[Paper Review] Robustly learning the Hamiltonian dynamics of a superconducting quantum processor

Dominik Hangleiter, Ingo Roth+3 more|arXiv (Cornell University)|Aug 18, 2021

Computational Physics and Python Applications4 citations

TL;DR

This paper presents a robust, scalable method for learning the Hamiltonian dynamics of superconducting quantum processors using time-series data of canonical coordinates. By combining a novel tensorESPRIT algorithm for super-resolution frequency extraction with constrained manifold optimization, the approach achieves sub-MHz precision in Hamiltonian parameter estimation and simultaneously diagnoses SPAM errors, enabling high-fidelity characterization of up to 14 coupled qubits with full spatial error mapping.

ABSTRACT

The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. The key to solving these issues are precise means of characterizing analog quantum simulators. Here, we robustly estimate the free Hamiltonian parameters of bosonic excitations in a superconducting-qubit analog quantum simulator from measured time-series of single-mode canonical coordinates. We achieve high levels of precision in estimating the Hamiltonian parameters by exploiting a priori knowledge, making it robust against noise and state-preparation and measurement (SPAM) errors. Importantly, we are also able to obtain tomographic information about those SPAM errors from the same data, crucial for the experimental applicability of Hamiltonian learning in dynamical quantum-quench experiments. Our learning algorithm is scalable both in terms of the required amounts of data and post-processing. To achieve this, we develop a new super-resolution technique coined tensorESPRIT for frequency extraction from matrix time-series. The algorithm then combines tensorESPRIT with constrained manifold optimization for the eigenspace reconstruction with pre- and post-processing stages. For up to 14 coupled superconducting qubits on two Sycamore processors, we identify the Hamiltonian parameters -- verifying the implementation on one of them up to sub-MHz precision -- and construct a spatial implementation error map for a grid of 27 qubits. Our results constitute an accurate implementation of a dynamical quantum simulation that is characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.

Motivation & Objective

• To develop a scalable and robust method for identifying Hamiltonian parameters in analog quantum simulators subject to noise and SPAM errors.
• To enable precise characterization of large-scale superconducting quantum processors beyond classical simulation limits.
• To simultaneously extract diagnostic information about state preparation and measurement (SPAM) errors from the same experimental data.
• To overcome limitations of prior methods that assume perfect mid-circuit quenches or are sensitive to experimental imperfections.
• To provide a practical toolkit for calibrating and improving analog quantum processors in real-world experimental settings.

Proposed method

• Proposes tensorESPRIT, a super-resolution technique for frequency extraction from matrix time-series, enabling high-precision spectral estimation from noisy data.
• Uses constrained manifold optimization to reconstruct the eigenspace of the Hamiltonian from time-evolved data, exploiting the underlying model structure.
• Integrates pre- and post-processing stages to mitigate the effects of SPAM errors and improve robustness.
• Employs a gauge-invariant formulation to reduce sensitivity to systematic errors from initial and final ramps.
• Applies parametric bootstrapping to estimate statistical errors due to finite measurement statistics.
• Uses a linear ramping model to estimate systematic errors from non-trivial final ramps, validated via separate experiments.

Experimental results

Research questions

• RQ1 Can Hamiltonian parameters be robustly estimated in the presence of SPAM errors and finite measurement statistics in superconducting quantum processors?
• RQ2 How can SPAM errors be diagnosed simultaneously with Hamiltonian learning from the same experimental data?
• RQ3 To what extent can the proposed method scale to large systems, such as 14 coupled qubits, while maintaining high precision?
• RQ4 How do systematic errors from non-ideal ramps affect Hamiltonian identification, and can they be quantitatively estimated?
• RQ5 Can the method be deployed efficiently on standard hardware, enabling real-time diagnostics for analog quantum simulators?

Key findings

• The method achieves sub-MHz precision in identifying Hamiltonian parameters for up to 14 coupled superconducting qubits on Sycamore processors.
• The algorithm successfully reconstructs a spatial implementation error map for a 27-qubit grid, enabling full spatial characterization of device imperfections.
• TensorESPRIT enables super-resolution frequency extraction with computational complexity of O(L²N³), making it scalable for large systems.
• The method is robust against SPAM errors and noise, with performance maintained even when baseline methods fail due to data limitations.
• Parametric bootstrapping and ramp modeling allow reliable estimation of both statistical and systematic errors in Hamiltonian identification.
• The entire identification pipeline runs efficiently on consumer-grade laptops, reconstructing Hamiltonians of size N=50 in approximately 5 minutes.