A Time Optimization Framework for the Implementation of Robust and Low-latency Quantum Circuits

Eduardo Inacio Duzzioni; Eduardo Willwock Lussi; Rafael de Santiago

REVIEW 3 major objections 5 minor 49 references

A Time Optimization Framework for the Implementation of Robust and Low-latency Quantum Circuits

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims a critical-path pulse scheduler can mix fast and more faithful gates in one circuit with no latency cost, improving absolute success probability by over 25% on tested hardware.

desk verdict A modest but real scheduling idea—using CPM slack to swap in longer, more robust pulses—supported by conditional hardware results that need error bars and a clearer statement of when longer pulses actually help. read the letter →

arxiv 2412.18533 v1 pith:V7RYQQP7 submitted 2024-12-24 quant-ph cs.SYeess.SY

Eduardo Willwock Lussi , Rafael de Santiago , Eduardo Inacio Duzzioni This is my paper · ORCID

classification quant-phcs.SYeess.SY PACS 03.67.Lx

keywords quantumcircuitcompilationpulse-levelschedulingcriticalpathmethoderrorsuppressionrandomizedbenchmarkingidleperiodscontrollow-latencycircuits

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that a quantum circuit does not have to choose between fast gates and robust gates: both can be used together at no extra latency. The framework models the circuit as a dependency graph, identifies the critical path that determines total execution time, and schedules the fastest pulses only on that path. Idle periods outside the path are filled with longer, more faithful implementations of the same logical operations, using a project-management scheduling rule. Randomized benchmarking on a 127-qubit superconducting processor shows absolute success-probability gains above 25%, with larger gains as the number of qubits grows.

What carries the argument

The machinery is the Quantum Operation Dependency Graph combined with the Critical Path Method (CPM). Each gate is a node with a duration; each dependency is an edge; a forward pass computes the earliest start and finish times and a backward pass computes the latest start and finish times. The algorithm then applies an 'as long as possible' policy: a gate not on the critical path is lengthened to the next allowed duration whenever its earliest start plus the new duration still fits before its latest finish, with gates prioritized by rotation angle divided by duration. This converts otherwise wasted idle time into longer, more faithful pulses without moving the overall completion time.

What would settle it

Measure the fidelity of each allowed pulse duration in the static gate set on a given device: if a 512 dt Gaussian pulse is not more faithful than a 32 dt pulse of the same rotation, the time-optimized schedule should show no gain over the fastest fixed schedule. A direct test is to run the paper's randomized-benchmarking comparison side by side with such per-duration fidelity measurements and check that the durations the scheduler chooses are exactly the higher-fidelity ones.

Watch

Extended reading notes

Core claim

The central claim is that robustness and speed can be mixed at the pulse level rather than traded off globally. Given a gate set with several calibrated implementations of the same operation at different durations, the algorithm computes early and late start/finish times for every gate in the circuit, marks the critical path, and extends every non-critical gate to the longest duration that still finishes before its deadline. The ordering in which gates are extended uses the rotation-per-unit-duration ratio so that different rotation angles get fair access to slack. The result is a schedule with exactly the same latency as the fastest possible schedule, but with most gates carried out by longer pulses that are expected to be more faithful. The experiments support this by showing consistent gains in randomized benchmarking, with the strongest gains in larger circuits where idle time is more abundant.

Load-bearing premise

The framework's measured gains rest on the premise that, within the allowed duration set, a longer pulse implementing the same rotation is more faithful than a shorter one; the paper's own dynamic experiments show this premise can fail when longer pulses are not fine-tuned.

