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Quantum information processing in modular cavity QED architectures

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Pith's one-line read Transient cavity output encodes qubit echo envelopes and exposes a purely quantum noise signature through even-odd revival alternation.

desk verdict A careful, self-aware thesis with a strong second chapter; the flagship quantum-noise signature is conditional on an environmental preparation the paper asserts but does not prove, and the rest is a useful collection of modular-QED protocols. read the letter →

arxiv 2505.04747 v1 pith:DZ7VIL4R submitted 2025-05-07 quant-ph

Z. M. McIntyre This is my paper · ORCID
classification quant-ph PACS 42.50.Pq03.67.Lx03.65.Yz
keywords cavityquantumelectrodynamicsqubitnoisespectroscopydynamicaldecouplingwhich-pathentanglementinterferometryerrorcorrectionmodularcomputing
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 thesis sets out to show that a single modular cavity-QED platform can supply the tools a scalable quantum processor needs: in-situ qubit noise spectroscopy, entanglement distribution, quantum-enhanced metrology, error-correction checks, and long-range gates. Its central claim is that in a high-Q cavity, the transient field leaking out during a Carr-Purcell-Meiboom-Gill decoupling sequence encodes the qubit echo envelope, and the discrete Fourier transform of that field alternates between the envelope and its complex conjugate on successive revivals. That even-odd alternation is presented as a signature of genuinely quantum noise, arising from non-commuting bath operators, that survives even when inhomogeneous broadening hides all structure in the stationary transmission spectrum. If correct, the protocol turns the cavity output into a direct in-situ probe of the antisymmetrized part of the qubit's noise spectrum. The remaining chapters apply the same light-matter toolbox to entangling distant qubits via which-path states, reaching the quantum Cramér-Rao bound with homodyne detection, performing parity checks without horizontal hook errors, and implementing time-bin-mediated two-qubit gates.

What carries the argument

The load-bearing object is the input-output identity $\langle \tilde a \rangle_\omega = -ig\chi_c(\omega) \langle \sigma_x \rangle_{\omega+\Delta}$ with cavity susceptibility $\chi_c(\omega) = [i(\delta-\omega)+\kappa/2]^{-1}$, combined with the toggling-frame decomposition of qubit coherence under an $N$-pulse CPMG sequence. Each $\pi$-pulse contributes a sign function $s(t) = (-1)^{n(t)}$, and that sign function enters two filter functions: the classical $F_c(\omega,t) = (\omega^2/2)|\int_0^t dt' e^{i\omega t'} s(t')|^2$, which controls the decay of the echo envelope through $\mathrm{Re}[S(\omega)]$, and the quantum $F_q(\omega,t) = \omega \int_0^t dt' \sin(\omega t') s(t')$, which controls its phase through $\mathrm{Im}[S(\omega)]$. Inserting these filter functions into the envelope and then into the output-field expression is what produces the even-odd $K$ action, making the quantum-noise phase observable in the leaked field.

What would settle it

Prepare the bath in its bare equilibrium state $[H_E,\bar\rho_E]=0$ and run the CPMG transient protocol: the thesis predicts the even-odd revival alternation should vanish, so observing a nonzero antisymmetrized phase in that preparation would falsify the quantum-noise claim as stated.

Watch

Extended reading notes

Core claim

The central discovery is that a high-Q cavity does not merely filter qubit coherence revivals; it makes their phase visible in the outgoing field. Under the conditions $g < \kappa \ll \tau^{-1}$ and $\kappa T_2^* \ll 1$, the output-field Fourier component at $\omega = \delta$ is $\langle \tilde a \rangle_{\omega=\delta} \simeq -i\langle\sigma_x\rangle_0 \sqrt{\pi} g T_2^* \kappa^{-1} [\tilde{C}_{N,\tau}(\delta) - \tfrac{1}{2} C(0)]$, where $\tilde{C}_{N,\tau}(\omega) = \sum_{n=0}^{N} e^{in(\omega+\Delta)\tau} \bar{G}_n K^n \tilde{C}(n\tau)$ and $K$ is complex conjugation. Because $K^n$ acts on the echo envelope $\tilde{C}(n\tau)$, even revivals expose $\tilde{C}$ while odd revivals expose $\tilde{C}^*$. The thesis attributes this alternation to the quantum-noise part $S_q(\omega) = \mathrm{Im}\,S(\omega)$ of the bath spectral density, entering through the phase $\Phi_q(n\tau) = \int (d\omega/2\pi) F_q(\omega,n\tau) S_q(\omega)/\omega^2$. This phase is the non-stationary analogue of a Lamb shift: in a Markovian bath it is simply a frequency shift, while in a non-Markovian bath it is a nontrivial phase that the cavity output field can track in real time.

