Abstract Circuit optimization is a fundamental task for practical applications of near-term quantum computers. In this work we address this challenge through the powerful lenses of tensor network theory. Our approach involves the full characterization of the influence of individual gates on the entire circuit, a process we call quantum landscape tomography. We derive the necessary and sufficient requirements of this process and propose two implementations, respectively based on 2-unitary design and Clifford tableaux. The latter implementation strikes a convenient balance between the number of shots and the number of circuits needed for the tomography. Numerical simulations based on a realistic noise model demonstrate the advantage of our approach with respect to both gradient-free and gradient-based methods. Overall, our findings highlight the potential of quantum landscape tomography to enhance circuit optimization in near-term quantum computing applications.
Abstract Circuit optimization is a fundamental task for practical applications of near-term quantum computers. In this work we address this challenge through the powerful lenses of tensor network theory. Our approach involves the full characterization of the influence of individual gates on the entire circuit, a process we call quantum landscape tomography. We derive the necessary and sufficient requirements of this process and propose two implementations, respectively based on 2-unitary design and Clifford tableaux. The latter implementation strikes a convenient balance between the number of shots and the number of circuits needed for the tomography. Numerical simulations based on a realistic noise model demonstrate the advantage of our approach with respect to both gradient-free and gradient-based methods. Overall, our findings highlight the potential of quantum landscape tomography to enhance circuit optimization in near-term quantum computing applications.
Flexible characterization techniques that provide a detailed picture of the experimental imperfections under realistic assumptions are crucial to gain actionable advice in the development of quantum computers.Gate set tomography self-consistently extracts a complete tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data.It has become a standard tool for this task but comes with high requirements on the number of sequences and their design, making it already experimentally challenging for only two qubits.In this work, we show that low-rank approximations of gate sets can be obtained from significantly fewer gate sequences and that it is sufficient to draw them at random.This coherent noise characterization however still contains the crucial information for improving the implementation.To this end, we formulate the data processing problem of gate set tomography as a rank-constrained tensor completion problem.We provide an algorithm to solve this problem while respecting the usual positivity and normalization constraints of quantum mechanics.For this purpose, we combine methods from Riemannian optimization and machine learning and develop a saddle-free second-order geometrical optimization method on the complex Stiefel manifold.Besides the reduction in sequences, we numerically demonstrate that the algorithm does not rely on structured gate sets or an elaborate circuit design to robustly perform gate set tomography.Therefore, it is more flexible than traditional approaches.We also demonstrate how coherent errors in shadow estimation protocols can be mitigated using estimates from gate set tomography.
The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from measurement data, remains the quintessential primitive to completely characterize quantum devices. However, due to the exponential scaling of the required data and classical post-processing, its range of applicability is typically restricted to one- and two-qubit gates. Here, we present a technique for performing quantum process tomography that addresses these issues by combining a tensor network representation of the channel with a data-driven optimization inspired by unsupervised machine learning. We demonstrate our technique through synthetically generated data for ideal one- and two-dimensional random quantum circuits of up to 10 qubits, and a noisy 5-qubit circuit, reaching process fidelities above 0.99 using several orders of magnitude fewer (single-qubit) measurement shots than traditional tomographic techniques. Our results go far beyond state-of-the-art, providing a practical and timely tool for benchmarking quantum circuits in current and near-term quantum computers.
Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A promising alternative method based on tensor networks was recently proposed []. In this paper, we adapt it for the characterization of noise channels on near-term quantum computers and investigate its performance thoroughly. In particular, we show how experimentally feasible tomographic samples are sufficient to accurately characterize realistic correlated noise models affecting individual layers of quantum circuits, and study its performance on systems composed of up to 20 qubits. Furthermore, we combine this noise characterization method with a recently proposed noise-aware tensor network error mitigation protocol for correcting outcomes in noisy circuits, resulting accurate estimations even on deep circuit instances. This positions the tensor-network-based noise characterization protocol as a valuable tool for practical error characterization and mitigation in the near-term quantum computing era. Published by the American Physical Society 2024
A Clifford circuit is a pivotal tool in quantum computing and has extensive applications in quantum error correction codes and topological quantum computing. Hence, it is essential to benchmark and verify the effect of Clifford circuits against noise and errors. Standard quantum process tomography is a fundamental technique for fully characterizing quantum dynamics, but at the cost of exponential time, space, and computation with an increasing number of qubits. Here, we propose an efficient quantum process tomography method for Clifford circuits. Combining with the stabilizer formalism, we prove theoretically that, for an n-qubit Clifford circuit, our method merely needs m ancillary qubits and $\ensuremath{\lceil}n/m\ensuremath{\rceil}$ input stabilizer states to obtain the quantum process. Numerical simulation results show that our method could perfectly rebuild the unknown Clifford quantum circuit with fidelity over 99.99 to six qubit cases. Our work provides an efficient and practical approach to benchmark and verify Clifford circuits.
Quantum circuits form a foundational framework in quantum science, enabling the description, analysis, and implementation of quantum computations. However, designing efficient circuits, typically constructed from single- and two-qubit gates, remains a major challenge for specific computational tasks. In this work, we introduce a novel artificial intelligence-driven protocol for quantum circuit design, benchmarked using shadow tomography for efficient quantum state readout. Inspired by techniques from natural language processing (NLP), our approach first selects a compact gate dictionary by optimizing the entangling power of two-qubit gates. We identify the iSWAP gate as a key element that significantly enhances sample efficiency, resulting in a minimal gate set of {I, SWAP, iSWAP}. Building on this, we implement a recurrent neural network trained via reinforcement learning to generate high-performing quantum circuits. The trained model demonstrates strong generalization ability, discovering efficient circuit architectures with low sample complexity beyond the training set. Our NLP-inspired framework offers broad potential for quantum computation, including extracting properties of logical qubits in quantum error correction.
Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking, quantum error mitigation, and so on. Here, we propose a universal compilation-based variational algorithm for the preparation and tomography of quantum states in low-depth quantum circuits. We apply the Fubini-Study distance to be a trainable cost function under various gradient-based optimizers, including the quantum natural gradient approach. We evaluate the performance of various unitary topologies and the trainability of different optimizers for getting high efficiency. In practice, we address different circuit ansatzes in quantum state preparation, including the linear and graph-based ansatzes for preparing different entanglement target states such as representative GHZ and W states. We also discuss the effect of the circuit depth, barren plateau, readout noise in the model, and the error mitigation solution. We next evaluate the reconstructing efficiency in quantum state tomography via various popular circuit ansatzes and reveal the crucial role of the circuit depth in the robust fidelity. The results are comparable with the shadow tomography method, a similar fashion in the field. Our work expresses the adequate capacity of the universal compilation-based variational algorithm to maximize the efficiency in the quantum state preparation and tomography. Further, it promises applications in quantum metrology and sensing and is applicable in the near-term quantum computers for verification of the circuits fidelity and various quantum computing tasks.