Editorial extensions

If this is right

A compiler can produce a minimum-latency schedule in which most gates are actually the slower, higher-fidelity versions, so robust pulse-generation techniques no longer need to be fast to be usable.
The benefit should scale with qubit count, because larger circuits create more idle periods and leave a smaller fraction of gates on the critical path.
Calibration practice could shift from calibrating a single waveform per operation to calibrating a small family of implementations with different durations and robustness profiles.
The polynomial running time makes the gate-duration selection feasible as a compile-time optimization, not just a post-processing step.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct implication the paper does not pursue is that the real objective should be per-duration fidelity: if a backend's longer pulses are not more faithful than its short ones, the scheduler has nothing to gain and may simply run the same errors for longer.
The same critical-path machinery could be extended to choose among pulse shapes and error-suppression techniques rather than durations alone, using measured fidelity of each candidate implementation.
On large devices, filling every idle period with longer gates may crowd out dynamical decoupling sequences, so a practical compiler would need to decide how much slack to reserve for decoupling.
The reported gains use only Gaussian pulses; optimization-based robust waveforms with longer durations should make the framework's advantage larger, since the paper only tested a moderate robustness gap.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague, here's my read of arXiv:2412.18533.

The genuinely new piece is small but real: taking the Critical Path Method slack from a circuit dependency graph and using that slack to pick longer, more robust pulse implementations for off-critical gates, while keeping fast gates on the critical path. That specific combination—using CPM slack to choose among multiple pulse-duration implementations of the same gate—is not in the cited graph-scheduling work [24,26,27]. The algorithm is clearly specified and runs in polynomial time; the static experiments on Brisbane show the intended effect, with the 3-qubit circuits showing the largest gains. The authors also deserve credit for acknowledging in Sec. VI.B that longer dynamic pulses are not automatically more faithful, which partially anticipates the main concern.

The soft spots are real but not disqualifying. First, the headline ">25% improvement" is not a general property. It appears in selected static 3-qubit configurations. The paper reports no error bars, no per-configuration variance, and no statistical test, so we can't tell which differences are stable. Second, the framework's benefit depends on the premise that each allowed longer duration is actually higher fidelity than the fast baseline. Algorithm 2 extends a gate whenever slack permits (g.ES + d <= g.LF), with no fidelity check. The dynamic results (Fig. 5) show exactly the failure mode: non-fine-tuned longer Gaussian pulses are not consistently better, and the time-optimized 48 and 64 dt cases show only slight gains. So the improvement is conditional on the gate set being calibrated such that longer equals better. That should be stated as a limitation, not a universal claim. Third, the experiments stop at 3 qubits; the scaling argument is extrapolation. On the citation side, the prior work is adequately cited; self-citations are fine.

Overall, this is a modest, honest engineering contribution. It is not a physics breakthrough, and the authors do not oversell it that way. With code and data plus confidence intervals, the empirical claim would be much stronger. The scheduling idea is worth engaging.

I'd send it to peer review. It is clearly specified and the experiments, while limited, support a conditional version of the claim. The authors should be pushed to release code and data and to be precise about which configurations actually improve by more than 25%.

Referee Report

3 major / 5 minor

Summary. The paper proposes a compile-time pulse scheduling framework that models a quantum circuit as a quantum operation dependency graph and applies the Critical Path Method (CPM) to identify the critical path. The scheduler keeps fast pulses on the critical path and extends the duration of non-critical gates to the longest allowed implementation that fits in the available slack, thereby claiming to improve gate robustness without increasing circuit latency. The framework is validated with randomized benchmarking experiments on IBMQ Brisbane using both static fine-tuned Gaussian pulses (durations 32-512 dt) and dynamic interpolated Gaussian pulses (durations up to 128 dt for pi/2 rotations). The authors report improvements in absolute success probability exceeding 25% in some 3-qubit static cases and argue that the benefits grow with circuit width.

Significance. If the reported improvements are robust, the framework is a simple and practical compiler-level technique for pulse scheduling, allowing a trade-off between fast noisy gates and longer robust gates without latency penalty. The paper's strengths are a clearly specified polynomial-time algorithm (Algorithms 1-2), real-hardware randomized benchmarking, and an explicit acknowledgment that longer pulses are not always more faithful in the dynamic approach. However, the evidence is preliminary and conditional: only 2- and 3-qubit circuits are tested, no error bars or significance tests are provided, and the central mechanism—that longer pulses have higher fidelity in the tested duration range—is not directly measured and is contradicted by the paper's own dynamic results in some regimes. If the mechanism is verified and the statistics strengthened, the work would be a useful contribution to pulse-level compilation.

major comments (3)