Load-bearing premise

The signature claim assumes the environment is prepared in the steady state it reaches while the qubit is held in its ground state; under the more standard bare-environment preparation the quantum-noise phase for the secular coupling vanishes and the even-odd alternation disappears.

Editorial extensions

If this is right

  • Spin and charge qubits whose stationary transmission spectrum is featureless because of inhomogeneous broadening can still have their full noise spectrum recovered from the transient cavity response.
  • The even-odd revival alternation turns the phase of qubit coherence into an observable amplitude effect, so the antisymmetrized noise spectrum $S_q(\omega)$ can be measured in situ rather than inferred indirectly.
  • In the Markovian limit the quantum-noise phase becomes a simple Lamb shift, while in non-Markovian environments it acquires nontrivial time dependence; a computation that ignores it will accumulate correctable phase errors.
  • Pulsing the cavity coupling or detuning can raise the information extracted per measurement cycle toward one bit, matching the efficiency of single-shot qubit readout.
  • The same light-matter toolbox yields which-path entanglement distribution, homodyne-only saturation of the quantum Cramér-Rao bound, parity checks free of horizontal hook errors under photon loss, and time-bin-based inter-module CZ gates.

Reading between the lines

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

  • If the even-odd signature is confirmed, it provides a practical witness for non-commutativity of bath operators: the sign and magnitude of $S_q(\omega)$ can be read directly from the revival Fourier amplitudes without full process tomography.
  • Comparing the two environment preparations in the same device, the ground-state-conditioned state versus the bare equilibrium state, would isolate the quantum-noise contribution from classical inhomogeneous broadening, since only the conditioned preparation should produce the even-odd alternation.
  • The which-path entangler requires a coherent-state source with amplitude noise below one photon per pulse; a natural extension is to test whether squeezed or non-Gaussian input states relax that stability requirement while preserving the entanglement protocol.
  • The chapters are largely independent, so the Chapter 3-6 protocols stand even if the Chapter 2 quantum-noise signature were to fail; conversely, a working even-odd signature would serve as a calibration tool for the environment characterization those protocols need.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. This manuscript is a manuscript-based PhD thesis presenting five connected works on modular cavity-QED quantum information processing. Chapter 2 derives a relation between the transient output field of a high-Q cavity and the echo envelope of a cavity-coupled qubit under CPMG dynamical decoupling, and shows that the discrete Fourier transform of the envelope alternates between the envelope and its complex conjugate for even and odd revivals; this alternation is attributed to the antisymmetrized quantum part Sq(ω) of the noise spectrum. Chapter 3 introduces a modulated-longitudinal-coupling which-path entangler for coherent-state wavepackets and uses it for entanglement distribution and metrology. Chapter 4 develops homodyne-only interferometric phase estimation that saturates the quantum Cramér-Rao bound for path-entangled coherent states. Chapter 5 analyzes flying-cat parity checks and argues that photon loss does not introduce horizontal hook errors in a subsystem surface code, and constructs a six-qubit tetrahedron resource state. Chapter 6 gives protocols for inter-module CZ gates mediated by Fock- or time-bin-encoded photons, including infidelity and erasure analysis. The thesis is technically rich, with full appendices and a clear approximation hierarchy at every stage of Chapter 2.

