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REVIEW 4 major objections 4 minor 91 references

A weighted success-probability metric, predicted by machine learning, ranks quantum circuits far better than gate count or depth.

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2026-08-02 08:49 UTC pith:4R5N52N6

load-bearing objection The wPST metric and its shot-budget analysis are genuinely useful; the ML predictor looks strong on transpiled circuits, but the compiler-benefit claim rests on a two-step pipeline the paper itself hasn't validated. the 4 major comments →

arxiv 2607.03275 v2 pith:4R5N52N6 submitted 2026-07-03 quant-ph

Comparing and learning figures of merit for quantum circuit compilation

Harshdeep Singh , Marvin Richter , Mats Granath , Anton Frisk Kockum This is my paper
classification quant-ph MSC 81P68 PACS 03.67.Lx
keywords quantum circuit compilationfigure of meritprobability of successful trialsweighted PSTmachine learningcircuit quality predictionnoise-aware compilationmirror circuits
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper aims to give quantum circuit compilers a cheap but reliable way to rank candidate circuits. It introduces wPST, a weighted version of the probability of successful trials that gives partial credit for partially correct measurement outcomes, and shows that wPST is linear in per-qubit marginals and degrades linearly with error rate instead of exponentially. Since evaluating wPST by execution is costly, the paper trains a decision-tree model on circuit features plus hardware data to predict PST and wPST. Across simulated and real quantum processors, the predicted metrics correlate substantially better with the true measured metrics than standard circuit-level figures such as depth and gate counts, improving correlation by over 50 percent. It also proposes a two-step predictor that estimates what transpilation will add to a circuit, making the metric usable during compilation before a circuit has been mapped to hardware.

Core claim

The central claim is that a machine-learning-predicted PST and wPST can serve as a figure of merit that combines the accuracy of execution-based metrics with the speed of structural metrics. wPST is defined as the thresholded, Hamming-weighted probability of measuring bit strings close to the all-zero reference in a mirror circuit, so it rewards partially correct outcomes. Because wPST is a linear functional of single-qubit marginals, it remains informative as system size grows, where PST collapses to zero; the paper shows the number of shots needed for fixed relative precision is O(1/n) under independent errors, versus exponential in n for PST. Empirically, predicted PST and wPST correlate

What carries the argument

The key object is wPST, defined as the weighted sum over measured bit strings with weight equal to the fraction of zero bits, restricted to strings whose weight exceeds a threshold. At threshold zero it reduces to the average single-qubit marginal; at threshold one it reduces to PST. This linearity in single-qubit marginals is what makes wPST degrade linearly with per-qubit error rate and keeps shot requirements polynomial rather than exponential. The predictive machinery is a feature vector of circuit DAG statistics (qubit count, gate counts, depth, two-qubit gates, program communication, entanglement ratio, parallelism, critical depth, liveliness) combined with per-qubit decoherence failur

Load-bearing premise

The central claim stands only if the machine-learning model, trained on random circuits with uniformly sampled angles and a fixed gate set, transfers to the structured circuits and noise conditions that a real compiler faces, and if the measured PST and wPST values used as ground truth are stable enough to train against.

What would settle it

Take a set of non-transpiled application-level circuits on a fixed device, apply several compilation strategies, and compare the two-step predicted wPST ranking with the measured wPST ordering; if the predicted ranking is no better than a depth- or gate-count-based ranking, the paper's central claim collapses.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Compilers can replace depth- and gate-count-based selection with a fast predicted score that tracks measured execution quality far better, so the circuits they select should run closer to ideal.
  • wPST can be measured accurately with far fewer shots than PST at large qubit counts, making it practical to benchmark and compare larger noisy circuits.
  • The two-step predictor allows figure-of-merit-aware decisions before a circuit is transpiled, opening the way to integrate it into routing and optimization loops.
  • The thresholded wPST has a known depolarizing noise floor, so practitioners can distinguish meaningful signal from a scrambled-noise regime.
  • Because wPST avoids exponential collapse with qubit count, it remains a usable quality metric in a size regime where PST is essentially always zero.

