Selective Addressing of Coupled Qubits via Complex Frequency Zero Targeting

Alex Krasnok; Deepanshu Trivedi; Laraib Niaz

REVIEW 5 major objections 4 minor 1 references

Selective Addressing of Coupled Qubits via Complex Frequency Zero Targeting

T0 review · 5 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper establishes that complex-frequency pulses matched to a coupled, lossy qubit system's reflection zeros selectively excite one qubit while strongly suppressing crosstalk to neighboring qubits.

desk verdict A genuinely interesting idea—targeting complex reflection zeros for selective qubit control—with a clean linearized theory but an ADS validation that is partly tuned, so the verdict is conditional rather than reject. read the letter →

arxiv 2506.03316 v1 pith:FH2LJRBW submitted 2025-06-03 quant-ph physics.app-phphysics.optics

Deepanshu Trivedi , Laraib Niaz , Alex Krasnok This is my paper

classification quant-phphysics.app-phphysics.optics

keywords complexfrequencypulsesselectivequbitaddressingcrosstalksuppressionreflectionzerostransmonqubitswaveguidequantumelectrodynamicsinput-outputformalismnon-Hermitiansystems

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

Parasitic coupling and spectral crowding make it hard to drive one qubit on a shared control line without disturbing its neighbors. This paper argues that the right drive is a complex-frequency (CF) pulse, built from a carrier frequency and an exponential envelope decay that together match one of the reflection zeros of the full, coupled, lossy qubit-waveguide system. Using a linearized input-output model for three two-level emitters, it derives the reflection coefficient and shows that a pulse aimed at one of its zeros is almost completely absorbed and funnels energy into a single target qubit. The same pulse construction is then validated in transient circuit simulations of three transmon qubits on a common microwave line, including Josephson-junction nonlinearity and intrinsic qubit losses. The result is a large reduction in off-resonant neighbor excitation compared with Gaussian pulses of comparable energy, provided the true zero, not the complex conjugate of a pole, is used.

What carries the argument

The load-bearing object is the complex reflection coefficient $r(\omega)$ of the coupled qubit-waveguide network, evaluated in the complex frequency plane $\omega = \omega_r - i\omega_i$. In the linearized weak-excitation limit, the Heisenberg equations reduce to a matrix system whose determinant gives $r(\omega)$; its zeros satisfy $r(\omega)=0$ and are the complex frequencies at which an incoming wave is perfectly absorbed. A complex-frequency (CF) pulse is a drive with carrier $\omega_r$ and exponential envelope $e^{-\omega_i t}$ matching one zero of the lossy system. Matching the zero makes the drive impedance-matched to a collective eigenmode and routes energy into the target qubit while destructive interference suppresses other excitation pathways.

What would settle it

The concrete test is to measure the reflection coefficient of a real three-transmon circuit, apply a complex-frequency pulse at one measured zero and a Gaussian pulse of equal energy, and compare per-qubit excitation; if the target qubit's advantage over the Gaussian disappears, or if the reflected power does not dip at the zero, the central claim fails. In a lossy system, the sharper test is to drive at the true zero and at its complex conjugate; the paper predicts the conjugate case is clearly worse in crosstalk suppression.

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Extended reading notes

Core claim

The central claim is that the zeros of the system's complex reflection coefficient are the right design targets for selective qubit addressing in dissipative multi-qubit circuits. In the weak-excitation limit, solving the Heisenberg equations gives a reflection coefficient $r(\omega)$; the complex frequencies with $r(\omega)=0$ are the perfectly absorbing input states of the coupled resonator-qubit network. A pulse whose carrier frequency is the real part of a zero and whose temporal envelope decays at the imaginary part is, to linear order, impedance-matched to one collective eigenmode, and because that mode is mostly localized on one qubit, the pulse excites that qubit while nearly nulling the excitation of the others. Transient simulations with a nonlinear Josephson-junction model confirm the mechanism: targeting the true zero yields roughly 10% crosstalk in the lossy case, whereas a Gaussian pulse of comparable energy produces up to 35% crosstalk. The paper further claims that in a lossy system this selectivity requires the true reflection zero; using the complex conjugate of a pole, the frequency suggested by time-reversal thinking in a lossless system, restores reflection and roughly doubles the relative crosstalk.