Significance. The core strength of the thesis is its constructive character: the derivations are carried out with explicit regimes of validity, and the results are benchmarked against external quantities such as the quantum Cramér-Rao bound, concurrence, and the independently measured hyperfine coupling A/2π = -0.25 MHz. If the central claim of Chapter 2 holds, transient spectroscopy would provide direct in-situ access to Sq(ω), the antisymmetrized (quantum) part of the qubit noise spectrum. The modular protocols of Chapters 3-6 are also valuable as concrete building blocks, with finite-bandwidth, loss, and dephasing corrections analyzed rather than assumed away. The main caveat is that the flagship quantum-noise signature rests on a bath-preparation assumption that is asserted but not experimentally demonstrated, which tempers the significance of that particular claim.

major comments (2)
  1. The even-odd revival modulation is presented as a 'robust signature of quantum noise' and as 'unique to quantum environments,' but the derivation itself shows that for the coupling hσz/2 the quantum-noise phase Φq(nτ) vanishes when the bath is stationary with respect to HE alone, i.e., when [HE, ρ̄E]=0, and the §2.6 example shows that it also vanishes for an infinite-temperature bath. The effect therefore rests entirely on the conditioned steady-state assumption [HE-h/2, ρ̄E]=0, which the text asserts 'should be realized generically in experiment' without providing a preparation protocol, a relaxation timescale, or a polarization criterion. This is load-bearing for the central claim: if a real spin or charge bath is instead prepared in the absence of the qubit, or is only weakly polarized, the even-odd signature disappears while the rest of the transient-spectroscopy protocol remains valid. I note that the manuscript is transparent about this conditional dependence; the issue is that the advertised robustness and uniqueness are stronger than what is demonstrated. I ask the authors to either show a concrete route to preparing and verifying the conditioned state for a candidate system, or explicitly rephrase the claim as conditional on this preparation, and to propose an experimental discriminator such as measuring the echo phase as a function of bath preparation time or nuclear polarization.
  2. The only fully worked application of the Chapter-2 formalism is a single 29Si nuclear spin at infinite temperature, for which the authors explicitly state that C̃(τ) is real and that there is no quantum-noise contribution. Consequently, the concrete example neither tests nor illustrates the central even-odd quantum-noise signature. No finite-polarization example is provided to show how the predicted phase of C̃(nτ) and the even/odd alternation of revival amplitudes would appear in the reconstructed signal. A polarized-bath example, even an analytic one for a spin-1/2 bath at finite polarization under Eq. (A4), would directly support the main claim and would also clarify the degree of polarization required for a detectable even-odd effect.
minor comments (3)
  1. The caption 'Correction operators for two-qubit controlled quantum teleortation' contains a typo; 'teleortation' should be 'teleportation'.
  2. The phrase 'robust even-odd modulation' is potentially misleading in view of the sensitivity to the initial bath state discussed in the same section; a qualified phrase such as 'even-odd modulation under the conditioned bath steady state' would better match the derivation.
  3. The sentence citing 'Evidence of such destructive interference was recently observed experimentally in Ref. [55]' would be more informative if the experimental system and the type of observed evidence were identified in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Chapter 2's quantum-noise phase is derived from an explicit initial-state condition, and Chapters 3–6 are parameter-free analytic results benchmarked against external quantities.

full rationale

I walked the derivation chain of each chapter and found no step in which a claimed prediction reduces by construction to its inputs or to a load-bearing self-citation. In Chapter 2, the central relation between the cavity output field and the CPMG echo envelope is derived from the input-output formalism, the quantum Langevin equation, and a restricted-subspace approximation (Eqs. (2.4), (A21)–(A23), (A50), (A56)). The even/odd alternation of K^n tilde-C(n tau) in Eq. (2.9) is a mathematical property of the discrete Fourier transform, but the physical claim is not that the alternation exists; it is that tilde-C(n tau) acquires a nonzero imaginary part from the antisymmetrized bath correlation. That phase is derived via a Magnus expansion (Eqs. (A60)–(A75)), and the paper explicitly states the phase vanishes for the weak-coupling initial condition [H_E, rho-bar_E]=0, citing independent references [41,42] rather than assuming the result. The environmental preparation [H_E - h/2, rho-bar_E]=0 is an unverified experimental precondition, but the paper's claim is conditional on it; a conditional limitation is a correctness/robustness concern, not circularity. In Chapter 3, the matching condition sqrt(kappa_1) alpha_0 u(t) = g-tilde_1(t) is a disclosed protocol design requirement, and the entangler dynamics are solved exactly for coherent states; the concurrence is computed against the standard entanglement measure and validated with external hyperfine parameters (A/2pi = -0.25 MHz from Ref. [43]). Chapters 4–6 are analytic or simulation-based results compared with the quantum Cramér-Rao bound, standard concurrence, and independent gate-fidelity benchmarks; I found no fitted parameter secretly serving as a prediction and no uniqueness theorem imported from the authors' own prior work. Self-citation in this manuscript-based thesis consists of identifying the published articles that form the chapters; none of the load-bearing derivations depend on an unverified self-citation. The honest finding is therefore 'no significant circularity' (score 0).

