Periodic Reporting for period 2 - HyNNet NISQ (Hybrid quantum-classical neural networks for the characterization of noisy intermediate scale quantum computers)
Berichtszeitraum: 2024-12-01 bis 2025-11-30
Existing noisy intermediate-scale quantum computers can perform computations that are challenging for classical computers. However, quantum computing hardware and quantum algorithms need to be further developed to enable the exploitation of quantum computers in areas such as the simulation of many-body systems and machine learning. One of the major challenges in developing scalable quantum computers is characterizing the noisy quantum data produced by near-term quantum hardware. With increasing system size, standard characterization techniques using direct measurements and classical post-processing become prohibitively demanding due to large measurement counts and computational efforts.
Directly processing quantum data on quantum processors can substantially reduce measurement costs. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data, to detect non-local quantum correlations with reduced measurement and computational efforts. Characterizing non-local correlations is crucial in condensed matter physics for classifying quantum phases of matter and understanding new strongly correlated materials such as topological quantum matter. However, such quantum neural networks often require deep quantum circuits that cannot be implemented on existing devices.
The objective of HyNNet NISQ was to overcome these challenges by integrating short-depth parametrized quantum circuits with classical artificial neural networks to design hybrid quantum-classical neural networks. Thanks to their short-depth quantum circuits, these hybrid neural networks can be readily implemented on existing quantum computers and thus open the way for the efficient characterization of quantum states. Employing machine learning techniques, we trained the hybrid neural networks to identify underlying characteristics of quantum phases in strongly correlated materials such as topological quantum matter, facilitating their simulation on quantum computers.
Directly processing quantum data on quantum processors can substantially reduce measurement costs. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data, to detect non-local quantum correlations with reduced measurement and computational efforts. Characterizing non-local correlations is crucial in condensed matter physics for classifying quantum phases of matter and understanding new strongly correlated materials such as topological quantum matter. However, such quantum neural networks often require deep quantum circuits that cannot be implemented on existing devices.
The objective of HyNNet NISQ was to overcome these challenges by integrating short-depth parametrized quantum circuits with classical artificial neural networks to design hybrid quantum-classical neural networks. Thanks to their short-depth quantum circuits, these hybrid neural networks can be readily implemented on existing quantum computers and thus open the way for the efficient characterization of quantum states. Employing machine learning techniques, we trained the hybrid neural networks to identify underlying characteristics of quantum phases in strongly correlated materials such as topological quantum matter, facilitating their simulation on quantum computers.
At the beginning of the project, we finished the study of explicitly constructed error-tolerant quantum convolutional neural networks (QCNNs) using multiscale entanglement renormalization ansatz that was initiated before the start of this project. During the revision of the manuscript, we provided a further analytical analysis, explained a general approach for achieving error tolerance in QCNNs and outlined its extension for two- and higher-dimensional systems. This manuscript was published in Phys. Rev. Research in month 11.
Together with my colleagues, I finished the study of explicitly constructed QCNNs for the two-dimensional toric code model, which was initially posted on the arXiv [arXiv:2407.04114] in month 11 of the outgoing phase. During the return phase of HyNNet NISQ, we substantially revised the manuscript to extend the QCNN to capture correlations between all stabilizer elements of the toric code, which cannot be accessed by direct measurements. This increases the probability of correlated incoherent errors that can be tolerated by the network and allows for the correct identification of the topological phase in the presence of strong correlated errors. This is not possible with methods based on direct measurements, showing the advantage achieved via the processing of quantum states on the quantum processor compared to direct measurements. To this end, we designed a new convolutional layer of the QCNN that takes correlations between error syndromes into account. This manuscript was published in Phys. Rev. Research in month 25.
We showed that these explicitly constructed QCNNs can be implemented as a short-depth quantum circuit, measurement and classical post-processing of measurement results. This motivates the design of trainable hybrid neural networks (HNNs), which are the main subject of this project. Therefore, these QCNNs provide an important input for the investigation of HNNs.