[Sec. VI.B, Fig. 5 and Algorithm 2] The dynamic experiments show that longer, non-fine-tuned Gaussian pulses are not consistently more faithful than shorter ones; indeed, the paper states that 'longer quantum gates do not necessarily have higher fidelity because they are not fine-tuned.' Algorithm 2 (line 34) extends a gate whenever g.ES + d <= g.LF, with no fidelity-based selection. If the next allowed duration for a gate has lower fidelity, the scheduler will still select it and can degrade overall performance. The reported >25% improvement is therefore not a property of the CPM scheduling method alone but of a gate set whose durations were fine-tuned so that longer pulses are better. To support the framework's generality, the authors should either (a) measure and report the fidelity of every allowed duration for the gates used, (b) make the scheduler fidelity-aware by optimizing an estimated success probability, or (c) explicitly state and verify the monotonicity assumption as a precondition for applying the framework.
[Sec. VI, Figs. 3 and 5] All results are means of 10 RB circuits with no error bars, confidence intervals, or significance tests. The headline 'more than 25%' improvement appears only in selected 3-qubit cases, and without statistical support the difference could be within shot noise or calibration drift. The authors should report standard deviations or standard errors, the number of shots per circuit, and ideally repeat the experiments on multiple days or backends.
[Abstract and Sec. VI.C] The claim that 'performance gains scale as the number of qubits increases' is extrapolated from circuits with at most 3 qubits. While idle periods do tend to increase with qubit count, larger circuits also introduce more multi-qubit gate errors, crosstalk, and routing overhead. This claim should be tempered or supported by experiments on circuits with, say, 5-10 qubits.

minor comments (5)

[Abstract and Sec. V] The text says the framework 'optimally' implements longer gates, but Algorithm 2 is a greedy heuristic with priority by rotation/duration ratio and no optimality proof. Suggest using 'heuristically' or adding an optimality analysis.
[References] References [17] and [33] appear to be the same work (Carvalho et al., Phys. Rev. Applied 15, 064054 (2021)), as do [18] and [34] (Baum et al., PRX Quantum 2, 040324 (2021)). These duplicates should be merged.
[Eq. (9)] The empirical formula for sigma(d) contains fitted constants (68.51, 17.19, 1/5) with no fitting data or validation range. Provide the data points used or a reference to justify this heuristic.
[Fig. 7 caption] The caption says results are 'averaged over subsequence durations with similar frequency values,' but the meaning of 'subsequence durations' is unclear. Please clarify how the averaging was performed.
[Sec. VI experimental setup] The 2-qubit circuits use Clifford lengths 1, 41, 81, 121, 161 while the 3-qubit circuits use 1, 3, 5, 7. The difference makes cross-comparison of scaling trends difficult; please explain why these lengths were chosen.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the scheduler is a heuristic whose claimed gains are measured against fixed-duration baselines, not derived from fitted parameters.

full rationale

The framework's core operation is a greedy CPM-based scheduler (Algorithm 2) that extends each gate's duration to the next allowed value from the gate set only when the extension fits within the gate's late-finish slack (g.ES + d <= g.LF). This is a constructive scheduling rule, not a fit to the success-probability data. The empirical claim of more than 25% absolute success probability improvement is obtained by running randomized benchmarking on IBMQ Brisbane and comparing time-optimized circuits to fixed-duration circuits of 32, 64, and 120 dt (Section VI.A, Figure 3), i.e., a measured benchmark rather than a prediction from a fitted model. The only fitted or heuristic constants are the Gaussian standard-deviation formula sigma(d) (Eq. 9) and the chosen duration ranges and limits, which are calibration choices used to build the gate set S; they do not determine the reported P(0) values. The paper also openly reports dynamic-pulse experiments where longer, non-fine-tuned pulses are not consistently higher fidelity (Section VI.B, Figure 5), which is evidence that the framework's benefit is recognized as conditional rather than an artifact of assuming the conclusion. The self-citations ([32], [36]) are contextual and not load-bearing for the central scheduling claim. No equation in the paper is defined in terms of the quantity it is used to predict, so no step reduces to its own input.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper adds no new physics or entities. It is a scheduling heuristic whose central claim is empirical. The main assumptions are standard circuit-DAG modeling and the availability of multiple pulse implementations per gate. The listed free parameters are calibration choices, not quantities fitted to force the reported success probabilities.