Where Pith is reading between the lines

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

  • The paper stops short of showing that using the predicted metric inside a real compiler improves end-to-end algorithm success; an immediate test is to run two compilation pipelines, one selecting circuits by predicted wPST and one by gate count, and compare measured output quality.
  • The training distribution, based on random circuits with uniformly sampled angles and a fixed gate set, may not cover structured application workloads; if a compiler targets a specific algorithm family, retraining or active learning on that family may be needed.
  • The two-step predictor's first stage, which predicts transpilation overhead, could be reused as a standalone cost model for other compiler heuristics, even outside PST-based selection.
  • Because wPST is linear in single-qubit marginals, it could be combined with cheap marginal-estimation or error-mitigation techniques more readily than PST, though the paper does not develop this.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper studies figures of merit for quantum circuit compilation. It introduces a weighted probability of successful trials (wPST): for a verification circuit formed by appending a circuit and its inverse, wPST averages over measured bit strings the fraction of zeros, with a threshold w_th=0.5 below which no credit is given. The paper shows that for w_th=0, wPST equals the average single-qubit marginal probability of measuring |0>; with a threshold it becomes a sum over Hamming-weight shells. It derives scaling under independent bit-flip noise (PST ~ (1-eps)^n, wPST ~ 1-eps) and a shot-budget analysis showing wPST requires many fewer shots for fixed relative error. The authors train XGBoost models on random circuits, using circuit-DAG features plus hardware coherence-time features, to predict PST and wPST; they evaluate Pearson correlations against true values on a 12-qubit simulator and four IBM devices, with separate MQT benchmark circuits. For transpiled circuits, predicted wPST/PST shows higher correlation than depth, gate count, and two-qubit gate count. Finally, they propose a two-step pipeline intended for non-transpiled circuits: first predict the transpiled feature vector, then predict wPST, and report RMSE on IBM Torino. The paper claims the ML-predicted FoMs outperform standard FoMs by over 50% in correlation and enable improved compilation.

Significance. The analytical core — the marginal formulation of wPST, the bit-flip scaling, and the shot-budget comparison — is clean and, as far as I checked, internally consistent; this is a genuine contribution that goes beyond the usual 'train a regressor' paper. The hardware evaluation across four IBM devices is transparent, uses a public benchmark suite (MQT), and reports per-device correlations. The paper also candidly acknowledges that the two-step process requires further research and that compiler integration is future work. My reservations concern the scope of the empirical claim: the >50% improvement is not uniform across the reported settings, and the two-step component that would make the method useful for compilation is not validated against any baseline. With those gaps addressed, the paper would be a solid contribution.

major comments (4)
  1. [Abstract; Sec. IV A, Tables I-IV] The statement that the predicted FoMs 'increase the correlation with true PST or wPST by over 50%' is not supported for several of the settings reported. In Table I, for random simulator circuits the best structural baseline is # gates (r=0.815) and predicted PST gives 0.945, an improvement of about 16%; in Table II for MQT wPST the improvement is about 27% (0.880 vs 0.695), and for random wPST about 4.5% (0.925 vs 0.885). The >50% figure is robust only for the hardware averages in Tables III-IV (e.g., 0.89 vs 0.53 for wPST) and for simulator MQT PST. Please qualify the claim to the setting in which it holds, align the abstract and conclusion ('nearly 50%'), and report confidence intervals or bootstrap errors for the correlations, since the hardware wPST labels are shot-noise limited.
  2. [Sec. V B, Fig. 10, conclusion] The two-step process is the bridge from the direct predictor (validated on transpiled circuits) to compilation workloads. Its evaluation is incomplete: Fig. 10 reports only RMSE (mean ~0.06 on Torino) and does not provide the Pearson/Spearman correlation of the two-step wPST predictions with true wPST, nor any comparison with circuit depth, gate count, or two-qubit-gate count on the same non-transpiled inputs. Section V B itself states that 'additional research is required into which features to choose and how the quantum compilers will perform using this process,' and the conclusion lists compiler integration as 'a first task for follow-up work.' The abstract's claim that the findings 'enable improvements in quantum circuit compilation' is therefore not established. A concrete test would be to report ranking-quality metrics for the two-step predictor against standard FoMs on a non-trans
  3. [Sec. II A 3; Tables I-IV] The baseline set is limited to naive structural metrics. The paper itself lists hardware-aware alternatives (expected fidelity, ESP, MQT Predictor) in Sec. II A 3. Since the ML predictor uses hardware data, comparing only against depth and gate counts may inflate the reported advantage. Please include at least one such hardware-aware baseline or explicitly restrict the claim to 'simple structural metrics.' This matters for the abstract's 'commonly used FoMs' wording.
  4. [Sec. V A; Figs. 7 and 9] The first-step feature prediction is not validated for ranking. Fig. 9 shows large RMSE for the two-qubit-gate count (for larger n, of the same order as the true counts) and for program communication, while Fig. 7 identifies these as among the most important features for wPST prediction. The paper does not quantify how feature-prediction errors propagate to the final wPST orderings. At minimum, report the correlation between two-step-predicted wPST and true wPST and show whether the predicted ordering is still significantly better than the standard FoMs.
minor comments (4)
  1. [Sec. II B 3, Eq. (16)] The notation is confusing: m_q is defined as the single-qubit marginal for qubit q, but then wPST_{wth=0} is written as m_q (or \bar m_q) to denote the average over q of these marginals. Please introduce a distinct symbol for the average.
  2. [Sec. III A, Eq. (28)] D_crit is described as 'the number of two-qubit interactions that lie along the critical path,' but the formula is a fraction N_ed/N_2. Adjust the description to 'fraction of two-qubit gates lying on the critical path.'
  3. [Sec. III B, Eq. (33)] The fixed value F=1000 for unused qubits is chosen 'according to the maximum depth of the training circuits used.' A brief sensitivity analysis or a sentence on how results depend on this constant would be helpful.
  4. [Conclusion vs Abstract] The abstract states 'over 50%' improvement; the conclusion says 'nearly 50%.' Please make these consistent (this is also related to Major Comment 1).

