arxiv: 2603.15534 · v2 · submitted 2026-03-16 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.stat-mech

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Analog-Digital Quantum Computing with Quantum Annealing Processors

Rahul Deshpande , Majid Kheirkhah , Chris Rich , Richard Harris , Jack Raymond , Emile Hoskinson , Pratik Sathe , Andrew J. Berkley

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Stefan Paul Brian Barch Daniel A. Lidar Markus M\"uller Gabriel Aeppli Andrew D. King Mohammad H. Amin

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Pith reviewed 2026-05-15 09:50 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.stat-mech

keywords analog-digital quantum computingquantum annealingXY modelquantum walkAnderson localizationsuperconducting qubitsauxiliary qubitseffective Hamiltonian

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The pith

Quantum annealing processors can implement single-qubit gates by sandwiching analog evolution under a fixed many-body Hamiltonian with auxiliary-qubit initialization and measurement.

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

The paper demonstrates that a superconducting quantum annealing processor can perform hybrid analog-digital operations by evolving under a fixed many-body Hamiltonian that reduces to an effective XY model in the weak-coupling regime. Arbitrary-basis initialization and readout are handled by auxiliary qubits, which is equivalent to placing single-qubit rotations before and after the analog evolution. This combination enables coherent single- and two-qubit oscillations, a multi-qubit quantum walk that reproduces fermionic dispersion, and Anderson localization in a disordered chain. A sympathetic reader cares because the method expands the reachable computations on existing large-scale annealing hardware without requiring full gate-based control.

Core claim

Evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits, is operationally equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution.

What carries the argument

Effective XY model arising from the fixed many-body Hamiltonian in the weak-coupling regime, combined with auxiliary qubits for basis initialization and measurement.

If this is right

Single- and two-qubit coherent oscillations become possible with arbitrary initialization and measurement bases.
Multi-qubit quantum walks can be realized that exhibit fermionic dispersion matching theoretical predictions.
Anderson localization can be observed in a disordered chain on the same hardware.
A broader class of quantum simulation and computation tasks becomes accessible on commercial annealing processors.

Where Pith is reading between the lines

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

The same fixed-Hamiltonian-plus-auxiliary approach might be extended to simulate other effective spin models by changing the annealing schedule or coupler strengths.
Hybrid sequences could allow longer effective coherence times for certain tasks by leveraging the analog segment's natural protection.
The method suggests a route to test quantum many-body effects at scales already available in annealing hardware without building a full universal gate set.
If the weak-coupling mapping holds for larger systems, it could enable direct analog simulation of XY-model Hamiltonians with digital control layers added only at the ends.

Load-bearing premise

The many-body Hamiltonian must remain in the weak-coupling regime so that its dynamics are accurately captured by the effective XY model.

What would settle it

Measured oscillation frequencies or walk dispersion relations that deviate systematically from the predictions of the effective XY model, after accounting for known noise sources, would falsify the description.

Figures

Figures reproduced from arXiv: 2603.15534 by Andrew D. King, Andrew J. Berkley, Brian Barch, Chris Rich, Daniel A. Lidar, Emile Hoskinson, Gabriel Aeppli, Jack Raymond, Majid Kheirkhah, Markus M\"uller, Mohammad H. Amin, Pratik Sathe, Rahul Deshpande, Richard Harris, Stefan Paul.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

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.

Desk Editor's Note private letter to a colleague

The paper adds a hybrid mode to annealing processors by running fixed XY-model analog evolution between auxiliary-qubit init and measure steps, with working demos of oscillations, walks, and localization.

read the letter

The core advance is showing that a superconducting annealing chip can run analog evolution under its native many-body Hamiltonian (treated as an effective XY model in the weak-coupling limit) while using auxiliary qubits to set and read out in arbitrary bases. This is not just standard annealing; it lets them do single-qubit rotations at the start and end of a continuous evolution without needing full gate-model control. They show this with coherent oscillations on one and two qubits, a multi-qubit fermionic quantum walk whose dispersion matches theory, and Anderson localization in a disordered chain. Those experiments are the strongest part: the data line up with independent predictions rather than being tuned to fit. The approach is practical because it reuses the existing hardware scaling of annealers without adding complex pulse sequences. The main soft spot is the weak-coupling assumption itself. The abstract and stress-test note both flag that the paper states the regime but does not appear to bound the size of neglected ZZ or higher-order terms for the actual device parameters and evolution times. If those corrections matter at the observed timescales, the reported agreement with pure XY theory could be partly accidental. No circularity or invented parameters show up, and the citation pattern looks standard. This is useful for groups already running quantum simulation on annealing hardware who want to expand the operation set without switching platforms. It is not yet a fully general digital simulator, but the experimental demonstrations are concrete enough that a serious editor should send it to referees rather than desk-reject.

Referee Report

2 major / 2 minor

Summary. The paper claims to enable analog-digital quantum computing on superconducting quantum annealing processors via evolution under a fixed many-body Hamiltonian that reduces to an effective XY model in the weak-coupling regime, augmented by auxiliary qubits for arbitrary-basis initialization and measurement. This framework is demonstrated through single- and two-qubit coherent oscillations, a multi-qubit fermionic quantum walk matching theoretical dispersion, and Anderson localization in a disordered chain.