free parameters (3)

sigma(d) heuristic constants = 68.51, 17.19, 0.2, 17.36
Equation 9 maps gate duration d to Gaussian standard deviation sigma. The constants were chosen empirically to avoid amplitude peaks for short pulses and to approach 20% of d for long pulses. This affects per-gate fidelity but is not the scheduling claim.
maximum duration limits = 512 dt (static), 128 dt (dynamic for pi/2)
The authors set these bounds because of IBM sample-count limits and diminishing returns. They shape the available gate set but not the algorithm's correctness.
candidate duration set = {32, 48, 64, 120, 256, 512} dt (static); {32, 48, 64, multiples of 8 up to 128} dt (dynamic)
These discrete pulse lengths were calibrated for the experiments. The particular set affects the magnitude of the reported gains.

assumptions (3)

domain assumption A quantum circuit is a DAG of gate dependencies with known durations.
Section V constructs the quantum operation dependency graph; standard for compilation, but it abstracts away pulse-level interactions between gates on different qubits.
domain assumption The gate set S contains multiple implementations of the same unitary operation with different durations.
Algorithm 2 iterates over 'next duration' for each gate; this requires the existence of logically equivalent pulses at various lengths, which the paper calibrates manually for the experiments.
standard math CPM forward and backward passes correctly compute earliest and latest start and finish times.
Section IV relies on textbook CPM; this is standard scheduling theory and not in dispute.

how reviews work

0 comments

Cite this review

Pith. "Pith review of A Time Optimization Framework for the Implementation of Robust and Low-latency Quantum Circuits." pith.science (2026). https://pith.science/paper/V7RYQQP7

@misc{pith2026241218533,
  author       = {Pith},
  title        = {Pith review of: A Time Optimization Framework for the Implementation of Robust and Low-latency Quantum Circuits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V7RYQQP7}},
  note         = {Machine review of arXiv:2412.18533}
}

read the original abstract

Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware remains challenging. Incoherent errors caused by decoherence restrict the total computation time, making it very short. While hardware advancements continue to progress, quantum software specialists seek to minimize quantum circuit latency to mitigate dissipation. However, at the pulse level, fast quantum gates often lead to leakage, leaving minimal room for further optimization. Recent advancements have shown the effectiveness of quantum control techniques in generating quantum gates robust to coherent error sources. Nevertheless, these techniques come with a trade-off -- extended gate durations. In this paper, we introduce an alternative pulse scheduling approach that enables the use of both fast and robust quantum gates within the same quantum circuit. The time-optimization framework models the quantum circuit as a dependency graph, implements the fastest quantum gates on the critical path, and uses idle periods outside the critical path to optimally implement longer, more robust gates from the gate set, without increasing latency. Experiments conducted on IBMQ Brisbane show that this approach improves the absolute success probability of quantum circuit execution by more than 25%, with performance gains scaling as the number of qubits increases.

Figures

Figures reproduced from arXiv: 2412.18533 by the authors.

**Figure 2.** The CPM algorithm is executed to define the ES, EF, LS, and LF times for each quantum gate. The gate duration considered by the CPM algorithm is the shortest control pulse calibrated for the operation. The time-optimization algorithm is then executed as presented in Algorithm 2. This algorithm attempts to extend each gate duration based on the CPM, as long as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 2.** FIG. 2. Example of a quantum operation dependency graph [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

Figures from the paper (5 more)

**Figure 3.** Figure 3: FIG. 3. Randomized benchmarking results for static fine [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]

**Figure 4.** Figure 4: FIG. 4. Randomized benchmarking results for static fine [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 6.** Figure 6: FIG. 6. Randomized benchmarking results for dynamic quan [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 5.** Figure 5: FIG. 5. Randomized benchmarking results for dynamic quan [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 7.** Figure 7: FIG. 7. Pulse duration distribution from the time [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 35 canonical work pages

