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arxiv: 2605.30110 · v1 · pith:46UHZ5E6new · submitted 2026-05-28 · 🪐 quant-ph

Alternative adiabatic quantum dynamics with algorithmic applications

Joseph Cunningham , J\'er\'emie Roland This is my paper

Pith reviewed 2026-06-29 06:30 UTC · model grok-4.3

classification 🪐 quant-ph
keywords adiabatic quantum computingquantum linear systems problemgate-based quantum computingadiabatic theoremTrotterisationquantum algorithmsQLSP
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The pith

Alternative processes achieve adiabatic tracking on gate-based quantum computers without Hamiltonian simulation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops discrete processes that track an eigenstate as parameters change, replacing the usual continuous time-dependent Hamiltonian evolution of adiabatic quantum computing. It supplies a general framework for proving that these processes still satisfy an adiabatic theorem. This matters for gate-based hardware because the new processes use only standard gates and avoid the cost of simulating continuous dynamics. The framework is then applied to produce quantum linear systems solvers whose runtime scales optimally with the condition number, including a randomized variant of a known discrete adiabatic method.

Core claim

Several alternative processes achieve the same goal as adiabatic evolution but are directly implementable on gate-based quantum computers without the overhead of simulating time-dependent Hamiltonian evolution. A general framework derives adiabatic theorems for these processes. The framework yields various algorithms for the Quantum Linear Systems Problem with optimal scaling in the condition number, one of which is a randomised version of the discrete adiabatic algorithm, and it also reproduces Trotterisation results in a randomised setting with asymptotically better fidelity-based error bounds.

What carries the argument

General framework for deriving adiabatic theorems for alternative discrete processes that replace time-dependent Hamiltonian evolution while preserving eigenstate tracking.

If this is right

  • QLSP algorithms achieve optimal scaling with the condition number.
  • A randomised version of the discrete adiabatic algorithm solves QLSP.
  • Trotterisation can be performed inside the framework in a randomised setting.
  • Trotter error bounds measured in fidelity are asymptotically tighter than conventional bounds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The discrete processes may reduce the resources needed to run adiabatic-style algorithms on near-term gate hardware.
  • The framework could be used to analyse other gate-based quantum algorithms that currently rely on adiabatic theorems.
  • Randomised variants might tolerate certain forms of noise better than their deterministic counterparts.

Load-bearing premise

The alternative discrete processes preserve the required eigenstate tracking property through the new framework when realized with standard gates.

What would settle it

A direct simulation or hardware run of one proposed process on a small QLSP instance that shows the final state fidelity falls below the bound predicted by the framework's adiabatic theorem.

Figures

Figures reproduced from arXiv: 2605.30110 by J\'er\'emie Roland, Joseph Cunningham.

Figure 1
Figure 1. Figure 1: An illustration of the spectrum of H(s). 2 Generalised adiabatic dynamics In this work we consider various processes that have similar features: they are all capable of tracking an eigenspace in a certain parameter regime. The underlying mechanism is similar in all cases; the process is described by a differential equation that contains a multiplicative scalar parameter. When this parameter is taken to be … view at source ↗
Figure 2
Figure 2. Figure 2: A realisation of a Poisson process. Lemma 5. Let U(s) be a path of unitaries that is twice continuously differentiable. The differential equation (31) satisfies the assumptions of Theorem 1 with X = [UP^′ , P]. (32) Here P is an eigenprojector of U and The twiddle is with respect to U, meaning it has the property that [U, Ye] = [P, Y ]. Proof. Let σ be an arbitrary trace-one operator on H. We need to prove… view at source ↗
Figure 3
Figure 3. Figure 3: An illustration of the spectrum of a normal operator [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: An illustration of the integration contours used in the proof of Proposition 19. The black dots [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: An illustration of the proof of Proposition 22. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
read the original abstract

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 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. One of these algorithms was previously developed in [Cunningham, Roland 2024] and another can be seen as a randomised version of the discrete adiabatic algorithm of [Costa et al. 2022]. 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. In particular, bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The manuscript proposes several alternative dynamical processes to standard adiabatic quantum computing that track eigenstates without requiring simulation of continuous time-dependent Hamiltonians, enabling direct implementation on gate-based quantum computers. It develops a general framework for deriving adiabatic theorems applicable to these processes. As an application, the framework yields QLSP algorithms with optimal scaling in the condition number, including a randomized version of the discrete adiabatic algorithm from Costa et al. (2022) and a reproduction of results from Cunningham and Roland (2024). The paper also presents randomized Trotterization variants that reproduce results from An et al. (2025) with asymptotically improved fidelity-based error bounds.

Significance. If the central claims hold, the work offers a useful generalization of adiabatic methods to discrete gate-based settings, removing simulation overhead while preserving tracking guarantees. The explicit reproduction of prior QLSP and Trotter results in a randomized context, together with improved error bounds, strengthens the contribution by providing both algorithmic alternatives and tighter analyses. The absence of free parameters or circular definitions in the high-level claims, as noted in the abstract, supports the framework's potential utility for future algorithm design.

minor comments (1)
  1. The abstract references results from An et al. (2025); ensure the reference list includes the full citation details and that the manuscript clarifies the precise overlap with the reproduced bounds.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their thorough and positive review, which accurately captures the manuscript's contributions to alternative adiabatic processes, QLSP algorithms, and randomized Trotterization. We are pleased by the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper presents a new general framework for alternative adiabatic processes implementable via standard gates, with applications to QLSP algorithms of optimal scaling. The self-reference to the authors' prior 2024 QLSP result is an acknowledgment that one listed algorithm was previously developed elsewhere; it does not serve as a load-bearing premise for the framework itself or force any new derivation by construction. No self-definitional equations, fitted inputs renamed as predictions, uniqueness theorems imported from the same authors, or ansatzes smuggled via citation are present. The derivation chain remains independent of the cited prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit free parameters, invented entities, or detailed axioms; the central claim rests on the domain assumption that the alternative processes preserve eigenstate tracking.

axioms (1)
  • domain assumption Alternative discrete processes can track an eigenstate of a changing Hamiltonian in a manner analogous to the standard adiabatic theorem.
    This is the load-bearing premise that allows the framework to replace continuous Hamiltonian evolution.

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discussion (0)

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Reference graph

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