhibit that noise would rapidly deteriorate the performance of most variational quantum algorithms in large-scale problems. Furthermore, VQLS suffers from the barren plateau phenomenon---the gradient generated by the classical optimizer vanishes exponentially with respect to the qubit number. Here we devise a resource and runtime efficient scheme, the quantum architecture search scheme (QAS), to maximally improve the robustness and trainability of VQLS. In particular, given a learning task, QAS actively seeks an optimal circuit architecture to balance benefits and side-effects brought by adding more quantum gates. Specifically, while more quantum gates enable a stronger expressive power of the quantum model, they introduce a larger amount of noise and a more serious barren plateau scenario. Consequently, QAS can effectively suppress the influence of quantum noise and barren plateaus. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. Numerical and experimental results show that QAS significantly outperforms conventional variational quantum algorithms with heuristic circuit architectures. Our work provides practical guidance for developing advanced learning-based quantum error mitigation techniques on near-term quantum devices.
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