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The central claims rest on standard cavity-QED formalism (input-output theory, quantum Langevin equations, RWA, adiabatic and polaron transformations) and on a clearly stated approximation hierarchy: weak-to-moderate coupling g < κ, long inter-pulse times κτ >> 1, high-Q cavity filter, Gaussian noise with second-order Magnus truncation, and the restricted-subspace replacement Eq. (A28). The most fragile premise is the conditioned environmental steady state [HE - h/2, ρ̄E] = 0, which the quantum-noise signature requires and which the paper argues but does not demonstrate is generic. Chapter 3 adds the design condition √κ1 α0 u(t) = g̃1(t) and symmetric decay κ1 = κ2 = κ/2; these are protocol requirements, disclosed as such. No parameters are fitted to data: the numbers in figures are illustrative, and the measured hyperfine coupling is imported from Ref. [43]. No new physical entities are postulated; the virtual cavities of Chapter 3 are bookkeeping tools of a cited formalism.

free parameters (2)
  • Illustrative magnetic-field and cavity parameters (Ch. 2, Fig. 2.2) = A/2π = -0.250 MHz (measured, Ref. [43]); γBz = γBx = A/2; κ/2π = 1 MHz; g/κ = 0.2; γφ^-1 = 100 μs
    Chosen for the numerical example so that echo-envelope visibility sin²(Δφ) is maximized; they illustrate the protocol and are not fitted to any data set.
  • Feasibility parameters for the entangler (Ch. 3, §3.3) = g̃1^max/2π = 1 MHz, τ = 1 μs, giving N ≈ 3, Nmax ≈ 19, C ≈ 0.95 at p = 0.01
    Illustrative values for a silicon DQD spin qubit with a magnetic-field gradient; the operative constraints N << (κτ)^4 and τ < T2* are stated in the text.
assumptions (7)
  • standard math Input-output theory and quantum Langevin equations (Gardiner-Collett)
    Used throughout Chapters 2 and 3 (Eqs. (1.50), (A18), (3.2)); standard quantum optics.
  • standard math Rotating-wave, adiabatic, and polaron transformations for the longitudinal-coupling Hamiltonian
    Chapter 3, Appendix B1, Eqs. (B2)-(B9); standard perturbative tools with stated validity conditions.
  • domain assumption Conditioned environmental steady state [HE - h/2, ρ̄E] = 0
    Eq. (A4); the quantum-noise phase Φq vanishes under the standard [HE, ρ̄E] = 0 preparation, so this premise is load-bearing for the central signature.
  • domain assumption Restricted-subspace replacement ⟨σ̃zã⟩ ≃ -⟨ã⟩ (even n) and ⟨σ̃zã†⟩ ≃ ⟨ã†⟩ (odd n)
    Eq. (A28), valid for g < κ and κτ >> 1; it turns the coupled qubit-cavity equations into a closed form.
  • domain assumption Gaussian noise statistics and second-order Magnus expansion for the environment
    Appendix A4, Eqs. (A60)-(A66); the single-nuclear-spin example avoids this approximation by exact solution.
  • domain assumption High-Q cavity filter max(|δ|, κ) << |Δ| and, for Eq. (2.8), the narrow-revival regime κT2* << 1
    Section 2.4 and Appendices A2-A3; a separate κT2* > 1 expression is used for the Fig. 2.2 example.
  • ad hoc to paper Matching condition √κ1 α0 u(t) = g̃1(t) with symmetric decay κ1 = κ2 = κ/2
    Chapter 3, Eqs. (3.3)-(3.4); defines the protocol's operating point rather than being derived from external input.