[1]

as soon as possible

“as soon as possible” applies the operation and idle

work page
[2]

as late as possible

“as late as possible” delays applying the operation until the last possible moment. Alternatively, we follow an “as long as possible” policy, where idle periods are used to apply longer and more robust quantum gates. Algorithm 1 presents the overall framework. Given that nq is the number of qubits, ng is the number of gates (which corresponds to the numbe...

work page 2022
[3]

Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp

P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp. 124–134

1994
[4]

Deutsch and R

D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 439, 553 (1992)

1992
[5]

L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the Twenty-Eighth An- nual ACM Symposium on Theory of Computing , STOC ’96 (Association for Computing Machinery, New York, NY, USA, 1996) p. 212–219

1996
[6]

Knill, R

E. Knill, R. Laflamme, R. Martinez, and C.-H. Tseng, An algorithmic benchmark for quantum information process- ing, Nature 404, 368 (2000)

work page 2000
[7]

Bernstein and U

E. Bernstein and U. Vazirani, Quantum complexity the- ory, SIAM Journal on Computing 26, 1411 (1997), https://doi.org/10.1137/S0097539796300921. 11

doi:10.1137/s0097539796300921 1997
[8]

I. L. Chuang, N. Gershenfeld, and M. Kubinec, Experi- mental implementation of fast quantum searching, Phys. Rev. Lett. 80, 3408 (1998)

1998

Show all 49 references

[9]

PR Newswire, Ibm makes quantum computing available on ibm cloud to accelerate innovation., PR Newswire
[10]

L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yan- noni, M. H. Sherwood, and I. L. Chuang, Experimental realization of shor’s quantum factoring algorithm using nuclear magnetic resonance, Nature 414, 883 (2001)

2001
[11]

EDN Staff, D-Wave demos quantum computer, https: //www.edn.com/d- wave- demos- quantum- computer/ (2007), (accessed: 2024-06-20)

2007
[12]

Wallman, C

J. Wallman, C. Granade, R. Harper, and S. T. Flam- mia, Estimating the coherence of noise, New Journal of Physics 17, 113020 (2015)

2015
[13]

Castelvecchi, Ibm releases first-ever 1,000-qubit quan- tum chip, Nature 624, 238 (2023)

D. Castelvecchi, Ibm releases first-ever 1,000-qubit quan- tum chip, Nature 624, 238 (2023)

2023
[14]

Gambetta and M

J. Gambetta and M. Steffen, Charting the course to 100,000 qubits (2023)

2023
[15]

Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Hug- gins, Y. Li, J. R. McClean, and T. E. O’Brien, Quantum error mitigation, Rev. Mod. Phys. 95, 045005 (2023)

2023
[16]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information , 10th ed. (Cambridge Univer- sity Press, Cambridge, 2010)

2010
[17]

A. R. Calderbank and P. W. Shor, Good quantum error- correcting codes exist, Phys. Rev. A 54, 1098 (1996)

1996
[19]

Temme, S

K. Temme, S. Bravyi, and J. M. Gambetta, Error mitiga- tion for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017)

2017
[20]

A. R. R. Carvalho, H. Bal, M. J. Biercuk, M. R. Hush, and F. Thomsen, Error-robust quantum logic optimiza- tion using a cloud quantum computing interface, Physical Review Applied 15 (2021)

2021
[21]

Q-CTRL, Get started, https://docs.q-ctrl.com/boul der-opal/get-started (2023)

2023
[22]

P. S. Mundada, A. Barbosa, S. Maity, Y. Wang, T. Merkh, T. Stace, F. Nielson, A. R. Carvalho, M. Hush, M. J. Biercuk, and Y. Baum, Experimental bench- marking of an automated deterministic error-suppression workflow for quantum algorithms, Phys. Rev. Appl. 20, 024034 (2023)

2023
[23]

Q-CTRL, Q-ctrl integrates its error suppression technol- ogy into ibm quantum services, https://q-ctrl.com/ blog/q-ctrl-integrates-its-error-suppression-t echnology-into-ibm-quantum-services (2023), press Release

2023
[24]

