[Paper Review] Arbitrarily accurate passband composite pulses for dynamical suppression of amplitude noise

Elica Kyoseva, Nikolay V. Vitanov|arXiv (Cornell University)|Oct 26, 2013

Laser-Matter Interactions and Applications36 references32 citations

TL;DR

This paper presents a novel analytical method to design arbitrarily accurate passband (PB) composite pulses for robust quantum control by concatenating broadband (B) and narrowband (N) pulse sequences. The approach yields exact analytic formulas for pulse phases and inversion profiles, enabling tunable, nearly rectangular excitation profiles with high-order suppression of amplitude noise around pulse areas π and 0, achieving ultrahigh fidelity beyond fault-tolerance thresholds.

ABSTRACT

We introduce flexible high-fidelity passband (PB) composite pulse sequences constructed by concatenation of recently derived arbitrarily large and arbitrarily accurate broadband $\mathcal{B}$ and narrowband $\mathcal{N}$ composite sequences. Our PB sequences allow to produce flexible and tunable nearly rectangular two-state inversion profiles as a function of the individual pulse area because the width and the rectangularity of these profiles can be adjusted at will. Moreover, these PB sequences suppress excitation around pulse area $0$ and $2\pi$, and suppress deviations from complete population inversion around pulse area $\pi$ to arbitrarily high orders. These features makes them a valuable tool for high-fidelity qubit operations in the presence of relatively strong amplitude noise. We construct two types of PB pulses: $\mathcal{N}(\mathcal{B})$ in which a broadband pulse is nested into a narrowband pulse, and $\mathcal{B}(\mathcal{N})$ in which a narrowband pulse is nested into a broadband pulse; the latter sequences deliver narrower profiles. We derive exact analytic formulas for the composite phases of the PB pulses and exact analytic formulas for the inversion profiles. These formulas allow an easy estimation of the experimental resources needed for any desired qubit inversion profile.

Motivation & Objective

• To develop a scalable, analytical method for designing high-fidelity composite pulses that suppress amplitude noise in quantum systems.
• To enable flexible, tunable excitation profiles with arbitrarily narrow rectangular regions around π pulse area and flat bottoms around 0 and 2π.
• To overcome limitations of prior numerical or iterative methods by providing exact analytic expressions for pulse phases and inversion profiles.
• To achieve arbitrarily high-order suppression of errors due to pulse amplitude fluctuations, particularly around π and 0.
• To support practical implementation in trapped ions, ultracold atoms, and quantum information processing with precise resource estimation.

Proposed method

• Constructing passband (PB) pulses via concatenation of broadband (B) and narrowband (N) composite sequences, each defined by analytic formulas for odd numbers of pulses.
• Deriving exact analytic expressions for composite pulse phases using the SU(2) propagator formalism and phase optimization to cancel errors to arbitrary order.
• Formulating two types of PB pulses: N(B) (broadband nested in narrowband) and B(N) (narrowband nested in broadband), with distinct profile widths.
• Using the Cayley-Klein parameterization of the unitary propagator to model population inversion as a function of pulse area A.
• Solving a system of algebraic equations to enforce zero derivatives of the U11 matrix element at A=π (for flat top) and A=0 (for flat bottom), achieving high-order error suppression.
• Providing closed-form analytic expressions for the full excitation profile, enabling direct estimation of required experimental resources for desired fidelity and profile shape.

Experimental results

Research questions

• RQ1 Can passband composite pulses be designed with arbitrarily high accuracy and large size using analytical methods rather than numerical optimization?
• RQ2 How can both flat-top (near-π) and flat-bottom (near-0) excitation profiles be simultaneously achieved with high-order suppression of amplitude noise?
• RQ3 What is the impact of pulse sequence architecture (N(B) vs. B(N)) on the width and steepness of the resulting inversion profile?
• RQ4 Can exact analytic formulas for the composite phases and inversion profiles be derived to enable precise experimental planning?
• RQ5 To what extent can such pulses exceed fault-tolerance thresholds in fidelity under realistic amplitude noise?

Key findings

• The proposed N(B) and B(N) composite pulse sequences achieve arbitrarily high-order suppression of amplitude noise: O(ǫ^Nb) around π and O(ǫ^Nn) around 0, where Nb and Nn are odd numbers of pulses.
• Exact analytic formulas are derived for the composite pulse phases and the full inversion profile, enabling precise prediction of pulse behavior without numerical simulation.
• The B(N) sequence produces narrower excitation profiles than N(B), offering better selectivity for local qubit addressing in arrays.
• The method allows arbitrary tuning of the rectangularity and width of the flat top region, enabling flexible design of excitation profiles for specific quantum control tasks.
• The approach supports scalable, high-fidelity quantum operations with fidelity well beyond the fault-tolerance threshold, even under moderate amplitude noise.
• The analytical framework allows direct estimation of required experimental resources (e.g., number of pulses, phase shifts) for any desired profile, enhancing practical feasibility.