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Cite this review

Pith. "Pith review of Quantum information processing in modular cavity QED architectures." pith.science (2026). https://pith.science/paper/DZ7VIL4R

@misc{pith2026250504747,
  author       = {Pith},
  title        = {Pith review of: Quantum information processing in modular cavity QED architectures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DZ7VIL4R}},
  note         = {Machine review of arXiv:2505.04747}
}
read the original abstract

This thesis contains a collection of articles exploring various aspects of quantum information processing with cavity quantum electrodynamics (QED), starting with qubit noise spectroscopy and building towards the longer-term goal of modular quantum-computing architectures equipped with protocols for controlling and correcting the states of distantly separated qubits. The first chapter presents a self-contained introduction to the field of cavity QED. Following this introductory material, we show in Chapter 2 how measurements of the field emitted by a cavity can be leveraged for in-situ qubit noise spectroscopy in the presence of significant inhomogeneous broadening. We also identify a signature of genuinely quantum noise in the cavity output field originating from the non-commutation of bath operators acting on the qubit. In Chapter 3, we present a novel quantum-optical effect whereby a suitable modulation of a longitudinal cavity-qubit coupling can be used to entangle the state of a qubit with the path taken by a multiphoton wavepacket. Entanglement between a qubit and a which-path degree-of-freedom can in turn be used to generate entanglement between distant stationary qubits. As shown in Chapter 4, qubit-which-path entanglement can also be exploited for maximally sensitive estimation of a phase in a Mach-Zehnder interferometry setup, i.e., sensing at the quantum Cram\'er-Rao bound. In Chapter 5, we discuss strategies for realizing stabilizer measurements using qubit-conditioned phase shifts applied to propagating pulses of radiation. We find that in the context of a subsystem surface code, photon loss during such stabilizer measurements would not introduce any horizontal hook errors on the code qubits. In the sixth and final chapter, we give protocols for performing entangling gates between distant stationary qubits using Fock- or time-bin encoded photons.

Figures

Figures reproduced from arXiv: 2505.04747 by the authors.

