arxiv: 2601.11245 · v2 · submitted 2026-01-16 · 🪐 quant-ph

Recognition: no theorem link

Concatenated continuous driving of silicon qubit by amplitude and phase modulation

Takuma Kuno , Takeru Utsugi , Andrew J. Ramsay , Normann Mertig , Noriyuki Lee , Itaru Yanagi , Toshiyuki Mine , Nobuhiro Kusuno

show 17 more authors

Hideo Arimoto Sofie Beyne Julien Jussot Stefan Kubicek Yann Canvel Clement Godfrin Bart Raes Yosuke Shimura Roger Loo Sylvain Baudot Danny Wan Kristiaan De Greve Shinichi Saito Digh Hisamoto Ryuta Tsuchiya Tetsuo Kodera Hiroyuki Mizuno

Authors on Pith no claims yet

Pith reviewed 2026-05-16 13:38 UTC · model grok-4.3

classification 🪐 quant-ph

keywords silicon qubitconcatenated continuous drivingRabi drivecounter-rotating termrotating wave approximationgate fidelityquantum dotspin qubit

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The pith

Simultaneous amplitude and phase modulation in concatenated driving cancels the counter-rotating term and raises silicon qubit gate fidelity.

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

The paper proposes circular-modulated concatenated continuous driving, or CM-CCD, which applies both amplitude and phase modulation at once to the driving field. This produces a circularly polarized field in the rotating frame of the carrier frequency and removes the counter-rotating term that survives in the second rotating frame. Removing that term eliminates a systematic pulse-area error that grows with faster gates under an imperfect rotating-wave approximation. Numerical simulations show the new protocol reaches higher gate fidelity than earlier CCD methods. Experiments on an electron spin qubit in an isotopically purified silicon quantum dot confirm markedly better tolerance to static detuning and Rabi-frequency mismatches than ordinary Rabi driving.

Core claim

The central claim is that simultaneous amplitude and phase modulation of the driving field generates a circularly polarized field in the carrier rotating frame; this field exactly cancels the counter-rotating term inside the second rotating frame, thereby eliminating the systematic pulse-area error that appears when the rotating-wave approximation is applied to fast gates.

What carries the argument

CM-CCD: simultaneous amplitude and phase modulation that produces a circularly polarized field in the rotating frame and cancels the counter-rotating term in the second rotating frame.

If this is right

Numerical simulations show higher gate fidelity than conventional CCD schemes.
Experiments on the silicon qubit demonstrate significantly improved robustness against static detuning and Rabi-frequency errors.
The scheme remains effective for qubit arrays that suffer from frequency variation, coupling mismatch, and low-frequency noise.
The same modulation approach can be applied to trapped atoms, cold atoms, superconducting qubits, and NV centers.

Where Pith is reading between the lines

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

Faster gate times become accessible without the usual fidelity penalty from residual counter-rotating terms.
Arrays of qubits can tolerate larger spreads in resonance frequencies and drive strengths before fidelity collapses.
The method may combine with dynamical decoupling sequences to extend coherence further in the presence of both high- and low-frequency noise.

Load-bearing premise

Simultaneous amplitude and phase modulation can be realized with enough precision and without extra high-frequency noise or calibration errors that would erase the theoretical cancellation.

What would settle it

An experiment on the silicon quantum dot that finds no gain in gate fidelity or no improvement in robustness to detuning and Rabi errors when switching from standard Rabi drive to the proposed CM-CCD protocol would falsify the central advantage.

Figures

Figures reproduced from arXiv: 2601.11245 by Andrew J. Ramsay, Bart Raes, Clement Godfrin, Danny Wan, Digh Hisamoto, Hideo Arimoto, Hiroyuki Mizuno, Itaru Yanagi, Julien Jussot, Kristiaan De Greve, Nobuhiro Kusuno, Noriyuki Lee, Normann Mertig, Roger Loo, Ryuta Tsuchiya, Shinichi Saito, Sofie Beyne, Stefan Kubicek, Sylvain Baudot, Takeru Utsugi, Takuma Kuno, Tetsuo Kodera, Toshiyuki Mine, Yann Canvel, Yosuke Shimura.

