Learning Mixed Quantum States in Large-Scale Experiments

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum State Tomography

Background:

• Accurately representing quantum states is crucial for quantum computation and simulation.
• Classical shadows offer a resource-efficient method for quantum state tomography.
• Matrix-product operator (MPO) is a powerful tool for describing many-body quantum systems.

Purpose of the Study:

• To develop and validate a protocol for learning matrix-product operator (MPO) representations of experimentally prepared quantum states.
• To enable efficient reconstruction and characterization of quantum states from classical shadow data.
• To enhance the scalability of quantum state learning for large quantum systems.

Main Methods:

• Inputting classical shadows from local randomized measurements.
• Optimizing MPO tensors sequentially to maximize fidelity with the experimental state.
• Utilizing a protocol similar to the density matrix renormalization group algorithm.

Main Results:

• Demonstrated provable efficiency under conditions relevant to short-range correlated states and noisy experiments.
• Developed an efficient scheme for estimating fidelities between learned and experimental states.
• Successfully learned entangled quantum states of up to 96 qubits on a superconducting quantum processor.

Conclusions:

• The presented protocol effectively upgrades classical shadows for large-scale quantum computation and simulation.
• This method provides a scalable approach to quantum state learning and characterization.
• The protocol shows promise for advancing experimental quantum information processing.