Decoherence mitigation by real-time noise acquisition

At a Glance

Metadata	Details
Publication Date	2021-08-04
Journal	Journal of Applied Physics
Authors	G. Braunbeck, Maximilian Kaindl, A. M. Waeber, Friedemann Reinhard
Institutions	Technical University of Munich, Schott (Germany)
Citations	1
Analysis	Full AI Review Included

Technical Documentation: Decoherence Mitigation in NV Qubits using Quasi-Feedforward Decoupling

6CCVD Reference Document: Q-SENSE-2024-001

Executive Summary

This research demonstrates a critical advancement in quantum control by successfully mitigating classical noise effects on Nitrogen-Vacancy (NV) center qubits using a quasi-feedforward (qff) decoupling scheme. This approach is highly relevant for high-bandwidth quantum sensing and computation applications.

Core Achievement: Neutralized the dephasing effect induced by classical current noise in nearby conductors, recovering the full intrinsic qubit coherence time (T₂).
Performance Gain: Coherence time (T₂) was increased sevenfold, from a noise-limited decay of (55 ± 13) ns up to (366 ± 133) ns, matching the unperturbed intrinsic T₂.
Gate Fidelity: Demonstrated single-qubit gates with an infidelity of approximately 10^-2, with theoretical projections indicating a potential limit of 10^-5 through hardware optimization.
Methodology: The scheme combines dynamical decoupling with feedforward control implemented via post-selection, correlating the qubit readout with real-time classical current measurements.
Critical Application: The technique is essential for nanoscale magnetic resonance imaging (MRI) and quantum control protocols requiring strong, fast control pulses (e.g., 100 mA peak currents with 100 MHz bandwidth).
Material Insight: The study highlights that current limitations (infidelity, 25 nm localization limit) are dominated by physical structure imperfections, such as the granularity of electroplated gold and thermal disposition, creating a direct need for high-purity MPCVD diamond and precision metalization.

Technical Specifications

The following hard data points were extracted from the experimental results, demonstrating the performance metrics of the quasi-feedforward decoupling scheme.

Parameter	Value	Unit	Context
Intrinsic Coherence Time (T₂)	1.4 ± 0.1	µs	Measured on the IIa diamond sample without current pulse perturbation.
Noise-Limited T₂ (Uncorrected)	55 ± 13	ns	Short decay observed in the presence of random-duration current pulses.
Corrected T₂ (qff)	366 ± 133	ns	Coherence time recovered using quasi-feedforward decoupling (sevenfold increase).
Achieved Gate Infidelity	$\approx$ 10^-2	N/A	Infidelity per $\pi$-pulse phase gate.
Potential Gate Infidelity Limit	10^-5	N/A	Theoretical limit based on 14-bit digitization accuracy.
Required Peak Current (MRI)	100	mA	Required for fast control pulses in nanoscale MRI.
Required Bandwidth (MRI)	100	MHz	Required for fast control pulses.
Current-Magnetic Field Coupling ($\Delta_{0}$)	9.48 ± 0.08	rad/(mA·µs)	Calibration constant for NV phase shift.
Conductor Cross-Section	$\approx$ 1	µm²	Cross-section of the microfabricated gold conductors.

Key Methodologies

The experiment utilized a modified Hahn Echo sequence combined with high-speed classical current acquisition and post-selection processing.

Qubit System: A single NV center in a diamond sample (both Ib and IIa grades tested) was positioned in close proximity (µm scale) to a microfabricated gold wire structure.
Pulse Sequence: A modified Hahn Echo sequence ($\pi/2 - \tau - \pi - \tau - \pi/2 - \text{Readout}$) was used. A current pulse of fixed amplitude ($I_{0}$) and varying duration ($T_{I}$) was applied during the second free evolution period ($\tau$).
Microwave Control Chain: Microwave pulses were generated, split into in-phase and quadrature components using a 90°-splitter (Mini-Circuits ZAPDQ-4+), individually switched (Mini-Circuits ZASWA-2-50DR+), combined (Mini-Circuits ZX10-2-442+), and amplified (Mini-Circuits ZHL-16W-43+).
Current Application: Current pulses (up to 60 mA tested) were sourced from a KORAD KA3005P, controlled by a high-side switch (iC-Haus iC-HGP), and delivered to the gold structure via a bias tee (Taylor BT-A1080-3).
Noise Measurement: Current fluctuations were measured simultaneously with the qubit evolution by monitoring the voltage drop across a 50 $\Omega$ series resistor using a differential probe (Yokogawa 701920).
Data Correlation: A high-speed oscilloscope (Spectrum M4i.4451-x8) with 500 MS/s and 14-bit resolution recorded the integrated current ($\int I(t) dt$) for every repetition.
Quasi-Feedforward Decoupling: The measured integrated current was converted into a phase shift ($\phi$) and used to condition the readout. Decoherence was mitigated by post-selecting only those measurements where the final $\pi/2$-pulse phase matched the required feedforward phase (discretized into four quadrants).

