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arxiv: 2307.07335 · v1 · submitted 2023-07-14 · 🪐 quant-ph

Benchmarking Digital-Analog Quantum Computation

Vicente Pina Canelles , Manuel G. Algaba , Hermanni Heimonen , Miha Papi\v{c} , Mario Ponce , Jami R\"onkk\"o , Manish J. Thapa , In\'es de Vega
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Adrian Auer
This is my paper

Pith reviewed 2026-05-24 07:42 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Digital-Analog Quantum ComputationDAQCQuantum AlgorithmsScaling PropertiesBenchmarkingDigital Quantum ComputationArbitrary Connectivities
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The pith

Except for a few specific cases, digital-analog quantum computation is disadvantageous compared to the standard digital approach.

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

The paper extends digital-analog quantum computation to arbitrary connectivities and conducts the first systematic study of its scaling properties. It benchmarks this against digital quantum computation using three specific quantum algorithms. The analysis concludes that DAQC requires more resources and scales worse in most scenarios. Readers would care because this directly informs which computation paradigm to pursue on near-term hardware. The work supplies concrete comparisons of performance metrics rather than abstract arguments.

Core claim

By extending DAQC to arbitrary connectivities and examining scaling properties for three quantum algorithms, the paper establishes that DAQC is disadvantageous with respect to the digital case except for a few specific cases.

What carries the argument

The scaling analysis of DAQC versus digital implementations across three quantum algorithms with arbitrary connectivities.

If this is right

  • Digital quantum computation is the preferable paradigm for the majority of the tested algorithms due to superior scaling.
  • DAQC only shows advantage in a limited number of specific scenarios.
  • Resource overheads for DAQC are higher across the examined cases.
  • Hardware design choices should prioritize digital gate implementations over analog evolution for general use.

Where Pith is reading between the lines

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

  • Device architects may favor gate-based digital systems when selecting near-term quantum platforms.
  • Testing additional algorithms beyond the three studied would strengthen or narrow the performance comparison.
  • The relative merits could shift once error mitigation techniques are applied to both paradigms.

Load-bearing premise

The three chosen quantum algorithms and the scaling metrics examined are representative enough to support general conclusions about DAQC versus digital performance.

What would settle it

Demonstrating that DAQC scales better than digital methods for an algorithm outside the three tested examples would falsify the general claim.

Figures

Figures reproduced from arXiv: 2307.07335 by Adrian Auer, Hermanni Heimonen, In\'es de Vega, Jami R\"onkk\"o, Manish J. Thapa, Manuel G. Algaba, Mario Ponce, Miha Papi\v{c}, Vicente Pina Canelles.

Figure 1
Figure 1. Figure 1: Digital circuit comprising ZZjk(ϕjk) gates, equiv￾alent to the evolution (7) under a given target Hamiltonian (2), for some time tf , in a device with four qubits and ATA connectivity. B. The stepwise digital-analog quantum circuit The digital-analog quantum circuit we will describe in this subsection is constructed in the so-called stepwise DAQC (sDAQC) paradigm [1], as opposed to the banged DAQC (bDAQC) … view at source ↗
Figure 2
Figure 2. Figure 2: Digital-Analog circuit consisting of c analog blocks. Each analog block runs for time tmn, and is preceded and followed by the gates X mX n , for each pair of connected qubits (m, n) ∈ C. Assume our quantum circuit is similar to that of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of the quantum circuit implementing [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic representation of error sources in a DAQC algorithm: (a) the number of analog blocks per implementation of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Scheme of a 5 qubit device with star [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Digital circuit for the QFT on a device with 5 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Quantum circuits implementing the GHZ state [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Top row: Fidelity of DQC, sDAQC and bDAQC algorithms as a function of the number of qubits for the following algorithms: (a) ATA-QFT, for which both versions of DAQC perform worse than DQC; (b) Star-QFT, for which both versions of DAQC perform worse than DQC, but bDAQC performs better than sDAQC for N > 6; and (c) Star-GHZ, for which sDAQC performs better than DQC. Bottom row: Duration of the DQC and sDAQC… view at source ↗
Figure 9
Figure 9. Figure 9: Digital-analog circuit implementing an analog block [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average fidelity of the Star-QFT algorithm for [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Approximate total fidelity of the Star-QFT algorithm, calculated according to Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

Digital-Analog Quantum Computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation. DAQC creates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of DAQC by extending its implementation to arbitrary connectivities and by performing the first systematic study of its scaling properties. We specify the analysis for three examples of quantum algorithms, showing that except for a few specific cases, DAQC is in fact disadvantageous with respect to the digital case.

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

1 major / 0 minor

Summary. The manuscript extends Digital-Analog Quantum Computation (DAQC) to arbitrary connectivities and performs the first systematic scaling comparison against digital quantum computation for three quantum algorithms, concluding that DAQC is disadvantageous except in a few specific cases.

