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APS March Meeting Abstracts

QSCOUT: Continuously parameterized Mølmer-Sørensen gates for quantum computing circuits (Part II)

Christopher G. Yale, Ashlyn D. Burch, Matthew N. H. Chow, Daniel Lobser, Megan Ivory, Melissa Revelle, Swarnadeep Majumder, Titus Morris, Raphael C. Pooser, Ryan Shaffer, Hang Ren, Emiliia Dyrenkova, Hartmut Häffner, Susan Clark

Published Mar 1, 2023• 0 citations

Abstract

Continuously Parameterized Mølmer-Sørensen Gates 2 • The MS gate has an entangling interaction of the form: 𝑀𝑆 𝜃, 𝜙 = exp -𝑖 𝜃 2 cos 𝜙 𝜎 𝑥 + sin 𝜙 𝜎 𝑦 ⊗2• 𝜃 is related to the amount of entanglement from the gate • Most quantum computers have not previously offered arbitrary 𝜃 for the two-qubit gate (IonQ only offers 𝑀𝑆( 𝜋 2 ), Quantinuum recently announced 𝑀𝑆(𝜃)) Enables: • Reduction in quantum circuit depth • Less error / more coherence per gate for smaller 𝜽 Key Elements of 𝑀𝑆(𝜃) 3• How do we realize an arbitrary-angle 𝑴𝑺(𝜽) gate?• Global tone and two individual tones to form the needed red-and blue-detuned Raman transition• All tones have a Gaussian pulse envelope to limit displacement errors [see B. Ruzic B67.00012 (this session)]• To set the angular enclosure, we adjust the global beam power Distortion correctionSources of Error:• 𝜹𝜽 (coherent rotation errors) → distortion/saturation in global beam control electronics• 𝜹𝝓 (coherent phase errors) → resulting AC Stark shifts

DOI: 10.2172/2431885

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Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally entangling gatesets. In this work, we provide a comprehensive and pedagogical discussion on how to practically implement these continuously parameterized Mølmer Sørensen gates on the Quantum Scientific Computing Open User Testbed (QSCOUT), a low-level trappedion processor. To generate the arbitrary entangling angles, θ, we simply scale the amplitude of light used to generate the entanglement. However, doing so requires careful consideration of amplifier saturation as well as the variable light shifts that result. As such, we describe a method to calibrate and cancel the dominant fourth-order effects, followed by a dynamic virtual phase advance during the gate to cancel any residual light shifts, and find a linear scaling between θ and the residual light shift. Once, we have considered and calibrated these effects, we demonstrate performance improvement with decreasing θ. Finally, we describe nuances of hardware control to transform the XX-type interaction of the arbitraryangle Mølmer-Sørensen gate into a phase-agnostic and crosstalk-mitigating ZZ interaction.

FINDING: Composite pulse sequences on the Bloch sphere achieve arbitrarily accurate SU(2) rotations by nesting error-compensating rotations, with the key structural insight being that any single-qubit gate is a 3D rotation in SU(2) ≅ SO(3), parameterized by Euler angles on the sphere. MATH: - Qubit state: |ψ⟩ = cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩, with θ ∈ [0,π], φ ∈ [0,2π) — the Bloch sphere coordinates. - SU(2) generators: Pauli matrices σ_x, σ_y, σ_z, satisfying [σ_i, σ_j] = 2iε_{ijk}σ_k. - Rotation operator: R_n̂(θ) = exp(−iθ n̂·σ/2) = cos(θ/2)I − i sin(θ/2)(n̂·σ). - Composite pulse: U_total = Π_k R_{n̂_k}(θ_k), designed so that first-order (and higher) error terms in pulse amplitude/duration vanish: ∂U_total/∂ε |_{ε=0} = 0, up to desired order N. - The arXiv paper (1810.03833) explicitly constructs sequences with arbitrary N, using nested commutators of rotation axes to cancel error terms — a Lie-algebraic approach. CONNECTION: - The Bloch sphere is the unit sphere S², and SU(2) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

The Mølmer-Sørensen (MS) gate is a two-qubit controlled-phase gate in ion traps that is highly valued due to its ability to preserve the motional state of the ions. However, its fidelity is obstructed by errors affecting the motion of the ions as well as the rotation of the qubits. In this work, we propose an amplitude-modulated composite MS gate which features high fidelity robust to gate timing, detuning and coupling errors and is also tolerant of a.c. Stark shifts and drifting detuning errors.