Circularity Check

0 steps flagged

No significant circularity: wPST definitions, analytical scaling derivations, and held-out ML evaluations are self-contained; the two-step compiler extension is explicitly presented as future work, not as a validated prediction.

full rationale

The paper's central derivation chain is not circular. wPST is defined in Sec. II B 3 (Eqs. 12-18) as a Hamming-weight-graded PST, and the analytical results in Sec. IV C and Appendix G follow from that definition under stated noise models (e.g., PST=(1-eps)^n vs wPST=1-eps, Eqs. G1-G2), with no hidden reuse of the target claim. The ML model is a supervised regressor trained on labels (PST/wPST) computed from simulation or hardware; the claimed correlations in Tables I-IV are evaluated on held-out random and MQT circuits with training/test separation described in Secs. III D and IV B. This is the honest framing of fitting versus prediction, not a fitted parameter being renamed as a prediction. The hardware/coherence features (Eqs. 30-33) and coupling-map encoding are independent inputs. The only self-citation involving a current author is Ref. [25] (A.F. Kockum), cited contextually for benchmarking KPIs in the introduction; it is not load-bearing for wPST, the ML predictor, or the two-step process. The two-step process in Sec. V is explicitly limited: Sec. V B states 'additional research is required into which features to choose and how the quantum compilers will perform using this process,' and the conclusion lists compiler integration as 'a first task for follow-up work.' That is an acknowledged open validation gap, not a circular inference. No equation or parameter in the paper reduces to its own output by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

No new physical entities are postulated. The free parameters w_th, F_unused and unspecified generator/device parameters are the main hand-chosen inputs. The analytical core (wPST linear-in-epsilon, shot budgets) is parameter-free after specifying the noise model; the ML predictor is a supervised fit with a modest set of unstated generator parameters.

free parameters (4)
  • w_th (weight threshold) = 0.5
    Set to 0.5 in all experiments; justified heuristically as 'majority-correct' and asymptotically inactive below the depolarizing floor (Sec. II.B.3, Sec. IV.C.a).
  • F_unused = 1000 for unused qubits = 1000
    Engineering choice chosen 'according to the maximum depth of the training circuits used' (Sec. III.B, Eq. 33). It is a number the model depends on, without a principled derivation.
  • Circuit generation ratio r (single vs two-qubit probability) = not given
    A generator parameter that shapes training distribution; no value specified in the text visible.
  • Gate durations tau_1, tau_2 = not given
    Assumed 'typical' single- and two-qubit gate times (Sec. III.B), values not specified.
axioms (4)
  • domain assumption PST is a proxy for algorithmic execution fidelity
    The whole paper treats PST/wPST as the target 'true' quality because of its correlation with fidelity; the correlation of PST with fidelity is cited to Ref. [45], not re-derived.
  • domain assumption The trained feature set plus XGBoost generalizes from random circuits to structured MQT benchmarks and unseen hardware conditions
    Core to the central claim; supported only by the reported test correlations, not by a generalization bound or error analysis.
  • domain assumption Depolarizing noise model and independent bit-flip model capture the relevant hardware noise for the scaling conclusions
    Sec. IV.C derives scaling under these channels; the paper acknowledges coherent errors and amplitude damping modify behavior.
  • domain assumption Hardware calibration data at training time is representative of hardware during testing
    The hardware feature vector uses T1/T2 and gate times; the model silently assumes stability across calibration drifts.

pith-pipeline@v1.3.0-alltime-deepseek · 29078 in / 6706 out tokens · 55553 ms · 2026-08-02T08:49:36.599083+00:00 · methodology

0 comments
read the original abstract

To make quantum algorithms executable on a particular quantum device, they need to be compiled into circuits that respect constraints of the quantum hardware. This compilation usually involves multiple steps, where many hardware-compatible circuits are generated, and the best circuit is selected. To say which circuit is best, the quality of a circuit is generally quantified by a $\textit{figure of merit}$ (FoM). For FoMs, there is a trade-off between ease of calculation and accuracy in predicted execution quality. Commonly used FoMs, e.g., the number of gates, circuit depth, etc., are easy to evaluate, but do not directly capture the effects of circuit structure and noise. On the other end of the spectrum are FoMs that require full circuit execution and take a prohibitively long time to evaluate. One example is the probability of successful trials (PST), i.e., the probability of obtaining the initial state after running the quantum circuit followed by its inverse. Here, we investigate advantages and disadvantages of different FoMs, and formulate the properties of an ideal FoM. Based on our results, we propose wPST, a weighted version of the PST that accounts for individual qubits, not just the whole state. To quickly predict PST and wPST, we design machine learning models that take into account both the quantum circuit and quantum hardware data. In numerical simulations and experiments on quantum processors, we find that our machine learning-predicted FoMs outperform commonly used FoMs, increasing the correlation with the true PST or wPST by over 50%. To make our model useful for quantum compilers, we devise a two-step process to predict the wPST for non-transpiled quantum circuits: first, we predict the additional quantum gates required for the given quantum circuit, and then we predict the wPST, accounting for coherence times in the quantum device.