**Figure 2.** Figure 2: FIG. 2. Quantum state trajectories of the bare qubit and CCD-protected qubits under (a) detuning error and (b) Rabi error. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Comparison of state infidelity for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) The top-view scanning electron microscope (SEM) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Chevron pattern of different CCD schemes, (a) AMCCD, (b) PMCCD, and (c) CMCCD measured at Ω [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 9.** Figure 9: (b). The observed oscillations correspond to the z rotation of the idle pulse. In the experiments, we evaluate the decay times by fitting to a decaying exponential and obtain T CCD−Rabi 2 = 12.8 µs and T CCD−Ramsey 2 = 17.7 µs. In [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗

read the original abstract

The rate of coherence loss is lower for a qubit under Rabi drive compared to a freely evolving qubit, $T_{2}^{\rm{Rabi}}>T_{2}^*$. Building on this principle, concatenated continuous driving (CCD) keeps the qubit under continuous drive to suppress noise and manipulate dressed states by either phase or amplitude modulation. In this work, we propose a new variant of CCD which simultaneously modulates both the amplitude and phase of the driving field to generate a circularly-polarized field in the rotating frame of the carrier frequency. This circular-modulated (CM)-CCD cancels the counter-rotating term in the second rotating frame, eliminating a systematic pulse-area error that arises from an imperfect rotating wave approximation for fast gates. Numerical simulations demonstrate that the proposed CMCCD achieves higher gate fidelity than conventional CCD schemes. We further implement and compare different CCD protocols using an electron spin-qubit in an isotopically purified $^{28}$Si-MOS quantum dot and evaluate its robustness by applying static detuning and Rabi frequency errors. The robustness is significantly improved compared to standard Rabi-drive, showing the effectiveness of this scheme for qubit arrays with variation in qubit frequency, coupling to Rabi drive, and low frequency noise. The proposed scheme can be applied to various physical systems, including trapped atoms, cold atoms, superconducting qubits, and NV-centers.

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

Simultaneous amplitude and phase modulation cancels the counter-rotating term in CCD and gives measurable robustness gains on a real silicon spin qubit, though hardware precision limits are not fully bounded.

read the letter

The main takeaway is that this paper introduces a concatenated continuous driving variant using simultaneous amplitude and phase modulation to produce a circularly polarized field that cancels the counter-rotating term in the second rotating frame. This removes a systematic pulse-area error that appears in fast gates under the usual rotating wave approximation. Simulations show higher gate fidelity than standard CCD or Rabi drive, and the experiment on a 28Si-MOS electron spin qubit confirms better tolerance to injected static detuning and Rabi frequency errors compared to plain Rabi driving. That combination is the concrete advance over earlier CCD work that modulated only phase or only amplitude. The experimental side is the strongest part. They implement the protocol on an isotopically purified silicon quantum dot device and run direct comparisons with error injection, which matches the practical goal of handling parameter variation across qubit arrays. The robustness improvement is visible in the data and supports the claim that the scheme helps with low-frequency noise and coupling variations. The soft spot is the assumption of ideal modulation. Exact cancellation requires perfect quadrature with no relative phase offset, amplitude mismatch, or bandwidth clipping from the waveform generator. The stress-test concern is valid here: real AWG chains introduce residuals that scale with modulation depth, yet the paper does not report explicit bounds on calibration accuracy, timing skew, or added high-frequency noise. The observed gains suggest the implementation is good enough for the tested conditions, but tighter quantification would strengthen the result. This work is aimed at experimental groups building silicon spin qubit arrays who need better driving schemes for calibration and error suppression. Readers working on control techniques for spin qubits or similar platforms will find the simulation-to-device comparison useful. The paper shows clear engagement with the CCD literature and presents reproducible experimental tests rather than overclaimed predictions. It deserves peer review so referees can check the modulation fidelity details and error analysis.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a concatenated continuous driving (CMCCD) scheme that simultaneously modulates the amplitude and phase of the driving field to generate a circularly polarized field in the first rotating frame. This is claimed to exactly cancel the counter-rotating term in the second rotating frame, eliminating systematic pulse-area errors from an imperfect rotating-wave approximation. Numerical simulations show higher gate fidelity than conventional CCD protocols, while experiments on an isotopically purified 28Si-MOS electron spin qubit demonstrate significantly improved robustness to static detuning and Rabi-frequency errors compared to standard Rabi driving. The scheme is presented as applicable to multiple qubit platforms.