This approach often leads to much faster pulse se- quences compared to the original implementations

follows this idea by proposing a method that ag- gregates instructions of quantum circuits and generates pulse sequences that implement these aggregated instruc- tions. This approach often leads to much faster pulse se- quences compared to the original implementations. How- ev...
[25]

Q-CTRL, Designing noise-robust single-qubit gates for ibm qiskit, https://docs.q-ctrl.com/boulder-opal/ application-notes/designing-noise-robust-singl e-qubit-gates-for-ibm-qiskit (2023)

2023
[26]

Semola, L

R. Semola, L. Moro, D. Bacciu, and E. Prati, Deep rein- forcement learning quantum control on ibmq platforms and qiskit pulse, in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) (2022) pp. 759–762

2022
[27]

Y. Shi, N. Leung, P. Gokhale, Z. Rossi, D. I. Schuster, H. Hoffmann, and F. T. Chong, Optimized compilation of aggregated instructions for realistic quantum computers, in Proceedings of the Twenty-Fourth International Con- ference on Architectural Support for Programming Lan- ...

2019
[28]

Gokhale, A

P. Gokhale, A. Javadi-Abhari, N. Earnest, Y. Shi, and F. T. Chong, Optimized quantum compilation for near- term algorithms with openpulse, in 2020 53rd Annual IEEE/ACM International Symposium on Microarchitec- ture (MICRO) (IEEE Computer Society, Los Alamitos, CA, USA, 2020) p...

2020
[29]

Murali, J

P. Murali, J. M. Baker, A. Javadi-Abhari, F. T. Chong, and M. Martonosi, Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers, in Pro- ceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Opera...

2019
[30]

L. Lao, H. van Someren, I. Ashraf, and C. G. Almude- ver, Timing and resource-aware mapping of quantum cir- cuits to superconducting processors, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 41, 359 (2022)

2022
[31]

Motzoi, J

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Simple pulses for elimination of leakage in weakly nonlinear qubits, Phys. Rev. Lett. 103, 110501 (2009)

2009
[32]

Hyypp¨ a, A

E. Hyypp¨ a, A. Veps¨ al¨ ainen, M. Papiˇ c, C. F. Chan, S. Inel, A. Landra, W. Liu, J. Luus, F. Marxer, C. Ockeloen-Korppi, S. Orbell, B. Tarasinski, and J. Heinsoo, Reducing leakage of single-qubit gates for su- perconducting quantum processors using analytical con- trol pul...

2024
[33]

Q-CTRL, How to automate calibration of control hard- ware, https://docs.q-ctrl.com/boulder-opal/user -guides/how-to-automate-calibration-of-control -hardware (2023)

2023
[34]

Y. Yan, J. Lu, L. Wan, and J. Moser, Robust pulses for high fidelity non-adiabatic geometric gate operations in an off-resonant three-level system, Physics Letters A383, 600 (2019)

2019
[35]

E. W. Lussi, L. C. de Sousa, J. Marchi, R. de Santi- ago, and E. I. Duzzioni, Implementing a quantum finite automaton in ibmq using custom control pulses (2024), arXiv:2412.06977 [quant-ph]

2024 arXiv
[36]

A. R. R. Carvalho, H. Ball, M. J. Biercuk, M. R. Hush, and F. Thomsen, Error-robust quantum logic optimiza- tion using a cloud quantum computer interface, Phys. Rev. Appl. 15, 064054 (2021)

2021
[37]

Y. Baum, M. Amico, S. Howell, M. Hush, M. Liuzzi, P. Mundada, T. Merkh, A. R. Carvalho, and M. J. Bier- cuk, Experimental deep reinforcement learning for error- robust gate-set design on a superconducting quantum computer, PRX Quantum 2, 040324 (2021)

2021
[38]

IBM Quantum, Celebrating five years of ibm quantum experience, https://www.ibm.com/quantum/blog/quant um-five-years (2021), (accessed: 2024-11-19)

2021
[39]

E. C. R. Rosa, E. I. Duzzioni, and R. de Santiago, Op- timizing gate decomposition for high-level quantum pro- gramming (2024), federal University of Santa Catarina, 12 Florian´ opolis, SC, Brazil, arXiv:2406.05581 [quant-ph]