Load-bearing premise

The pulses are designed from reflection zeros of the linearized, weak-excitation system, so the selectivity is assumed to survive the nonlinearity of the Josephson junctions at the drive powers actually used.

Editorial extensions

If this is right

Qubit frequencies no longer need to be separated as widely, since selectivity comes from matching zeros rather than from spectral avoidance; denser frequency allocation becomes feasible.
Single-qubit gates on a shared control line should show higher fidelity, because the dominant off-resonant driving error is reduced.
The pulse can be derived deterministically from a measured scattering matrix, reducing the need for numerical pulse search and recalibration.
In lossy hardware, control design must use measured complex zeros; any strategy that conjugates lossless poles will underperform.
The technique transfers to other qubit platforms and coupling architectures where a target is embedded in a lossy interacting network.

Reading between the lines

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

Editorial extension: because the zeros are computed under weak-excitation linearization, the selectivity advantage is expected to weaken as drive power grows and the transmon's Kerr nonlinearity shifts the real response; a natural test is to sweep drive amplitude until crosstalk rises.
Editorial extension: a short complex-frequency pulse has broad transient spectral content, so leakage out of the computational subspace to the second excited state could become the next dominant error; combining the zero-matched envelope with derivative-based leakage suppression is an obvious next step.
Editorial extension: the same zero-targeting logic should apply to readout pulses or photon capture on a bus, where the goal is to route energy into one mode of a coupled network without disturbing the others.
Editorial extension: the quantitative advantage of the true zero over its complex conjugate is a distinctive signature that could be checked before full gate calibration, because it only requires measuring reflection and qubit excitation rather than a full two-qubit gate.

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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

Here's my read of 2506.03316.

The genuinely new thing is not complex-frequency excitation itself—that's from the same group's prior work (refs 42, 46)—but the translation to a multi-qubit, explicitly lossy setting where time-reversal symmetry is broken. The linearized Heisenberg derivation leading to Eq. (5) is clean, and the demonstration that exciting at the complex conjugate of a pole fails in the lossy case is a real, useful point. The selectivity numbers in the lossless ADS tables (S3) are impressive if they hold: target efficiencies 77–85% with crosstalk suppression ratios of 7–13, versus Gaussian baselines with ~35% crosstalk. The paper is also unusually honest in the Discussion about Kerr nonlinearity, leakage, and parameter drift—those are acknowledged open questions, not hidden.

The soft spots are real but manageable. First, the ADS validation used the built-in Random Optimizer to fine-tune component values and the time step with the explicit goal of minimizing reflected power. That makes the near-perfect absorption partly a fitted result, not an independent prediction of Eq. (5). You can't tell how much of the 85% efficiency is physics and how much is optimizer. Second, the efficiency metric η(t) is defined for the resonator mode |⟨a(t)⟩|², but it's applied to the qubit excitation efficiencies in the tables. That's a mismatch—either the formula is being reused loosely or the qubit energies are computed in a way the paper doesn't state. Third, the Gaussian baseline is matched in energy but not in duration or bandwidth, so the comparison isn't apples-to-apples. The stress-test note about linearized zeros versus the nonlinear transmon at 77–85% efficiency is fair: the design rests on ⟨σ_z⟩≈−1, and at those efficiencies that assumption is violated. The Discussion concedes the point but supplies no bound or error estimate. That said, the theoretical model of Fig. 1 simulates the full nonlinear Heisenberg equations and still shows selectivity, so the mechanism isn't obviously invalid—it's just not quantitatively supported at the claimed operating point.

Overall: the core idea is sound and the theory is honest, but the empirical validation is under-reported. This deserves a serious referee because the idea is useful and the flaws are fixable reporting/calibration issues, not a demonstrated failure of the physics. I'd ask for disclosure of all optimizer-adjusted values, a duration- and bandwidth-matched Gaussian baseline, a proper definition of qubit excitation efficiency, and ideally a code/ADS project release. Without that, I'd treat the headline numbers as provisional.

For peer review: accept, with heavy revision demands.

