Engineering of the qubit initialization in an imperfect physical system
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-06-16 |
| Journal | Journal of Physics B Atomic Molecular and Optical Physics |
| Authors | Tianfeng Chen, Lin Wan, Jiamin Qiu, Hong Yan Peng, Jie Lu |
| Institutions | Shanghai University, Soochow University |
| Citations | 2 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research details an advanced quantum control protocol utilizing invariant-based inverse engineering (Shortcuts to Adiabaticity, STA) to achieve robust, high-fidelity qubit initialization in imperfect physical systems, specifically focusing on Rare-Earth Ion (REI) ensembles.
- Enhanced Robustness: The method minimizes the systematic error sensitivity (qs) to laser intensity variations by a factor of 43 compared to previous pulses, achieving >97% fidelity despite ±30% fractional variation in the Rabi frequency.
- Decoherence Mitigation: The time the ions spend in the intermediate excited state is reduced by a factor of 17 (to 0.04 µs) during the 4 µs operation, significantly decreasing the probability of spontaneous decay and increasing operational fidelity in coherence-limited systems.
- High Fidelity in Ensemble Qubits: The protocol maintains an operational fidelity greater than 99.7% across a tightly packed frequency interval (±270 kHz), ensuring uniform control over the inhomogeneously broadened ensemble.
- Spatial Inhomogeneity Tolerance: The robustness against spatial inhomogeneity in the Gaussian laser beam profile allows for high effective fidelity (93%) without requiring a small-throughput pinhole in the detection system, thereby increasing the signal-to-noise ratio (SNR).
- Low Off-Resonant Excitation: The engineered pulses suppress unwanted excitations to neighboring qubits, limiting off-resonant excitation to approximately 5.8% at 3.5 MHz detuning.
- Universal Applicability: The pulse design methodology is applicable to any quantum system addressed in frequency, including nitrogen-vacancy (NV) centers, superconducting qubits, quantum dots, and molecular qubits.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Operation Time (tf) | 4 | µs | Total pulse duration for initialization. |
| Excited State Time | 0.04 | µs | Time spent in the intermediate excited state (17x reduction vs. prior work). |
| Maximum Rabi Frequency (Ωs,p) | < 2 | MHz | Maximum required magnitude, ensuring physical feasibility. |
| High-Fidelity Detuning Range | ±270 | kHz | Frequency range where fidelity remains >99.7%. |
| Off-Resonant Excitation | 5.8 | % | Excitation level at ±3.5 MHz detuning (neighboring qubits). |
| Robustness to Intensity Variation (η) | ±30 | % | Fractional Rabi frequency variation where fidelity remains >97% (at zero detuning). |
| Systematic Error Sensitivity (qs) | 0.0137 | Unitless | Measure of robustness against laser intensity inhomogeneity (43 times smaller than previous pulses). |
| Effective Fidelity (Gaussian Beam) | 93 | % | Achieved when collecting signal from a beam diameter of 2w0. |
| Target State | (1/√2)( | 1⟩ + i | 0⟩) |
Key Methodologies
Section titled “Key Methodologies”The robust pulse design relies on combining invariant-based inverse engineering with perturbation theory to minimize sensitivity to systematic errors.
- Hamiltonian and Invariant Definition: The three-level Λ-configuration system Hamiltonian H0(t) is defined under the rotating wave approximation. The Lewis-Riesenfeld (LR) invariant I(t) is constructed, whose eigenstates define the desired state evolution path |Φ0(t)⟩.
- Pulse Parameterization: The Rabi frequencies (Ωs, Ωp) are derived from two time-dependent parameters, γ(t) and β(t). These parameters are defined using complex ansatz functions composed of multiple Gaussian terms (for γ(t)) and sinusoidal terms (for β(t)).
- Boundary Condition Enforcement: Parameters are optimized to satisfy initial and final state conditions (|Φ0(0)⟩ = |1⟩ and |Φ0(tf)⟩ = |Ψtarget⟩). Additionally, parameters are constrained to ensure Rabi frequencies start and end at zero (Ωs,p(0, tf) = 0) to maintain smooth pulse profiles.
- Robustness Optimization: The total Hamiltonian H = H0 + H1 includes a perturbation term H1 representing spatial inhomogeneity in laser intensity. The systematic error sensitivity (qs) is calculated using perturbation theory.
- Multi-Objective Optimization: The multiple degrees of freedom introduced by the Gaussian (Am, Bm, Cm) and sinusoidal (an) components are optimized simultaneously to minimize qs (maximizing robustness) while ensuring low off-resonant excitation and fast operation time.
- Physical Generation: The resulting time-dependent Rabi frequency profiles are designed to be physically feasible, with magnitudes less than 2 MHz, suitable for generation via an arbitrary waveform generator driving an acousto-optical modulator (AOM).
Commercial Applications
Section titled “Commercial Applications”The robust quantum control methods developed are critical for advancing quantum technologies where environmental noise, manufacturing imperfections, and laser inhomogeneity limit performance.
- Quantum Computing: Essential for high-fidelity, fast initialization of qubits (the startup step for all quantum algorithms) in solid-state platforms.
- Quantum Memory: Directly applicable to Rare-Earth Ion (REI) doped crystals, improving the reliability and speed of data storage and retrieval in quantum repeaters and networks.
- Solid-State Quantum Devices: Provides robust control solutions for frequency-addressed systems, including:
- Nitrogen-Vacancy (NV) centers in diamond.
- Quantum dots.
- Molecular qubit systems.
- Superconducting Qubits: The inverse engineering approach can be adapted to design robust control pulses for superconducting circuits, mitigating the effects of flux noise and control parameter inaccuracies.
- Quantum Metrology: Enables the creation of highly coherent superposition states necessary for sensitive quantum sensors operating in noisy, real-world environments.
View Original Abstract
Abstract We propose a method to engineer the light matter interaction while initializing a qubit present of physical constraints utilizing the inverse engineering. Combining the multiple degrees of freedom in the pulse parameters with the perturbation theory, we develop pulses to initialize the qubit within a tightly packed frequency interval to an arbitrary superposition state with high fidelity. Importantly, the initialization induces low off-resonant excitations to the neighboring qubits, and it is robust against the spatial inhomogeneity in the laser intensity. We apply the method to the ensemble rare-earth ions system, and simulations show that the initialization is more robust against the variations in laser intensity than the previous pulses, and reduces the time that ions spend in the intermediate excited state by a factor of 17. The method is applicable to any systems addressed in frequency such as nitrogen-vacancy centers, superconducting qubits, quantum dots, and molecular qubit systems.