Figure 1
Figure 1. An LC oscillator capacitively coupled to a transmission line . . . . . . . . . . . . . . [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 5
Figure 5. Tetrahedron state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Gate infidelity in the presence of imperfections . . . . . . . . . . . . . . . . . . . . . [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figures from the paper (24 more)
Figure 1.1
Figure 1.1. Figure 1.1: Left: At zero detuning (δ = ωq − ωc = 0) and for gx = 0, the product states |e,n⟩ and |g,n+1⟩ form degenerate doublets separated in energy from the ground state |g,0⟩ by integer multiples of ωc = ωq. For δ = 0 and gx ̸= 0, the eigenstates of the Jaynes-Cummings Hamil…
Figure 1.2
Figure 1.2. Figure 1.2: In the strong coupling regime and for weak resonant driving, the probability [PITH_FULL_IMAGE:figures/full_fig_p018_1_2.png]
Figure 1.3
Figure 1.3. Figure 1.3: Phase-space trajectories generated by a parametrically modulated longitudinal coupling: Within a rotating-wave ap [PITH_FULL_IMAGE:figures/full_fig_p022_1_3.png]
Figure 1.4
Figure 1.4. Figure 1.4: The incoming [rin(t)] and outgoing [rout(t)] fields in the transmission line can be related to the field of the LC oscillator through a boundary condition called the input-output relation [Eq. (1.50)]. In terms of circuit parameters, the resonance frequency ωc of the…
Figure 2.1
Figure 2.1. Figure 2.1: A typical cavity-QED setup. The transmission spectrum is obtained from the linear response of the output signal [PITH_FULL_IMAGE:figures/full_fig_p033_2_1.png]
Figure 2.2
Figure 2.2. Figure 2.2: (a) Inhomogeneously broadened cavity transmission at [PITH_FULL_IMAGE:figures/full_fig_p038_2_2.png]
Figure 3.1
Figure 3.1. Figure 3.1: In the presence of a longitudinal cavity-qubit coupling modulated at the cavity frequency with envelope ˜g [PITH_FULL_IMAGE:figures/full_fig_p062_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: An interferometry setup can be used to entangle the which-path degree of freedom with a target qubit initialized in [PITH_FULL_IMAGE:figures/full_fig_p066_3_2.png]
Figure 4.1
Figure 4.1. Figure 4.1: A Mach-Zehnder interferometer can be used to estimate the differential phase shift [PITH_FULL_IMAGE:figures/full_fig_p087_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: Reduced Wigner distribution W(x+, p+) = R dx−d p−W(x+, p+, x−, p−) of mode a+, where here, W(x+, p+, x−, p−) is the Wigner distribution of the state resulting from an initial ECS [Eq. (4.8)] for α = 3, φ1 = 0.5, and φ2 = 0. Homodyne detection of mode a+ with a local-…
Figure 4.3
Figure 4.3. Figure 4.3: Precision δ φ [Eq. (4.6)] as a function of φ, relative to the standard quantum limit δ φSQL ≡ [(1− p)Mn¯] −1/2 , for an ECS with ¯n = 10 and p = 0.05 (5% photon loss). The values that can be achieved with homodyne detection (solid black line) and photon counting (das…
Figure 4.4
Figure 4.4. Figure 4.4: Left axis: Precision given by the quantum CRB, [PITH_FULL_IMAGE:figures/full_fig_p092_4_4.png]
Figure 5.1
Figure 5.1. Figure 5.1: A qubit-state-selective phase shift on an incoming coherent state [PITH_FULL_IMAGE:figures/full_fig_p106_5_1.png]
Figure 5.2
Figure 5.2. Figure 5.2: (a) The unit cell of the subsystem surface code [43]. Physical qubits represented by solid black dots are located on the [PITH_FULL_IMAGE:figures/full_fig_p107_5_2.png]
Figure 5.3
Figure 5.3. Figure 5.3: Horizontal hook error Z2Z3 due to photon loss during a parity check. simply applied before/after the Z-basis parity check, as described in Eq. (5.3). In that case, we take |Ξ⟩ to describe the state of the three qubits after the first set of Hadamards. In the presence…
Figure 5.4
Figure 5.4. Figure 5.4: The total error ptot [Eq. (5.18)] is given by the sum of competing terms: measurement errors, which decrease with α, and errors due to photon loss, which increase with α. For simplicity, we assume that ηi = η for all i. The total probability of an error occurring as …
Figure 5.5
Figure 5.5. Figure 5.5: (a) Six qubits can be associated with the six edges of a tetrahedron. Each of the stabilizers in Eq. (5.20) is a product of [PITH_FULL_IMAGE:figures/full_fig_p114_5_5.png]
Figure 5.6
Figure 5.6. Figure 5.6: The preparation fidelity F = ⟨T|ρ|T⟩ accounting for measurement errors and errors due to photon loss. produce states orthogonal to |T⟩. To leading order in p1,2, and neglecting corrections O(p1,2 pM), we then have ⟨W ⟩ ≃ −1 2 +[1−(1− pM) 6 ] +3(p1 + p2). (5.24) Here,…
Figure 6.1
Figure 6.1. Figure 6.1: A cavity-assisted Raman process with tunable strength [PITH_FULL_IMAGE:figures/full_fig_p132_6_1.png]
Figure 6.2
Figure 6.2. Figure 6.2: Two ways of realizing qubit-state-conditioned phase shifts on the photonic waveform: (a) Strong resonant coupling [PITH_FULL_IMAGE:figures/full_fig_p135_6_2.png]
Figure 6.3
Figure 6.3. Figure 6.3: (a) Two qubits Q1 and Q2, each coupled to their own cavity mode, are connected by a long transmission line. A CZ gate between Q1 and Q2 can be realized by sending a Fock-state qubit, encoded in the presence or absence of a photon having a waveform of duration τ, from…
Figure 6.4
Figure 6.4. Figure 6.4: (a) Schematic of the imagined setup for the ancilla-assisted CZ gate: A two-qubit gate can be applied to cavity-coupled [PITH_FULL_IMAGE:figures/full_fig_p139_6_4.png]
Figure 6.5
Figure 6.5. Figure 6.5: (a) The gate infidelity ε = 1 − F evaluated as a function of τ for a fixed value of κ/2π = 50 MHz and a total gate duration T = 16τ. In the absence of qubit decoherence (T1 → ∞), the gate infidelity is proportional to (κτ) −2 for κτ ≳ 10, while for a finite T1, compe…
Figure 6
Figure 6. Figure 6: (c), we have [PITH_FULL_IMAGE:figures/full_fig_p148_6.png]

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