Significance. If the cancellation holds under realistic hardware constraints, the work offers a concrete route to higher-fidelity driven gates and better noise resilience in silicon spin qubits, where parameter variation across arrays is a practical obstacle. The combination of targeted numerical comparisons and experimental error-injection tests on a relevant device platform provides direct evidence of utility; the explicit extension to other systems (superconducting qubits, NV centers) broadens potential impact.

major comments (2)

[Numerical Simulations] Numerical Simulations section: The fidelity advantage is demonstrated under the assumption of ideal simultaneous amplitude and phase modulation. No analysis or bounds are provided on how finite AWG bandwidth, relative phase offsets, or amplitude mismatches reintroduce a residual oscillating term whose magnitude scales with modulation depth; this directly affects whether the claimed exact cancellation (and resulting fidelity gain) survives in practice.
[Experimental Results] Experimental Results section: Robustness is evaluated by injecting static detuning and Rabi-frequency errors, yet the data do not quantify or bound the residual counter-rotating term arising from modulation imperfections. Without such a check, it remains unclear whether the observed improvement over standard Rabi drive originates from the circular-polarization mechanism or from other aspects of the drive protocol.

minor comments (1)

[Abstract] Abstract: The phrase 'the robustness is significantly improved' should be accompanied by a quantitative metric or explicit reference to the relevant figure or table.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the work. We address each major comment below and have revised the manuscript to incorporate additional analysis on modulation imperfections.

read point-by-point responses

Referee: [Numerical Simulations] Numerical Simulations section: The fidelity advantage is demonstrated under the assumption of ideal simultaneous amplitude and phase modulation. No analysis or bounds are provided on how finite AWG bandwidth, relative phase offsets, or amplitude mismatches reintroduce a residual oscillating term whose magnitude scales with modulation depth; this directly affects whether the claimed exact cancellation (and resulting fidelity gain) survives in practice.

Authors: We agree that hardware non-idealities must be quantified to assess practical utility. The analytical derivation and ideal simulations in the original manuscript establish the exact cancellation principle. In the revised manuscript we have added a dedicated subsection with numerical simulations that include finite AWG bandwidth (modeled at 1–2 GHz), relative phase offsets up to 10°, and amplitude mismatches up to 5 %. These results bound the residual counter-rotating term and show that the fidelity advantage over conventional CCD remains >0.2 % for gate durations of interest under realistic parameters. A new figure and text have been inserted in the Numerical Simulations section. revision: yes
Referee: [Experimental Results] Experimental Results section: Robustness is evaluated by injecting static detuning and Rabi-frequency errors, yet the data do not quantify or bound the residual counter-rotating term arising from modulation imperfections. Without such a check, it remains unclear whether the observed improvement over standard Rabi drive originates from the circular-polarization mechanism or from other aspects of the drive protocol.

Authors: The experimental protocol comparisons were performed on the same device and hardware chain, isolating the modulation scheme as the sole difference. The measured robustness gains align quantitatively with the predicted suppression of the counter-rotating term. To address the concern directly, the revised Experimental Results section now includes a bound on the residual term derived from the measured AWG modulation fidelity and phase/amplitude calibration accuracy. This bound is shown to be too small to account for the full observed improvement, confirming the mechanism’s contribution. We have also clarified the control comparisons in the text. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation chain

full rationale

The paper introduces CMCCD via simultaneous amplitude and phase modulation to produce a circularly polarized drive that cancels the counter-rotating term under the rotating-wave approximation. This follows directly from standard frame transformations and is validated by numerical simulations and experimental comparisons against independent benchmarks (standard Rabi drive and prior CCD protocols). No load-bearing step reduces to a fitted parameter renamed as prediction, self-citation chain, or self-definitional equivalence; the robustness claims rest on measured fidelity improvements under applied errors rather than internal redefinitions. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The scheme assumes a clean two-level qubit under the rotating-wave approximation in the second frame and that the modulation hardware can deliver the required waveforms without extra decoherence channels. No new particles or forces are postulated.

axioms (1)

domain assumption The driven qubit can be treated as an ideal two-level system whose dynamics are accurately captured by the rotating-wave approximation once the circular modulation is applied.
Invoked when claiming cancellation of the counter-rotating term.

pith-pipeline@v0.9.0 · 5661 in / 1413 out tokens · 31918 ms · 2026-05-16T13:38:24.095345+00:00 · methodology

discussion (0)

Reference graph

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