Figures

Figures reproduced from arXiv: 2607.03275 by Anton Frisk Kockum, Harshdeep Singh, Marvin Richter, Mats Granath.

Figure 1
Figure 1. Figure 1: Measurement-based FoMs and their variation with noise for two four-qubit circuits. (a) A quantum circuit preparing [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Values of fidelity, PST, distance-based metrics, and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Values of fidelity, PST, distance-based metrics, and [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Workflow of our machine learning-based FoM prediction. The process involves constructing a feature vector from the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Directed acyclic graph (DAG, right) representation [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Workflow of our machine learning-based FoM prediction. The process involves constructing a feature vector from the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Root mean square error (RMSE) between the true [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: Directed acyclic graph (DAG, right) representation [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Importance of different features across different quantum devices in the (a) PST and (b) wPST prediction models. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 6
Figure 6. Figure 6: Root mean square error (RMSE) between the true [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Root mean square error in prediction of (a) the number of two-qubit gates and (b) programme communication (PC) [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Root mean squared error for predicted wPST us [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of different damping rates γ on average wPST of circuits of different depths (lines of different colors) for systems of size (a) four, (b) six, (c) eight, and (d) ten qubits. The simulations were carried out on a ten-qubit simulator based on the IBM Miami device; 20 circuits were used for average results over each depth. The error bars show ±1 standard deviation. We also tried other methods of coupl… view at source ↗
Figure 10
Figure 10. Figure 10: Layouts of the four IBM quantum processors we used for training and testing in this article. The orange nodes mark [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: Root mean square error in prediction of (a) the number of two-qubit gates and (b) programme communication (PC) [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Performance (in terms of RMSE) in wPST pre [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Root mean squared error for predicted wPST us [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Performance of the three coupling-map-encoding methods (different colors). (a) Root mean square error in prediction [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 12
Figure 12. Figure 12: Layouts of the four IBM quantum processors we used for training and testing in this article. The orange nodes mark [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Performance (in terms of RMSE) in wPST pre [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Performance of the three coupling-map-encoding methods (different colors). (a) Root mean square error in prediction [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗

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Reference graph

Works this paper leans on

91 extracted references · 6 linked inside Pith

  1. [1]

    The totalnumber of qubits,n, used in the circuit

  2. [2]

    The totalnumber of quantum gatesin the circuit, Ng =|G|,(21) whereGis the ordered set of all single- and multi- qubit gates in the circuit

  3. [3]

    We call this FoM theweightedprobability of successful trials (wPST)

    Weighted probability of successful trials To overcome these drawbacks of PST, we introduce a variant of PST that takes into account how many ze- ros are measured (down to some limit), rather than just counting the number of all-zero measurement results. We call this FoM theweightedprobability of successful trials (wPST). a. Definition of wPST.Consider an ...

  4. [4]

    Thecircuit depth,D, defined as the longest path of sequential layers that need to be executed in the full quantum circuit, D= max π∈P |π|,(22) wherePis the set of all gate paths when gates acting on disjoint qubits are parallelized

  5. [5]

    Thenumber of two-qubit (entangling) gates,N 2

  6. [6]

    The totalnumber of edges, Nedges =|E|.(23)

  7. [7]

    The length of thelongest pathin the DAG, Lmax = max π∈P (|π|−1),(24) whereπis a directed path inG

  8. [8]

    Let⟨k⟩denote the aver- age degree of the DAG

    Theprogram communicationfeature,C prog, de- fined as a normalized measure of qubit interactions within a quantum circuit. Let⟨k⟩denote the aver- age degree of the DAG. We normalize this quantity by the average degree of a complete graph with the same number of qubits, nodes, and edges, which is given by⟨k complete⟩=n−1. The program commu- nication feature...

  9. [9]

    Quantum circuit Feature vector Hardware data Figure of merit prediction Figure 4

    Theentanglement ratio, defined as the fraction of two-qubit gates in the circuit: Rent = N2 Ng .(26) 9 q0 H Ry(π/4) Rz(π/6) q1 X H q2 X Rx(π/3) q3 H Rz(π/5) Z Ry(π/7) # qubits, # gates, program entanglement communication, ratio, . . . Quantum circuit Feature vector Hardware data Figure of merit prediction Figure 4. Workflow of our machine learning-based F...