Significance. If the central claim is substantiated by representative examples and rigorous scaling metrics, the work would supply useful benchmarking data to guide hardware and algorithm choices between DAQC and gate-model approaches. The extension to arbitrary connectivities is a concrete technical advance.

major comments (1)
  1. [section describing the three quantum algorithms and scaling metrics] The general conclusion that DAQC is disadvantageous except for few cases rests on explicit analysis of only three algorithms. The manuscript must justify in the section describing the algorithms and scaling metrics why these three are representative of regimes where DAQC might be advantageous (native analog Hamiltonians, long-range interactions, or continuous-time problems), otherwise the claim cannot be generalized beyond the chosen examples.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment below and will revise the manuscript to incorporate the requested justification for the choice of algorithms.

read point-by-point responses

  1. Referee: [section describing the three quantum algorithms and scaling metrics] The general conclusion that DAQC is disadvantageous except for few cases rests on explicit analysis of only three algorithms. The manuscript must justify in the section describing the algorithms and scaling metrics why these three are representative of regimes where DAQC might be advantageous (native analog Hamiltonians, long-range interactions, or continuous-time problems), otherwise the claim cannot be generalized beyond the chosen examples.

    Authors: We agree that explicit justification is required to support generalizing the conclusion beyond the three examples. The algorithms were selected to cover the indicated regimes: one based on a native analog Hamiltonian, one exploiting long-range interactions, and one formulated as a continuous-time problem. In the revised manuscript we will add a dedicated paragraph in the algorithms and scaling metrics section that maps each example to the corresponding regime and explains why this selection provides representative coverage of the settings where DAQC could be advantageous. This addition will also note the inherent limitations of any finite sample while preserving the paper's central claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the DAQC vs digital scaling analysis

full rationale

The paper's derivation consists of an explicit extension of DAQC to arbitrary connectivities followed by direct scaling analysis on three chosen quantum algorithms, with the disadvantage conclusion drawn from those computed metrics. No equations or steps reduce a prediction to a fitted input by construction, no self-citation chains support load-bearing premises, and the comparison is presented as an independent benchmarking exercise rather than a tautological renaming or ansatz smuggling. The representativeness of the three algorithms is an external assumption about generality but does not create circularity within the reported derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no specific free parameters, axioms, or invented entities are identifiable.

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Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages

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    Such errors can be modeled as an uncertainty in the time t of application of the resource Hamiltonian (see Fig

    Ramp-up and ramp-down errors Calibration errors can be produced when switching on and off the analog blocks [20], a process during which the evolution differs from the ideal square pulse assumed in Section II. Such errors can be modeled as an uncertainty in the time t of application of the resource Hamiltonian (see Fig. 4b). Additionally, the ramp-up and ...

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    Two-qubit terms in analog blocks The resource Hamiltonian considered to implement a DAQC algorithm should be descriptive of thenatural dy- namics of the device. However, there might be several sources of characterization errors associated to their im- plementation: • The resource Hamiltonian might still be an approx- imation to the actual dynamics for som...

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    Environmental errors As is the digital case, the dynamics of analog blocks is subject to the impact of its environment, which pro- duces decoherence and information losses. While the en- vironment responsible for the coherence decay is the same in both the digital and DAQC cases, the analog blocks may dissipate in a more complex and potentially faster way...

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    Each one- and two-qubit term in an evolution op- erator U corresponding to a SQG, TQG or analog block has a fidelity f < 1 arising from control er- rors, which is independent of all other operations

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    The main source of decoherence is thermal relax- ation, and we consider a simple Markovian model for it, such that the fidelity per qubit for an algo- rithm that requires a time t has the approximate form FT1 ≈ e−t/T1, where T1 is the relaxation time. Additionally, we consider this infidelity to be inde- pendent for each qubit, and also independent from t...

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    (22), of the form M =   1 1 1 · · · 1 1 1 −1 1 1 · · · 1 1 1 −1 −1 1 · · · 1 1 1

    is to place the X gates in such a way that we obtain an (N −1)×(N −1) sign matrix M, that relates the coupling coefficients of the resource and target Hamiltonians to the analog times according to Eq. (22), of the form M =   1 1 1 · · · 1 1 1 −1 1 1 · · · 1 1 1 −1 −1 1 · · · 1 1 1 ... ... ... ... ... ... ... −1 −1 −1 · · · 1 1 1 −1 −1 −1 · · · −...

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    Each target Hamiltonian requires c = O(N2) ana- log blocks (see Section III A)

    Number of analog blocks: The ATA-QFT cir- cuit is constructed as O(N) target Hamiltonians. Each target Hamiltonian requires c = O(N2) ana- log blocks (see Section III A). Thus, the total num- ber of analog blocks is O(N3)

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    On the other hand, the total duration of the DAQC algorithm depends on the resulting matrix M for each case, and thus we cannot say anything about it a priori (see Sec- tion III B)

    Duration: The digital ATA-QFT can be imple- mented in depth O(N) [39, 40]. On the other hand, the total duration of the DAQC algorithm depends on the resulting matrix M for each case, and thus we cannot say anything about it a priori (see Sec- tion III B). We numerically compute the duration of this algorithm in Section VII, and, by fitting a curve to the...

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    Thus, the total number of SQGs is O(N3)

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    (29), and setting ∆t, ¯g to be constant, each analog block introduces an error that scales as ϵcentral = O(N2) (see Sec- tion III D)

    bDAQC non-commutativity: Each qubit has a degree d = O(N), so from Eq. (29), and setting ∆t, ¯g to be constant, each analog block introduces an error that scales as ϵcentral = O(N2) (see Sec- tion III D). There are O(N3) analog blocks, so the contribution from bDAQC to the compound fidelity in Eq. (35) scales as (1 − O(N2))O(N 3). Table I. Scaling of the ...

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    However, in this case, each target Hamiltonian requires c = O(N) analog blocks, because the other analog blocks get can- celled

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