Significance. If the weak-coupling approximation holds with sufficient accuracy, the work meaningfully expands the operational scope of existing quantum annealing hardware beyond standard annealing schedules, enabling hybrid analog-digital protocols for quantum simulation and computation on scalable commercial devices. The reported agreement between experiment and independent theoretical predictions for dispersion and localization constitutes a concrete strength, as does the use of auxiliary qubits to achieve basis flexibility without full gate-based control.

major comments (2)

[Hamiltonian description and experimental sections] The central claim that the fixed many-body Hamiltonian is well-described by an effective XY model in the weak-coupling regime (invoked for all three demonstrations) lacks explicit derivation or quantitative bounds on neglected terms such as ZZ couplings or higher-order corrections for the device parameters and evolution times used. This is load-bearing because the observed matches to XY theory could be affected by unaccounted dynamics if the regime is not sufficiently weak.
[Results on fermionic quantum walk and Anderson localization] The experimental sections on the quantum walk and Anderson localization do not provide sufficient detail on control calibration, error analysis, or data selection criteria to allow independent verification that the reported agreement with theory is robust rather than influenced by post-selection or uncharacterized noise.

minor comments (2)

[Figures 2-4] Figure captions would benefit from explicit statements of the number of experimental repetitions and how error bars are computed.
[Methods] Notation for the auxiliary-qubit coupling strengths and the precise definition of the weak-coupling parameter should be introduced earlier and used consistently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us identify areas for improvement. We address each major comment below and have revised the manuscript to incorporate additional derivations, quantitative bounds, and experimental details as requested.

read point-by-point responses

Referee: The central claim that the fixed many-body Hamiltonian is well-described by an effective XY model in the weak-coupling regime (invoked for all three demonstrations) lacks explicit derivation or quantitative bounds on neglected terms such as ZZ couplings or higher-order corrections for the device parameters and evolution times used. This is load-bearing because the observed matches to XY theory could be affected by unaccounted dynamics if the regime is not sufficiently weak.

Authors: We agree that an explicit derivation and quantitative bounds on the neglected terms are necessary to fully substantiate the central claim. In the revised manuscript, we will add a dedicated subsection deriving the effective XY model from the full many-body Hamiltonian under the weak-coupling approximation, including perturbative estimates of ZZ couplings and higher-order corrections evaluated at the specific device parameters and evolution times used in the experiments. These bounds will demonstrate that the approximation error remains below the threshold that could affect the observed agreement with XY theory. revision: yes
Referee: The experimental sections on the quantum walk and Anderson localization do not provide sufficient detail on control calibration, error analysis, or data selection criteria to allow independent verification that the reported agreement with theory is robust rather than influenced by post-selection or uncharacterized noise.

Authors: We acknowledge that the current experimental descriptions lack sufficient detail for independent verification. In the revised version, we will expand the methods and supplementary information sections to include: (i) detailed control calibration procedures and pulse sequences, (ii) a comprehensive error analysis quantifying contributions from decoherence, control errors, and readout noise with their estimated impacts on the observed signals, and (iii) explicit data selection criteria along with robustness checks against post-selection. We will also add raw data plots and statistical comparisons to confirm the agreement with theory is robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation chain rests on the physical assumption that the fixed many-body Hamiltonian operates in the weak-coupling regime and is thereby well-approximated by an effective XY model; this is presented as an external modeling choice rather than a quantity fitted to the target data or defined in terms of the claimed results. Experimental demonstrations (coherent oscillations, fermionic quantum walks, Anderson localization) are compared against independent theoretical predictions for dispersion relations and localization lengths that are not constructed from the same measurements. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the central claim to its own inputs appear in the derivation. The approach is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the fixed Hamiltonian reduces to an effective XY model in the weak-coupling regime and that auxiliary qubits enable independent arbitrary-basis control without introducing uncontrolled errors.

axioms (1)

domain assumption The many-body Hamiltonian in the weak-coupling regime is well-described by an effective XY model
Invoked directly in the abstract as the basis for the analog evolution step.

pith-pipeline@v0.9.0 · 5550 in / 1172 out tokens · 50166 ms · 2026-05-15T09:50:55.493540+00:00 · methodology

discussion (0)

Reference graph

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For simplicity, we only consider the initial states prepared in the experiments in Fig

This equation can be solved analytically, giving the exact solutions for an arbitrary initial state and measurement basis. For simplicity, we only consider the initial states prepared in the experiments in Fig. 3 here. Forψ(t= 0) =|10⟩, we get ⟨σz 1⟩= 1−e − t T1 −e −t( 1 T1 + 1 Tϕ ) cosh νt Tϕ + 1 ν sinh νt Tϕ ,(S4) whereν= q 1− J 2T 2 ϕ /ℏ2. This express...

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local” measurement operator on the individual target qubits, and we can also calculate the fidelity of the two-qubit (“non-local

Provided the evolution remains adiabatic, that superposition will survive into the projection phase, albeit with an accrued azimuthal phase differenceδφthat depends on the details of that evolution. The final superposition then projects onto the coupled system flux bases |LdetRtarget⟩and|R detLtarget⟩. In this case, one achieves readout of the target in i...

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