  10. [10]

    Thecircuit parallelism, which quantifies how effi- ciently gates are scheduled across available qubits: P= max ( 0, Ng D −1 n−1 ) .(27) This normalized measure lies in[0,1]; higher values indicate greater simultaneous gate execution

  11. [11]

    The critical path is defined as the longest sequence of operations that must be executed sequentially due to qubit dependencies

    Thecritical depth,D crit, of a quantum program, which quantifies the number of two-qubit interac- tions that lie along thecritical pathof the circuit. The critical path is defined as the longest sequence of operations that must be executed sequentially due to qubit dependencies. Formally, Dcrit = Ned N2 (28) whereN ed is the number of two-qubit gates alon...

  12. [12]

    sweet spot

    Theliveliness,L, of a quantum circuit, which char- acterizes how well a program utilizes its qubits throughout its execution. During the execution of a quantum circuit, the qubits can either beac- tive(currently involved in gate operations) oridle (waiting for the next operation). In ideal settings, the idle qubits can preserve their quantum state, but on...

    2022

  13. [13]

    The adjacency matrixA∈R n×n then encodes the connectivity between all qubits in a compact form

    Adjacency matrix LetG= (V,E)be a graph representing the connectiv- ity of a quantum device, whereVis the set ofnqubits (|V|=n) andEis the set of allowed two-qubit interac- tions. The adjacency matrixA∈R n×n then encodes the connectivity between all qubits in a compact form. It is defined as Aij = { 1,if qubitsiandjare connected 0,otherwise. (E1) Herei,j∈{...

  14. [14]

    Graph features The following features from the coupling graphGwere used as a feature vector:

  15. [15]

    Number of edges: f1 =|E|(E3) This is the total number of connections in the cou- pling map, reflecting the connectivity of the hard- ware

  16. [16]

    This measures the av- erage number of connections per qubit

    Mean degree: f2 = 1 n ∑ v∈V deg(v),(E4) wheredeg(v)is the total degree (sum of in-degree and out-degree) of nodev. This measures the av- erage number of connections per qubit

  17. [17]

    Maximum degree: f3 = max v∈V deg(v).(E5) This comes from the most connected qubit in the device, capturing potential bottlenecks or hubs in the connectivity

  18. [18]

    This feature captures the overall directed connectivity of the device

    Number of strongly connected components (f 4): A strongly connected component is a maximal sub- set of qubitsC⊆Vsuch that for every pair u,v∈C, there is a directed path fromutov. This feature captures the overall directed connectivity of the device

  19. [19]

    (E6) Here,UGis the undirected version ofG, and the diameter is defined as diameter(UG) = max u,v∈V d(u,v),(E7) whered(u,v)is the shortest path length between the nodesuandv

    Graph diameter: f5 = { diameter(UG),ifUGis connected −1,otherwise. (E6) Here,UGis the undirected version ofG, and the diameter is defined as diameter(UG) = max u,v∈V d(u,v),(E7) whered(u,v)is the shortest path length between the nodesuandv. If the graph is disconnected, the diameter is set to−1

  20. [20]

    (E8) This feature captures the typical distance between qubits in the hardware and reflects how efficiently two-qubit gates can be implemented across the de- vice

    Average shortest path length: f6 = { 1 |V|(|V|−1) ∑ u̸=vd(u,v),ifUGis connected −1,otherwise. (E8) This feature captures the typical distance between qubits in the hardware and reflects how efficiently two-qubit gates can be implemented across the de- vice

  21. [21]

    14((a)) and Fig

    Comparison of performance In Fig. 14((a)) and Fig. 14((b)), we plot the RMSE for the three different coupling-map-encoding methods in the prediction of two-qubit gate counts and program commu- nication. These two features are the most important to get right for the wPST prediction in the next step to be accurate (cf. Fig. 7). We see that all three methods...

  22. [22]

    (G1) For wPST we use the marginal representation in Eq

    Exact values Since PST is the probability of the single all-zero out- come, we can factorize the joint distribution for indepen- dent noise: PST = Pr [⋀n q=1xq = 0 ] = n∏ q=1 Pr[xq = 0] = (1−ϵ) n. (G1) For wPST we use the marginal representation in Eq. (16) and set the single-qubit marginal asm q = Pr[xq = 0] = 1−ϵindependently ofq, yielding wPSTwth=0 = 1...

    arXiv

  23. [23]

    Effect of the threshold In practice, we usew th = 0.5and remove the shells withk <k th =⌈n/2⌉from the sum in Eq. (G4) above: wPSTwth=0.5 = (1−ϵ)− 1 n kth−1∑ k=0 kQ(k).(G5) The correction term is bounded by the probability of the discarded shells,Pr[k <n/2], which forϵ<1/2is expo- nentially small innby the Chernoff bound: Pr [ k< n 2 ] ≤exp [ −nD (1 2 1−...

