Protocol Learns Quantum State Representation from Local Randomized Measurements and Fidelity Estimation

Understanding the quantum states of complex systems remains a significant challenge in physics, yet accurately characterising these states is crucial for advancing quantum technologies. Researchers, led by Matteo Votto from Université Grenoble Alpes, Marko Ljubotina from Technical University of Munich, and Cécilia Lancien, also at Université Grenoble Alpes, now demonstrate a new method for learning these states in large-scale experiments. Their approach successfully reconstructs the properties of entangled quantum states using data from readily available measurements, effectively upgrading classical techniques for use in advanced quantum computation and simulation. This breakthrough, achieved with states comprising up to several quantum bits, represents a substantial step towards fully harnessing the potential of complex quantum systems and opens new avenues for verifying and improving quantum devices.

Efficiently Learning Quantum States with Operators

Researchers are developing new methods to fully characterize quantum states, essential for advancing quantum computing and simulation technologies. Fully understanding a quantum system becomes increasingly difficult as the number of quantum bits, or qubits, grows, creating a bottleneck in the field. A team including Matteo Votto, Marko Ljubotina, and Cécilia Lancien have introduced a new protocol to efficiently learn the quantum state of many-body systems, even in the presence of experimental noise. This approach focuses on states that can be accurately represented using a mathematical tool called a matrix product operator, or MPO, providing a compact way to describe states commonly found in noisy quantum devices and certain types of quantum simulations.

The team’s protocol leverages a technique called “classical shadows,” which involves performing randomized measurements on the quantum system to gather statistical information. This method combines the efficiency of MPO representations with the robustness of classical shadows, allowing researchers to reconstruct the quantum state from a relatively small number of measurements. The protocol sequentially optimizes each component of the MPO to best match the experimentally prepared state, demonstrating that this optimization and assessment of its accuracy can be achieved with a manageable number of measurements, even for systems with a large number of qubits. The team successfully implemented this protocol on a superconducting quantum processor with up to 96 qubits, demonstrating its ability to learn complex entangled states. This advancement unlocks the potential to probe the properties of large-scale quantum systems, quantify the effects of noise, and develop more effective error mitigation strategies, bringing us closer to realizing the full potential of quantum technologies.

Randomized Measurements and Matrix-Product Operator Reconstruction

Researchers have developed a novel method to reconstruct the complete description of a quantum state, even when dealing with a large number of qubits, by leveraging the power of matrix-product operators (MPOs). This approach addresses a significant challenge in quantum information science, building upon existing techniques like randomized measurements and classical shadows. The team aimed to combine the benefits of these established methods with the efficiency of MPOs, offering a compact way to represent certain types of quantum states. The core of the methodology involves using randomized measurements to gather data about the quantum state, similar to how classical shadows are created, but with a focus on reconstructing an MPO representation.

This MPO is built from interconnected tensors, and the researchers developed a process to optimize these tensors based on the measurement data, effectively “learning” the quantum state. Crucially, the method focuses on optimizing each tensor individually, simplifying the complex task of reconstructing the entire quantum state at once. This approach distinguishes itself from previous methods by combining analytical guarantees of efficiency with the practical benefits of the classical shadow framework, allowing for accurate reconstruction even in the presence of experimental noise. The team split the collected measurement data into learning and testing sets, using the first to refine the MPO and the second to verify its accuracy, ensuring a robust and reliable reconstruction.

This allowed them to successfully demonstrate the ability to learn the quantum state of up to 96 qubits, significantly exceeding the capabilities of previous techniques. The resulting MPO representation provides a complete description of the quantum state, enabling researchers to directly access its properties without the need for complex calculations or re-processing of the data. This full description also allows for detailed analysis of experimental noise and the implementation of error mitigation strategies, paving the way for more accurate and reliable quantum simulations and computations.

Learning Entangled States with Matrix Product Operators

Researchers have developed a new method to learn and accurately represent complex quantum states using a technique called matrix-product operator (MPO) learning. This approach allows for the reconstruction of a quantum state’s information from a relatively small number of measurements performed on a quantum processor, effectively upgrading classical data processing to tackle large-scale quantum computations. The method involves sequentially refining a mathematical description of the quantum state, similar to established techniques used in materials science, but adapted for quantum information. The team successfully demonstrated this protocol by learning the characteristics of entangled quantum states comprising up to 96 qubits, a significant leap beyond previous experimental limitations.

Crucially, the learned MPO representation accurately captures the effects of experimental noise, achieving fidelities of approximately 75% for certain states, indicating the method models the actual, imperfect state observed in the experiment. Further analysis revealed that the learned representation closely matches key properties of the quantum state, such as magnetization and two-body correlations, aligning with measurements obtained directly from the experimental data. The researchers also measured the state’s entropy and found it adhered to a weak-volume law, suggesting that readout errors are a dominant source of imperfection in these low-depth quantum circuits. Beyond simply characterizing quantum states, this method opens the door to quantum error mitigation, a technique for improving the accuracy of quantum computations. By leveraging the learned MPO representation, researchers can partially correct for errors and obtain more reliable results from quantum experiments, paving the way for more complex and accurate quantum simulations and computations.

Compact Quantum State Representation via Measurements

This research team presents a protocol that learns a compact representation of a quantum state using classical data obtained from randomized measurements. This method effectively compresses the information from numerous quantum measurements into a single, manageable classical object, specifically a matrix-product operator (MPO). Having this MPO approximation allows researchers to efficiently estimate physical properties of the quantum state without repeatedly processing experimental data. The team successfully demonstrated this protocol by learning entangled quantum states on a quantum processor, showcasing its potential to upgrade classical shadows for large-scale quantum computation and simulation. Importantly, the method also provides a means for quantum error mitigation by leveraging powerful tensor-network algorithms.