Optimal Effective Hamiltonian for Quantum Computing and Simulation

TL;DR

This paper introduces the Least Action Unitary Transformation (LAUT) as a novel, symmetry-preserving method for constructing effective Hamiltonians in quantum systems, validated through experiments on superconducting quantum processors.

Contribution

It establishes LAUT as a fundamental principle for effective Hamiltonian construction, resolving gauge freedom issues and improving accuracy over traditional methods.

Findings

LAUT accurately reproduces interaction rates in driven entangling gates.

It captures non-rotating-wave contributions in tunable coupler architectures.

Reveals physical multi-body interactions beyond standard models.

Abstract

The effective Hamiltonian serves as the conceptual pivot of quantum engineering, transforming physical complexity into programmable logic; yet, its construction remains compromised by the mathematical non-uniqueness of block diagonalization, which introduces an intrinsic "gauge freedom" that standard methods fail to resolve. We address this by establishing the Least Action Unitary Transformation (LAUT) as the fundamental principle for effective models. By minimizing geometric action, LAUT guarantees dynamical fidelity and inherently enforces the preservation of symmetries--properties frequently violated by conventional Schrieffer-Wolff and Givens rotation techniques. We identify the Bloch-Brandow formalism as the natural perturbative counterpart to this principle, yielding analytic expansions that preserve symmetries to high order. We validate this framework against experimental data from superconducting quantum processors, demonstrating that LAUT quantitatively reproduces interaction rates in driven entangling gates where standard approximations diverge. Furthermore, in tunable coupler architectures, we demonstrate that the LAUT approach captures essential non-rotating-wave contributions that standard models neglect; this inclusion is critical for quantitatively reproducing interaction rates and revealing physical multi-body interactions such as $XZX+YZY$, which are verified to be physical rather than gauge artifacts. By reconciling variational optimality with analytical tractability, this work provides a systematic, experimentally validated route for high-precision system learning and Hamiltonian engineering.