Referee Report

5 major / 4 minor

Summary. The paper proposes a pulse-shaping method for selective addressing of coupled superconducting qubits. The authors derive a linearized Heisenberg-Langevin model of three two-level emitters coupled to a resonator and waveguide, obtain the reflection coefficient r(ω) in Eq. (5), and identify its complex zeros. They then construct pulses whose carrier frequency and decay rate match these zeros, claiming near-perfect absorption and selective excitation. The concept is validated with ADS transient simulations of three transmon qubits, comparing Gaussian and complex-frequency (CF) pulses, and the lossy case compares excitation at a true reflection zero against excitation at the complex conjugate of a pole. Headline quantitative results are target efficiencies of 77–85% with crosstalk suppressed to about 10% for CF pulses, versus substantial crosstalk for Gaussian pulses.

Significance. The manuscript has several genuine strengths: it gives an explicit analytic expression for the reflection zeros of a lossy multi-emitter system; it demonstrates in a lossy transmon circuit that the complex-conjugate pole frequency is suboptimal compared with the true reflection zero (Fig. 5 and Table S4); it provides quantitative selectivity and crosstalk metrics; and it includes nonlinear Josephson-junction effects in the ADS validation. It is also worth emphasizing that the selectivity/crosstalk result is not purely definitional: while r(ω_z)=0 guarantees a reflection zero at the exact complex frequency, the distribution of absorbed energy among the three qubits is a separate, nontrivial outcome. If the validation concerns below are resolved, the method could be a useful addition to the toolbox for qubit control under spectral crowding. The paper is clearly within the scope of the journal and the experimental relevance is plausible, though the present evidence is not fully out-of-sample because of the ADS optimization step.

major comments (5)

[§3, ADS Random Optimizer paragraph] The text states that the Random Optimization controller in ADS was used to 'fine tun[e] component values' in addition to the simulation time step, with the explicit optimization goal of minimizing reflected power at the end of the excitation pulse. This means that the near-perfect absorption shown in Figs. 4 and 5 is not an independent prediction of the zero-targeting theory: the optimizer could have adjusted the circuit components so that the actual response better matches the pulse frequency. To support the central claim, please report the initial and optimized component values, state whether the CF pulses were recomputed from the zeros of the optimized circuit, and provide at least one out-of-sample simulation (for example, with an untuned parameter set or with the objective changed to something other than reflected-power minimization) showing that the absorption and selectivity improvements survive.
[§2 and §3, linearization versus operating point] The pulse design is based on the linearized approximation ⟨σ_z⟩≈−1 and on steady-state reflection zeros of Eq. (5), but the headline efficiencies in Section S3 are η1=85.0%, η2=77.0%, and η3=80.7%, which are far from the weak-excitation regime. At these amplitudes the transmon Kerr nonlinearity shifts the qubit frequency during the pulse, and a finite-duration CF pulse has spectral support away from the designed zero; neither effect is quantified anywhere in the paper. The Discussion in Section 4 acknowledges these as open questions, but no bound, error estimate, or drive-amplitude scan is provided. Please add simulations at several drive powers spanning the linearization threshold and quantify how the selectivity and absorption change when the finite pulse width and nonlinearity are varied.
[S1, expectation-value factorization] The main text claims that the nonlinear terms such as ⟨a(t)⟩⟨σ_z^(j)(t)⟩ 'appear directly from the expectation value of operator products without invoking a mean-field factorization at this stage,' but S1 explicitly writes ⟨âσ_z^(j)⟩ ≈ ⟨â⟩⟨σ_z^(j)⟩ and states that terms are 'often factorizing.' This is an internal inconsistency in the derivation. Since the nonlinear dynamics displayed in Fig. 1(d-f) and the later transmon simulations rely on the factorized semiclassical equations, the paper should state the factorization assumption explicitly and justify its validity at the drive amplitudes used, or present the unapproximated equations and explain how they are solved.
[Eq. (6) and Figs. 3-4] Equation (6) defines the excitation efficiency as η(t)=|⟨a(t)⟩|² divided by the integrated input energy, which refers to a resonator mode amplitude. However, the transmon circuit in Section 3 has no single-mode resonator in the theoretical-model sense, and Figs. 3 and 4 plot 'Excitation Efficiency' for the individual qubits. The quantitative crosstalk claims (35% for Gaussian, roughly 10% for CF) depend entirely on this metric, yet the qubit-level version of η(t) is never defined. Please define the qubit-energy metric used in the ADS post-processing and either reconcile it with Eq. (6) or replace Eq. (6) with the metric actually used.
[§3 and S3, Gaussian baseline comparison] The comparison states that Gaussian and CF pulses have comparable energy, but no pulse durations, peak powers, or spectral bandwidths are reported for either pulse type. Selectivity in a coupled multi-qubit system depends strongly on pulse duration and bandwidth, so matching energy alone is not sufficient to establish that CF pulses 'markedly outperform' Gaussian pulses; a longer CF decay can trivially reduce off-resonant excitation. Please report the full pulse parameters (width, decay rate, peak amplitude, duration, and bandwidth) and include comparisons at equal duration and equal bandwidth in addition to the equal-energy comparisons.

