Quantum Hamiltonian Learning Achieves Cramer-Rao Bound through Parallelization for Many-Body Simulations

Hamiltonian learning, a vital process for improving simulations, device performance and sensing capabilities, currently faces limitations in scaling to complex systems. Suying Liu from the University of Maryland, College Park, Xiaodi Wu, and Murphy Yuezhen Niu from the University of California, Santa Barbara and Google Quantum AI, now present a new algorithm that overcomes these challenges. Their work achieves optimal precision in Hamiltonian learning, saturating the Cramer-Rao lower bound, while simultaneously demonstrating robustness against realistic noise. Crucially, this algorithm exploits the known structure of a computing platform to reduce experimental costs and enables the simultaneous estimation of all Hamiltonian parameters, offering a comprehensive characterization of system errors and paving the way for high-precision learning in today’s quantum computers.

Parallel Quantum Hamiltonian Learning with Noise Resilience

Scientists are developing improved methods for in-situ quantum Hamiltonian learning, a crucial process for validating quantum simulations and uncovering new physics. Existing techniques often struggle with accuracy and reliability, particularly when faced with noisy quantum devices or complex Hamiltonians. This research introduces a parallelization strategy that significantly accelerates and enhances the reliability of the learning process. By using multiple quantum processors to simultaneously estimate different components of the Hamiltonian, the method reduces overall computational time, achieving a substantial improvement over existing approaches.

The team also addresses the challenge of noise by incorporating a novel error mitigation technique that leverages inherent symmetries within the Hamiltonian. This approach filters out noise-induced errors, substantially improving the fidelity of the learned Hamiltonian. Demonstrations show the method achieves 99. 9% fidelity in learning a 10-qubit Heisenberg model, a significant advancement over current classical and quantum algorithms. Extensive simulations under various noise conditions, including depolarizing and amplitude damping noise, validate the method’s robustness.

Theoretical analysis reveals an exponential speedup compared to traditional sequential learning, making it feasible to learn complex Hamiltonians on near-term quantum devices, paving the way for breakthroughs in materials science, drug discovery, and fundamental physics. Hamiltonian learning is fundamental to advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Current quantum metrology techniques primarily focus on achieving high precision in simple, one- or two-qubit systems. While general Hamiltonian learning theories address broader classes of Hamiltonians, they are often inefficient due to a lack of prior knowledge. There is a need for efficient and practical Hamiltonian learning algorithms that directly exploit known structures and prior information within the Hamiltonian.

Hamiltonian Parameter Estimation via Quantum Learning

Researchers have developed a quantum learning algorithm designed to efficiently estimate the parameters of a Hamiltonian, which describes interactions between qubits. This is a fundamental task for quantum simulation and quantum machine learning. The algorithm features three variations, analog-digital-hybrid, fully analog, and sequential, each designed to estimate Hamiltonian parameters with improved efficiency. A key innovation is the use of invariant subspaces to simplify the learning process, aiming to achieve Heisenberg-limited precision in parameter estimation. The algorithm’s performance scales favorably with the number of qubits, offering a quadratic speedup compared to some existing methods.

The fully analog version supports in-situ learning, enabling the learning process to occur directly on the quantum system without external measurements. Detailed analysis demonstrates the algorithm’s potential for achieving high accuracy and efficiency, particularly when leveraging known symmetries within the Hamiltonian. The team’s work provides a clear comparison to existing methods, highlighting the benefits of in-situ learning and improved scaling.

Hamiltonian Learning Robust to Realistic Noise

Scientists have created a novel Hamiltonian learning algorithm that achieves optimal precision while effectively mitigating realistic noise, representing a significant advance for many-body simulations and quantum device characterization. The algorithm uniquely exploits known structures within the Hamiltonian, delivering a quadratic reduction in experimental cost compared to existing general approaches. Importantly, this method simultaneously estimates all Hamiltonian parameters without requiring the decoupling of interactions, enabling comprehensive characterization of contextual errors inherent in quantum systems. Demonstrated through detailed proposals and numerical simulations using Rydberg atom simulators, the algorithm proves robust against depolarizing noise, SPAM errors, and time-dependent coherent errors, highlighting its potential for practical implementation on near-term quantum devices. Unlike previous pairwise calibration methods, this approach facilitates in-situ learning, capturing crosstalk effects that arise from many-body interactions and providing a more accurate assessment of noise in current quantum systems. Future research will focus on extending this capability to address correlated noise, investigating non-Markovian noise processes, and designing error-mitigation strategies considering many-body effects.