In the HyNNet NISQ project, we designed trainable HNNs depicted in the figure below. Analogously to the explicitly constructed QCNNs, they consist of a quantum circuit, measurement and classical-post processing. In contrast to the previous works, where the quantum circuits and classical post-processing procedures were explicitly constructed, here we studied their parametrization and training. Note that in this project, we considered small system sizes up to 25 qubits, and we, thus, did not impose translational invariance in these HNNs.
We designed HNNs for the detection of the topological phase of the surface code in a magnetic field, which features intrinsic topological order. The parametrized quantum circuit depicted in the figure below consists of native gates of the superconducting quantum processor in the group of Prof. Andreas Wallraff at ETH Zurich. This facilitated the implementation of these HNNs on the quantum processor, which complements the theoretical investigation performed in this project. We focused on supervised learning, where these HNNs are trained to uncover characteristics of the topological phase from training data. The trained HNN distinguishes the topological phase not only from a topologically trivial magnetic phase but also from product states.
To investigate the practical advantages of these HNNs, we compared their sample complexity to alternative methods for quantum phase recognition using direct randomized measurements of quantum states in conjunction with classical shadow methods. In particular, we showed that the HNN learns the features of the topological phase with smaller sample complexity than a classical neural network trained with the outcomes of such local randomized measurements. We are currently preparing a manuscript presenting these results.
In parallel to this theoretical effort, we realized, together with the group of Prof. Andreas Wallraff at ETH Zurich, these HNNs on a superconducting quantum processor to test their training and performance in the presence of noise due to decoherence and experimental imperfections. In this collaboration, we optimized the hybrid two-loop training procedure for their quantum processor, significantly reducing the classical neural-network training time to mitigate latency in the exploitation of the quantum device. Furthermore, we devised variational circuits for the preparation of the surface code ground states in a magnetic field on the quantum processor. We optimized these variational circuits in classical preprocessing using state vector simulations and estimated their performance taking into account detailed noise models of the superconducting chip via Kraus vector simulations. We are currently preparing a manuscript presenting these results.
Together with my colleagues, I finished the study of explicitly constructed QCNNs for the two-dimensional toric code model, which was initially posted on the arXiv [arXiv:2407.04114] in month 11 of the outgoing phase. During the return phase of HyNNet NISQ, we substantially revised the manuscript to extend the QCNN to capture correlations between all stabilizer elements of the toric code, which cannot be accessed by direct measurements. This increases the probability of correlated incoherent errors that can be tolerated by the network and allows for the correct identification of the topological phase in the presence of strong correlated errors. This is not possible with methods based on direct measurements, showing the advantage achieved via the processing of quantum states on the quantum processor compared to direct measurements. To this end, we designed a new convolutional layer of the QCNN that takes correlations between error syndromes into account. This manuscript was published in Phys. Rev. Research in month 25.
We showed that these explicitly constructed QCNNs can be implemented as a short-depth quantum circuit, measurement and classical post-processing of measurement results. This motivates the design of trainable hybrid neural networks (HNNs), which are the main subject of this project. Therefore, these QCNNs provide an important input for the investigation of HNNs.
In the HyNNet NISQ project, we designed trainable HNNs depicted in the figure below. Analogously to the explicitly constructed QCNNs, they consist of a quantum circuit, measurement and classical-post processing. In contrast to the previous works, where the quantum circuits and classical post-processing procedures were explicitly constructed, here we studied their parametrization and training. Note that in this project, we considered small system sizes up to 25 qubits, and we, thus, did not impose translational invariance in these HNNs.
We designed HNNs for the detection of the topological phase of the surface code in a magnetic field, which features intrinsic topological order. The parametrized quantum circuit depicted in the figure below consists of native gates of the superconducting quantum processor in the group of Prof. Andreas Wallraff at ETH Zurich. This facilitated the implementation of these HNNs on the quantum processor, which complements the theoretical investigation performed in this project. We focused on supervised learning, where these HNNs are trained to uncover characteristics of the topological phase from training data. The trained HNN distinguishes the topological phase not only from a topologically trivial magnetic phase but also from product states.