minor comments (4)

[S2, figure cross-reference] The S2 text refers to 'the CF pulses used in the main text (Fig. 2),' but the theoretical CF-pulse dynamics appear in Fig. 1 of the main text, not Fig. 2.
[S4, figure cross-reference] The S4 text refers to 'Fig. 6c' of the main text, but the lossy-system results are presented in Fig. 5, and Fig. 6 does not exist in the manuscript.
[S3, efficiency table] In the final efficiency table of S3, the entry for η3 when targeting Qubit 1 reads '1.7.' with a stray period; this should be '1.7'.
[Throughout] Several symbols are introduced without explicit numerical values, especially the Gaussian pulse width σ_i and the CF decay rates used in the ADS simulations; providing these values would improve reproducibility.

Circularity Check

2 steps flagged · score 5.0 of 10

Near-zero reflection is definitional and the ADS validation includes an optimizer target minimizing reflected power, but the crosstalk selectivity and lossy zero-vs-conjugate test retain independent content.

self definitional [Section 2, Figure 1 paragraph following Eq. (5)]
"According to our model, an input pulse whose carrier frequency and temporal envelope are tailored to match one of these specific complex zeros will be efficiently absorbed by the system, ideally with no reflection."

The reflection coefficient r(omega) is defined as the reflected-field amplitude relative to the input; by construction, any complex frequency satisfying r(omega)=0 gives zero reflected field in the linearized model. Designing a CF pulse exactly at omega_z and then reporting suppressed reflection is therefore restating the design condition, not an independent prediction. The nontrivial content of the paper is the selectivity and crosstalk comparison, not the vanishing reflection itself.
fitted input called prediction [Section 3, ADS simulation methodology paragraph (Random Optimization controller)]
"In addition to fine tuning component values, we also optimized the simulation time step ... The optimization goal was to minimize reflected power at the end of the excitation pulse."

The ADS validation presents near-perfect absorption and high efficiency as evidence for the CF design, but the stated simulation setup includes a Random Optimizer whose explicit goal is to minimize reflected power while also fine tuning component values. Low reflection is therefore an imposed optimization objective of the numerical experiment, not a quantity predicted solely by targeting the reflection zero. This makes the ADS absorption evidence partly fitted rather than emergent.

full rationale

The paper's derivation of r(omega) in Eq. (5) and its interpretation of zeros as complete absorption is self-consistent but partly definitional: r(omega_z)=0 means zero reflected field by definition, so any pulse centered at that complex frequency will show no reflection in the linear steady-state model. That component of the claimed performance is built into the design target. The central selectivity claim, however, is not definitional: the nonlinear Bloch dynamics and the ADS transmon simulations showing that one qubit is excited while neighbors remain largely unexcited, and especially the lossy-system comparison between the true reflection zero and its complex conjugate (Fig. 5 and Tables S4), are genuine dynamical outputs that do not reduce to the definition of r(omega). The paper's self-citations (refs. 42, 46) introduce the complex-frequency concept but are not load-bearing here, because the qubit-specific equations, zero locations, and pulse construction are derived in the paper. The main circularity concern beyond the definitional absorption step is the ADS optimizer: the text states that component values were fine-tuned and that the optimization goal was to minimize reflected power, so the reported low reflection in the ADS validation is at least partly a fitted objective. Overall, the selectivity results retain independent content, but the near-zero-reflection part is by construction and the ADS evidence is partially fitted, giving a moderate partial-circularity score.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard quantum-optics approximations plus several hand-chosen simulation parameters. No new physical entity is introduced. The most consequential ledger entries are the undisclosed ADS optimizer adjustments, which act as fitted parameters in the validation, and the weak-excitation linearization, which is the stated regime of validity for both the theory and the low-power transmon simulations.