  24. [24]

    LetNbe the number of shots for a quantum circuit execution

    Shot budget This section discusses an operational reason to prefer wPST over the standard PST, which is the precision with the shot budget. LetNbe the number of shots for a quantum circuit execution. a. PST The PST estimator can be written as ˆPST =n 0n/N(G7) and follows a binomial distribution with success proba- bilityp= PST. The variance of the estimat...

  25. [25]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information(Cambridge University Press, 2000)

    2000

  26. [26]

    A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.-F. Chen, A. Gily´ en, C. T. Hann, M. J. Kastoryano, E. T. Khabiboulline, A. Kubica, G. Salton, S. Wang, and F. G. S. L. Brand˜ ao,Quantum Algorithms(Cambridge Univer- sity Press, 2025)

    2025

  27. [27]

    B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, Towards quantum chemistry on a quan- tum computer, Nature Chemistry2, 106 (2010)

    2010

  28. [28]

    Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. John- son, M. Kieferov´ a, I. D. Kivlichan, T. Menke, B. Per- opadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru- Guzik, Quantum Chemistry in the Age of Quantum Com- puting, Chemical Reviews119, 10856 (2019)

    2019

  29. [29]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Re- views of Modern Physics92, 015003 (2020)

    2020

  30. [30]

    Wiebe, D

    N. Wiebe, D. W. Berry, P. Høyer, and B. C. Sanders, Simulating quantum dynamics on a quantum computer, Journal of Physics A: Mathematical and Theoretical44, 445308 (2011)

    2011

  31. [31]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum sim- ulation, Reviews of Modern Physics86, 153 (2014)

    2014

  32. [32]

    Bauer, S

    B. Bauer, S. Bravyi, M. Motta, and G. Kin-Lic Chan, 24 Quantum Algorithms for Quantum Chemistry and Quan- tum Materials Science, Chemical Reviews120, 12685 (2020)

    2020

  33. [33]

    Pyrkov, A

    A. Pyrkov, A. Aliper, D. Bezrukov, Y.-C. Lin, D. Polykovskiy, P. Kamya, F. Ren, and A. Zhavoronkov, Quantum computing for near-term applications in gener- ative chemistry and drug discovery, Drug Discovery To- day28, 103675 (2023)

    2023

  34. [34]

    Y. Cao, J. Romero, and A. Aspuru-Guzik, Potential of quantum computing for drug discovery, IBM Journal of Research and Development62, 6:1 (2018)

    2018

  35. [35]

    N. S. Blunt, J. Camps, O. Crawford, R. Izs´ ak, S. Leon- tica, A. Mirani, A. E. Moylett, S. A. Scivier, C. S ¨un- derhauf, P. Schopf, J. M. Taylor, and N. Holzmann, Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications, Journal of Chemical Theory and Computation18, 7001 (2022)

    2022

  36. [36]

    L. S. Madsenet al., Quantum computational advantage with a programmable photonic processor, Nature606, 75 (2022)

    2022

  37. [37]

    Bluvsteinet al., Logical quantum processor based on reconfigurable atom arrays, Nature626, 58 (2024)

    D. Bluvsteinet al., Logical quantum processor based on reconfigurable atom arrays, Nature626, 58 (2024)

    2024

  38. [38]

    Acharyaet al., Quantum error correction below the surface code threshold, Nature638, 920 (2025)

    R. Acharyaet al., Quantum error correction below the surface code threshold, Nature638, 920 (2025)

    2025

  39. [39]

    Ransfordet al., A 98-qubit trapped-ion quantum com- puter with all-to-all connectivity, Nature 10.1038/s41586- 026-10676-4 (2026)

    A. Ransfordet al., A 98-qubit trapped-ion quantum com- puter with all-to-all connectivity, Nature 10.1038/s41586- 026-10676-4 (2026)

    doi:10.1038/s41586- 2026

  40. [40]

    Yin, Z.-R

    J.-W. Yin, Z.-R. Chen, S. Peng, H.-C. Luo, C.-N. Tao, S.- W. Tan, and L.-Q. Lu, A Review of Quantum Computing Systems and Software, Journal of Computer Science and Technology41, 147 (2026)

    2026

  41. [41]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    2018

  42. [42]

    G. Yan, W. Wu, Y. Chen, K. Pan, X. Lu, Z. Zhou, Y. Wang, R. Wang, and J. Yan, Quantum Circuit Syn- thesis and Compilation Optimization: Overview and Prospects (2025), arXiv:2407.00736

    arXiv 2025

  43. [43]

    Maronese, L

    M. Maronese, L. Moro, L. Rocutto, and E. Prati, ” Quan- tum Compiling” , inQuantum Computing Environments, edited by S. S. Iyengar, M. Mastriani, and K. L. Kumar (Springer International Publishing, Cham, 2022) pp. 39– 74