To investigate the practical advantages of these HNNs, we compared their sample complexity to alternative methods for quantum phase recognition using direct randomized measurements of quantum states in conjunction with classical shadow methods. In particular, we showed that the HNN learns the features of the topological phase with smaller sample complexity than a classical neural network trained with the outcomes of such local randomized measurements. We are currently preparing a manuscript presenting these results.
In parallel to this theoretical effort, we realized, together with the group of Prof. Andreas Wallraff at ETH Zurich, these HNNs on a superconducting quantum processor to test their training and performance in the presence of noise due to decoherence and experimental imperfections. In this collaboration, we optimized the hybrid two-loop training procedure for their quantum processor, significantly reducing the classical neural-network training time to mitigate latency in the exploitation of the quantum device. Furthermore, we devised variational circuits for the preparation of the surface code ground states in a magnetic field on the quantum processor. We optimized these variational circuits in classical preprocessing using state vector simulations and estimated their performance taking into account detailed noise models of the superconducting chip via Kraus vector simulations. We are currently preparing a manuscript presenting these results.
The achievements of this project are:
1) The design of error-tolerant quantum convolutional neural networks and the shortening of their quantum circuits from logarithmic to constant depth in system size by performing a part of the computation in classical postprocessing, thereby introducing hybrid convolutional neural networks.
2) The construction of the quantum convolutional neural network that recognizes quantum phases in two-dimensional systems, where classical approximation methods face the most significant challenges and hence quantum computers will be particularly useful. This network can also be cast as a hybrid convolutional neural network by performing a large part of the computation in classical post-processing.
3) The training of hybrid neural networks consisting of parametrized quantum circuits and classical neural networks.
The hybrid neural networks (HNNs) developed in this project open a new way for the efficient characterization of quantum states generated as an output of quantum algorithms. Standard techniques have become limited due to the quickly increasing system size and complexity of quantum hardware. The HNNs developed here can be readily realized on existing quantum computers, as we demonstrated in collaboration with the group of Prof. Andreas Wallraff at ETH Zurich. Moreover, we investigated the sample complexity of these HNNs, and compared it to alternative methods based on direct local measurements and classical shadows. For investigated system sizes, we showed that the HNNs reduce the sample complexity compared to the alternative randomized measurement methods. Provided that these favorable sampling costs can be retained for larger system sizes, the HNNs can enable the efficient characterization of quantum states produced on the world’s largest quantum computers with hundreds of qubits. These networks will be potentially applicable for next-generation quantum computers with thousands of qubits, providing important benchmarks for the development of quantum computers. Moreover, these HNNs are a promising method for studying strongly correlated materials such as topological quantum matter on quantum computers.
1) The design of error-tolerant quantum convolutional neural networks and the shortening of their quantum circuits from logarithmic to constant depth in system size by performing a part of the computation in classical postprocessing, thereby introducing hybrid convolutional neural networks.
2) The construction of the quantum convolutional neural network that recognizes quantum phases in two-dimensional systems, where classical approximation methods face the most significant challenges and hence quantum computers will be particularly useful. This network can also be cast as a hybrid convolutional neural network by performing a large part of the computation in classical post-processing.
3) The training of hybrid neural networks consisting of parametrized quantum circuits and classical neural networks.
The hybrid neural networks (HNNs) developed in this project open a new way for the efficient characterization of quantum states generated as an output of quantum algorithms. Standard techniques have become limited due to the quickly increasing system size and complexity of quantum hardware. The HNNs developed here can be readily realized on existing quantum computers, as we demonstrated in collaboration with the group of Prof. Andreas Wallraff at ETH Zurich. Moreover, we investigated the sample complexity of these HNNs, and compared it to alternative methods based on direct local measurements and classical shadows. For investigated system sizes, we showed that the HNNs reduce the sample complexity compared to the alternative randomized measurement methods. Provided that these favorable sampling costs can be retained for larger system sizes, the HNNs can enable the efficient characterization of quantum states produced on the world’s largest quantum computers with hundreds of qubits. These networks will be potentially applicable for next-generation quantum computers with thousands of qubits, providing important benchmarks for the development of quantum computers. Moreover, these HNNs are a promising method for studying strongly correlated materials such as topological quantum matter on quantum computers.