2024 arXiv
[40]

T. J. Maldonado, J. Flick, S. Krastanov, and A. Galda, Error rate reduction of single-qubit gates via noise-aware decomposition into native gates, Scientific Reports 12, doi.org/10.1038/s41598-022-10339-0 (2022)

2022 doi
[41]

D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta, Efficient z gates for quantum comput- ing, Phys. Rev. A 96, 022330 (2017)

2017
[42]

Qiskit 0.45 Documentation, Qiskit Documentation - U3Gate, https://docs.quantum.ibm.com/api/qiski t/qiskit.circuit.library.U3Gate (2023)

2023
[43]

D. G. Almeida, K. Ferris, N. Kanazawa, B. Johnson, and R. Davis, New fractional gates reduce circuit depth for utility-scale workloads, https://www.ibm.com/quantum/ blog/fractional-gates (2024), (accessed: 2024-11-20)

2024
[44]

J. E. Kelley and M. R. Walker, Critical-path planning and scheduling, in Papers Presented at the December 1- 3, 1959, Eastern Joint IRE-AIEE-ACM Computer Con- ference, IRE-AIEE-ACM ’59 (Eastern) (Association for Computing Machinery, New York, NY, USA, 1959) p. 160–173

1959
[45]

S. W. Kramer and J. L. Jankins, Understanding the ba- sics of cpm calculations: what is scheduling software re- ally telling you? (PMI ® Global Congress 2006, 2006)

2006
[46]

The topological sort offers an ordering of the vertices that respects the dependencies indicated by the edges

A topological sort of a directed and acyclic graph G = (E, V) is a linear ordering of all its vertices such that if (u, v) ∈ E, u appears before v in the ordering [47]. The topological sort offers an ordering of the vertices that respects the dependencies indicated by the edges
[47]

Ezzell, B

N. Ezzell, B. Pokharel, L. Tewala, G. Quiroz, and D. A. Lidar, Dynamical decoupling for superconducting qubits: A performance survey, Phys. Rev. Appl. 20, 064027 (2023)

2023
[48]

basic (2023)

Qiskit 0.43 Documentation, Qiskit Documentation - Qiskit Scheduler Methods, https://docs.quantum.i bm.com/api/qiskit/0.43/qiskit.scheduler.methods. basic (2023)

2023
[49]

Emerson, R

J. Emerson, R. Alicki, and K. ˙Zyczkowski, Scalable noise estimation with random unitary operators, Journal of Optics B: Quantum and Semiclassical Optics 7, S347 (2005)

2005
[50]

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms , 4th ed. (The MIT Press, 2022)

2022

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

as soon as possible

“as soon as possible” applies the operation and idle

work page

[2] [2]

as late as possible

“as late as possible” delays applying the operation until the last possible moment. Alternatively, we follow an “as long as possible” policy, where idle periods are used to apply longer and more robust quantum gates. Algorithm 1 presents the overall framework. Given that nq is the number of qubits, ng is the number of gates (which corresponds to the numbe...

work page 2022

[3] [3]

Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp

P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (1994) pp. 124–134

1994

[4] [4]

Deutsch and R

D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 439, 553 (1992)

1992

[5] [5]

L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the Twenty-Eighth An- nual ACM Symposium on Theory of Computing , STOC ’96 (Association for Computing Machinery, New York, NY, USA, 1996) p. 212–219

1996

[6] [6]

Knill, R

E. Knill, R. Laflamme, R. Martinez, and C.-H. Tseng, An algorithmic benchmark for quantum information process- ing, Nature 404, 368 (2000)

work page 2000

[7] [7]

Bernstein and U

E. Bernstein and U. Vazirani, Quantum complexity the- ory, SIAM Journal on Computing 26, 1411 (1997), https://doi.org/10.1137/S0097539796300921. 11

doi:10.1137/s0097539796300921 1997

[8] [8]

I. L. Chuang, N. Gershenfeld, and M. Kubinec, Experi- mental implementation of fast quantum searching, Phys. Rev. Lett. 80, 3408 (1998)

1998