Alternative adiabatic quantum dynamics for gate-based quantum computing with applications to quantum linear systems

[Submitted on 28 May 2026]

2d ago· 2 min readenInsight

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Summary

This paper proposes alternative processes for adiabatic quantum computing that can be implemented on gate-based quantum computers without the overhead of simulating time-dependent Hamiltonian evolution. The authors provide a general framework for deriving 'adiabatic' theorems for these processes. As applications, they present algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number, including a randomized version of the discrete adiabatic algorithm. They also describe Trotterisation versions within their framework, achieving asymptotically better bounds on Trotter error in terms of fidelity compared to standard bounds.

Key quotes

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We propose several alternative processes that achieve the same goal, but can easily be implemented on a gate-based quantum computer without the overhead of simulating time-dependent Hamiltonian evolution.

We give a general framework for deriving `adiabatic' theorems for these processes.

As an application, we give various algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number.

We also describe versions of Trotterisation in our framework, which allows several results from [An et al. 2025] to be reproduced in a randomised setting.

Bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.

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In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the adiabatic theorem. We

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