    2022

  44. [44]

    Cowtan, S

    A. Cowtan, S. Dilkes, R. Duncan, A. Krajenbrink, W. Simmons, and S. Sivarajah, On the qubit routing problem, in14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019), Vol. 135, edited by W. van Dam and L. Mancin- ska (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik,

    2019

  45. [45]

    Botea, A

    A. Botea, A. Kishimoto, and R. Marinescu, On the Com- plexity of Quantum Circuit Compilation, Proceedings of the International Symposium on Combinatorial Search9, 138 (2021)

    2021

  46. [46]

    Mohammadi and M

    M. Mohammadi and M. Eshghi, On figures of merit in reversible and quantum logic designs, Quantum Informa- tion Processing8, 297 (2009)

    2009

  47. [47]

    P. Hopf, N. Quetschlich, L. Schulz, and R. Wille, Improv- ing Figures of Merit for Quantum Circuit Compilation, in 2025 Design, Automation & Test in Europe Conference (DATE)(2025) pp. 1–7

    2025

  48. [48]

    Proctor, K

    T. Proctor, K. Young, A. D. Baczewski, and R. Blume- Kohout, Benchmarking quantum computers, Nature Re- views Physics7, 105 (2025)

    2025

  49. [49]

    Zimbor´ as, A

    Z. Zimbor´ as, A. Portik, D. Aguirre, R. Pe˜ na, D. Svastits, A. P´ alyi,´Aron M´ arton, J. K. Asb´ oth, A. F. Kockum, M. Sanz, O. K´ alm´ an, T. Monz, and F. Wilhelm-Mauch, The EU Quantum Flagship’s Key Performance Indicators for Quantum Computing (2025), arXiv:2512.19653

    arXiv 2025

  50. [50]

    Kurniawan, L

    H. Kurniawan, L. Rodr ´ ıguez-Soriano, D. Cuomo, C. G. Almudever, and F. G. Herrero, On the use of calibration data in error-aware compilation techniques for NISQ de- vices (2024), arXiv:2407.21462

    Pith/arXiv arXiv 2024

  51. [51]

    Dangwal, G

    S. Dangwal, G. S. Ravi, L. M. Seifert, P. Das, J. Sud, and F. T. Chong, COMPASS: Compiler Pass Selection For Improving Fidelity Of NISQ Applications (2025), arXiv:2306.15020

    Pith/arXiv arXiv 2025

  52. [52]

    S. S. Tannu and M. K. Qureshi, Not All Qubits Are Created Equal: A Case for Variability-Aware Policies for NISQ-Era Quantum Computers, inProceedings of the Twenty-Fourth International Conference on Architec- tural Support for Programming Languages and Operating Systems, ASPLOS ’19 (Association for Computing Ma- chinery, New York, NY, USA, 2019) p. 987–999

    2019

  53. [53]

    G. M. D’Ariano, L. Maccone, and M. Paini, Spin tomog- raphy, Journal of Optics B: Quantum and Semiclassical Optics5, 77 (2003)

    2003

  54. [54]

    Watrous, Limits on the power of quantum statistical zero-knowledge, inThe 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002

    J. Watrous, Limits on the power of quantum statistical zero-knowledge, inThe 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. (2002) pp. 459–468

    2002

  55. [55]

    Aamlof and G

    J. Aamlof and G. Bjork, Fidelity as a figure of merit in quantum error correction, Quantum Information and Computation13, 9 (2013)

    2013

  56. [56]

    M. Bina, A. Mandarino, S. Olivares, and M. G. A. Paris, Drawbacks of the use of fidelity to assess quantum re- sources, Physical Review A89, 012305 (2014)

    2014

  57. [57]

    H. Zou, M. Treinish, K. Hartman, A. Ivrii, and J. Lishman, LightSABRE: A Lightweight and Enhanced SABRE Algorithm (2024), arXiv:2409.08368

    Pith/arXiv arXiv 2024

  58. [58]

    Kharkov, A

    Y. Kharkov, A. Ivanova, E. Mikhantiev, and A. Kotel- nikov, Arline Benchmarks: Automated Bench- marking Platform for Quantum Compilers (2022), arXiv:2202.14025

    Pith/arXiv arXiv 2022

  59. [59]

    M. Salm, J. Barzen, F. Leymann, B. Weder, and K. Wild, Automating the Comparison of Quantum Compilers for Quantum Circuits, inService-Oriented Computing (Springer International Publishing, 2021) pp. 64–80

    2021

  60. [60]

    Quetschlich, L

    N. Quetschlich, L. Burgholzer, and R. Wille, MQT Pre- dictor: Automatic Device Selection with Device-Specific Circuit Compilation for Quantum Computing, ACM Transactions on Quantum Computing6, 10 (2025)

    2025

  61. [61]

