Quantum Hamiltonian Learning From High-Temperature Gibbs States
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Solution Overview
Problem
Noise in quantum devices impedes the efficient learning of quantum many-body systems, particularly in characterizing or validating properties such as spin states or orbital states, and existing quantum algorithms are susceptible to decoherence and require complex quantum processors.
Innovation Solution
A classical model is used to learn a special class of Hamiltonians, minimizing sample and time complexity by obtaining copies of Gibbs states and employing a decoding unit to estimate Hamiltonian coefficients robustly, even in noisy environments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Difficulty of detecting and measuring
If quantum algorithms are used to learn quantum many-body systems, then learning capability is improved, but noise susceptibility and decoherence increase
Solution Approach 1:
The patent introduces a classical machine learning model as an intermediary between the quantum device and the learning process. Instead of using quantum algorithms that are susceptible to noise, the classical model processes measurement data from the quantum device to learn Hamiltonian parameters, thereby avoiding direct exposure of the learning algorithm to quantum decoherence and noise.
Solution Approach 2:
The patent replaces quantum computational mechanisms with classical computational mechanisms. Rather than using quantum algorithms running on quantum processors, the system uses classical machine learning algorithms (such as neural networks or statistical models) to process quantum measurement data, substituting the fragile quantum computational path with a robust classical computational path.
2Measurement precision
If quantum processors are used to characterize quantum device properties, then measurement precision is improved, but device complexity and cost increase
Solution Approach 1:
The patent uses a classical model that copies and processes the essential information from quantum measurement data without requiring a full quantum simulation. The classical model learns from copies of measurement outcomes to infer Hamiltonian parameters, avoiding the need for complex quantum processors while maintaining characterization precision.
Solution Approach 2:
The patent changes the approach from using quantum processors (complex hardware) to using classical algorithms with optimized parameter estimation. By focusing on estimating Hamiltonian parameters through classical machine learning on measurement data, the system achieves precise characterization without the complexity of quantum processors.
3Productivity
If learning techniques are applied to quantum systems, then information processing capability is improved, but sample complexity increases due to noise
Solution Approach 1:
The classical machine learning model acts as an intermediary that efficiently processes measurement data with reduced sample complexity. Instead of requiring numerous quantum algorithm executions susceptible to noise, the classical model can learn from fewer measurement samples by using statistical techniques and optimization algorithms that are more robust to noise and require fewer samples to converge.
Data Source
AI summary
Embodiments of the present disclosure include systems and methods for reducing a sample complexity and a time complexity associated with noise-robust characterization of a quantum device. A plurality of copies of a Gibbs state of the quantum device in thermal equilibrium at a high-temperature. A plurality of estimates for expectation values of the plurality of copies of the Gibbs state. A plurality of cluster derivatives for a plurality of connected clusters of a low-degree Hamiltonian are calculated. A function is inverted on the plurality of estimates based on the plurality of cluster derivatives and a set of Hamiltonian coefficients are estimated for the low-degree Hamiltonian of the quantum device.