6CCVD Solutions & Capabilities

The research successfully validates the quasi-feedforward scheme but identifies that the ultimate performance limit (10^-5 infidelity) is currently constrained by the physical quality and stability of the microfabricated conductors and the diamond substrate interface. 6CCVD provides the high-specification MPCVD diamond materials and precision fabrication services necessary to overcome these limitations and achieve next-generation quantum performance.

Applicable Materials

To replicate or extend this research, particularly targeting the 10^-5 infidelity limit, 6CCVD recommends the following materials:

Electronic Grade Single Crystal Diamond (SCD): Required for maximizing the intrinsic coherence time (T₂). Our SCD material offers ultra-low nitrogen content, minimizing background noise and strain, which is crucial for high-fidelity quantum operations.
Optical Grade SCD: Ideal for applications requiring precise NV center creation (e.g., ion implantation) and optimal photon collection efficiency during readout.
Thick SCD Substrates: The paper noted thermal disposition and heat expansion as potential noise sources. 6CCVD offers SCD substrates up to 500 µm thick, providing superior thermal management and heat sinking compared to the glass/polymer bonded structures used in the experiment.

Customization Potential

The paper explicitly cites limitations arising from the granularity of electroplated gold and uncertainty in the current path (up to 25 nm). 6CCVD’s internal fabrication capabilities directly address these challenges:

Research Requirement / Limitation	6CCVD Customization Solution	Technical Advantage
Granularity of Electroplated Gold	Precision Metalization Stacks (Ti/Pt/Au, W, Cu)	We utilize high-vacuum evaporation and sputtering, ensuring uniform, low-roughness metal films, eliminating the granularity issues inherent to electroplating.
Sub-micron Current Path Definition	Ultra-Smooth Polishing (Ra < 1 nm for SCD)	Our atomically smooth SCD surfaces enable high-resolution lithography, ensuring the current path geometry is defined with sub-10 nm precision, overcoming the 25 nm uncertainty limitation.
Complex Device Geometry	Custom Laser Cutting and Etching	We provide custom shaping and laser cutting services for complex microfabricated wire geometries (e.g., star-shaped structures) on SCD wafers up to 125mm in size.
Integration Flexibility	Custom Thicknesses (0.1 µm to 500 µm)	We supply SCD and PCD plates tailored to specific integration needs, whether for thin membranes or robust, thick substrates for thermal stability.

Engineering Support

6CCVD’s in-house team of PhD material scientists and quantum engineers specializes in optimizing diamond properties for demanding applications. We offer comprehensive support for projects involving:

Quantum Sensing and Nanoscale MRI: Assisting with material selection, NV creation strategies, and optimizing substrate interfaces to minimize decoherence from thermal and structural noise.
High-Bandwidth Quantum Control: Consulting on metalization schemes and substrate thickness to manage high current densities (100 mA) and thermal load required for fast control pulses.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

We present a scheme to neutralize the dephasing effect induced by classical noise on a qubit. The scheme builds upon the key idea that this kind of noise can be recorded by a classical device during the qubit evolution, and that its effect can be undone by a suitable control sequence that is conditioned on the measurement result. We specifically demonstrate this scheme on a nitrogen-vacancy center that strongly couples to current noise in a nearby conductor. By conditioning the readout observable on a measurement of the current, we recover the full qubit coherence and the qubit’s intrinsic coherence time T2. We demonstrate that this scheme provides a simple way to implement single-qubit gates with an infidelity of 10−2 even if they are driven by noisy sources, and we estimate that an infidelity of 10−5 could be reached with additional improvements. We anticipate this method to find widespread adoption in experiments using fast control pulses driven from strong currents, in particular, in nanoscale magnetic resonance imaging, where control of peak currents of 100 mA with a bandwidth of 100 MHz is required.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0048140