    Vadali, R

    A. Vadali, R. Kshirsagar, P. Shyamsundar, and G. N. Perdue, Quantum circuit fidelity estimation using ma- chine learning, Quantum Machine Intelligence6, 1 (2023)

    2023

  62. [62]

    Murali, D

    P. Murali, D. C. Mckay, M. Martonosi, and A. Javadi- Abhari, Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum Computers, inProceedings of the Twenty-Fifth International Conference on Archi- tectural Support for Programming Languages and Oper- ating Systems, ASPLOS ’20 (Association for Computing Machinery, New York, NY, USA, 2020) p. 1001–1016

    2020

  63. [63]

    Schmid, D

    L. Schmid, D. F. Locher, M. Rispler, S. Blatt, J. Zeiher, M. M¨uller, and R. Wille, Computational capabilities and compiler development for neutral atom quantum proces- sors—connecting tool developers and hardware experts, Quantum Science and Technology9, 033001 (2024)

    2024

  64. [64]

    Bandic, C

    M. Bandic, C. G. Almudever, and S. Feld, Interaction 25 graph-based characterization of quantum benchmarks for improving quantum circuit mapping techniques, Quan- tum Machine Intelligence5, 40 (2023)

    2023

  65. [65]

    Venturelli, M

    D. Venturelli, M. B. Do, B. O’Gorman, J. D. Frank, E. G. Rieffel, K. E. C. Booth, T. Nguyen, P. Narayan, and S. Nanda, Quantum Circuit Compilation : An Emerg- ing Application for Automated Reasoning, inProceedings of the Scheduling and Planning Applications Workshop (SPARK)(2019)

    2019

  66. [66]

    K. Fang, M. Zhang, R. Shi, and Y. Li, Dynamic Quantum Circuit Compilation, IEEE Transactions on Computers 75, 748 (2026)

    2026

  67. [67]

    Mills, S

    D. Mills, S. Sivarajah, T. L. Scholten, and R. Duncan, Application-Motivated, Holistic Benchmarking of a Full Quantum Computing Stack, Quantum5, 415 (2021)

    2021

  68. [68]

    Qiskit, Depolarizing Error (2025)

    2025

  69. [69]

    H. Wang, Z. Liang, J. Gu, Z. Li, Y. Ding, W. Jiang, Y. Shi, D. Z. Pan, F. T. Chong, and S. Han, TorchQuan- tum Case Study for Robust Quantum Circuits (Invited Paper), in2022 IEEE/ACM International Conference On Computer Aided Design (ICCAD)(2022) pp. 1–9

    2022

  70. [70]

    Proctor, S

    T. Proctor, S. Seritan, K. Rudinger, E. Nielsen, R. Blume-Kohout, and K. Young, Scalable Randomized Benchmarking of Quantum Computers Using Mirror Cir- cuits, Physical Review Letters129, 150502 (2022)

    2022

  71. [71]

    Peres, Stability of quantum motion in chaotic and reg- ular systems, Physical Review A30, 1610 (1984)

    A. Peres, Stability of quantum motion in chaotic and reg- ular systems, Physical Review A30, 1610 (1984)

    1984

  72. [72]

    R. A. Jalabert and H. M. Pastawski, Environment- Independent Decoherence Rate in Classically Chaotic Systems, Physical Review Letters86, 2490 (2001)

    2001

  73. [73]

    Katsuda, K

    M. Katsuda, K. Mitarai, and K. Fujii, Simulation and performance analysis of quantum error correction with a rotated surface code under a realistic noise model, Phys- ical Review Research6, 013024 (2024)

    2024

  74. [74]

    Breiman, J

    L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone,Classification And Regression Trees(Routledge, 2017)

    2017

  75. [75]

    Breiman, Random Forests, Machine Learning45, 5 (2001)

    L. Breiman, Random Forests, Machine Learning45, 5 (2001)

    2001

  76. [76]

    Breiman, Bagging predictors, Machine Learning24, 123 (1996)

    L. Breiman, Bagging predictors, Machine Learning24, 123 (1996)

    1996

  77. [77]

    Chen and C

    T. Chen and C. Guestrin, XGBoost: A Scalable Tree Boosting System, inProceedings of the 22nd ACM SIGKDD International Conference on Knowledge Dis- covery and Data Mining, KDD ’16 (Association for Computing Machinery, New York, NY, USA, 2016) p. 785–794

    2016

  78. [78]

    A. V. Dorogush, V. Ershov, and A. Gulin, CatBoost: gra- dient boosting with categorical features support (2018), arXiv:1810.11363

    Pith/arXiv arXiv 2018

  79. [79]

    RandomizedSearchCV — scikit-learn.org,https: //scikit-learn.org/stable/modules/generated/ sklearn.model_selection.randomizedsearchCV.html, [Accessed 27-04-2026]

    2026

  80. [80]

    Pedregosa, G

    F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cour- napeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research12, 2825 (2011)

    2011

Showing first 80 references.