free parameters (5)

Qubit-resonator coupling g = omega_c/100 (about 2 pi x 57.7 MHz)
Chosen equally for all three qubits in the theoretical model; it sets the collective eigenmode structure used to assign target zeros.
Resonator quality factor Q = 31
Chosen for the illustrative model; it fixes the external coupling rate 1/tau_r and shapes the complex zeros in Fig. 1.
Coupling capacitor scaling delta = 0.1 (C_c1=10 fF, C_c2=11 fF, C_c3=12.1 fF)
Deliberately creates the spectrally crowded configuration in the ADS model; the capacitance steps determine eigenmode localization.
Qubit shunt resistance R_shunt = 0.2 MOhm
Introduced ad hoc to model intrinsic qubit losses in the lossy validation; the value is not tied to a measured device.
ADS Random Optimizer component adjustments = not reported
The optimizer was used to fine-tune component values with the goal of minimizing reflected power, so the final circuit parameters used for the CF-pulse comparison are undisclosed fitted values.

assumptions (6)

domain assumption Born-Markov approximation for the waveguide and qubit baths.
Used in S1 to eliminate bath operators and obtain decay rates 1/tau_r and Gamma_s; standard for this regime but unverified for the specific transmon parameters.
domain assumption Rotating wave approximation for qubit-resonator coupling.
Invoked in S1 for the Tavis-Cummings interaction; assumes weak coupling relative to transition frequencies.
domain assumption Weak-excitation linearization with <sigma_z^(j)> approximately -1 and factorization of operator expectation values.
Invoked in Section 2 to derive the linear algebraic system and Eq. (5); the ADS simulations rely on low drive power (below 5% of I_c) to remain in this regime.
domain assumption Single-port input-output relation b_out = -b_in + k_r a, so r(omega)=0 implies complete absorption.
Eq. (5) assumes the waveguide is the only port and there is no transmissive output channel, an idealization of the real control-line geometry.
domain assumption The ADS JJ2 RCSJ junction model faithfully represents transmon nonlinearity at the simulated drive powers.
The quantitative ADS results depend on the behavioral JJ2 model and its default parameters; this is not independently benchmarked against experiment.
ad hoc to paper A finite-duration CF pulse can be approximated as an ideal complex-frequency exponential.
The zero-reflection property r(omega_z)=0 is defined for a steady-state complex exponential; the paper does not analyze transient startup effects of a truncated CF pulse.

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Cite this review

Pith. "Pith review of Selective Addressing of Coupled Qubits via Complex Frequency Zero Targeting." pith.science (2026). https://pith.science/paper/FH2LJRBW

@misc{pith2026250603316,
  author       = {Pith},
  title        = {Pith review of: Selective Addressing of Coupled Qubits via Complex Frequency Zero Targeting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FH2LJRBW}},
  note         = {Machine review of arXiv:2506.03316}
}

read the original abstract

Achieving precise, individual control over qubits within scalable quantum processors is critically hampered by parasitic couplings and spectral crowding, leading to detrimental crosstalk. While optimal absorption strategies based on time-reversal symmetry have shown promise for single emitters, their applicability is limited in realistic multi-qubit systems where realistic losses break time-reversal symmetry. This work introduces a robust approach using complex frequency (CF) pulses specifically tailored to the complex reflection zeros of the complete, coupled, and explicitly lossy qubit-waveguide system. This method circumvents the limitations of idealized time-reversal arguments by directly engaging with the dissipative system's true response characteristics. We first develop a theoretical framework for a system of three coupled two-level emitters, employing Heisenberg equations to derive the system's response and design appropriate CF pulses that inherently account for the system's dissipative nature. The efficacy and practicality of this approach are then validated through comprehensive transient simulations for a realistic model of three Josephson junction-based transmon qubits, explicitly including intrinsic qubit losses. Our results demonstrate that CF pulses can selectively excite a target qubit with significantly suppressed crosstalk to neighboring qubits, markedly outperforming conventional Gaussian pulses of comparable energy.

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Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

1. D. Walls, G. Milburn, Quantum Optics (2006)

work page 2006

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

1. D. Walls, G. Milburn, Quantum Optics (2006)

work page 2006