Quantum Fourier transform for nanoscale quantum sensing

At a Glance

Metadata	Details
Publication Date	2021-08-09
Journal	npj Quantum Information
Authors	Vadim Vorobyov, Sebastian Zaiser, Nikolas Abt, Jonas Meinel, Durga Bhaktavatsala Rao Dasari
Institutions	University of Stuttgart, Center for Integrated Quantum Science and Technology
Citations	36
Analysis	Full AI Review Included

Technical Documentation & Analysis: Quantum Fourier Transform for Nanoscale Quantum Sensing

This document analyzes the requirements and achievements detailed in the research paper “Quantum Fourier transform for nanoscale quantum sensing” (Vorobyov et al., npj Quantum Information (2021) 7:124). It outlines how 6CCVD’s specialized MPCVD diamond materials and fabrication services are essential for replicating, scaling, and advancing this high-performance quantum sensing technology.

Executive Summary

The research successfully demonstrates the application of the Quantum Fourier Transform (QFT) algorithm to significantly enhance the performance of a diamond-based quantum sensor, specifically targeting high dynamic range nanoscale NMR.

QFT Implementation: The QFT algorithm was implemented in a hybrid quantum register consisting of a Nitrogen-Vacancy (NV) center electron spin, a ¹⁴N nuclear spin (qutrit), and two ¹³C nuclear spins (qubits).
Enhanced Dynamic Range: The QFT-based protocol improved the dynamic range (DR ≈ 84√Hz) by a factor of 4.2 compared to single-qubit Ramsey measurements, overcoming the traditional sensitivity-dynamic range trade-off.
High-Resolution Sensing: Achieved high-resolution correlation spectroscopy for nanoscale NMR, resolving ¹³C nuclear spins with a spectral resolution of ~70 Hz (~10 ppm).
Unambiguous Digitization: The QFT$^+$ algorithm enables efficient and unambiguous phase-to-population mapping, localizing the signal probability distribution within a narrow interval.
Material Requirement: The protocol relies critically on the long coherence time (T₂ = 430 µs) of the NV electron spin, necessitating ultra-high purity Single Crystal Diamond (SCD) substrates.
Scalability Demonstrated: The study confirms that multi-qubit algorithms benefit quantum sensing, showing improved signal-to-noise ratio (SNR) scaling with the number of qubits, analogous to classical Analog-to-Digital Conversion (ADC).

Technical Specifications

The following hard data points were extracted from the experimental results:

Parameter	Value	Unit	Context
NV Electron Spin Coherence Time (T₂)	430	µs	Measured via Hahn echo at ambient conditions
Operating Magnetic Field (B₀)	0.7	T	Ambient conditions
Quantum Register Size	12	Levels	Hybrid system (1 NV e⁻ spin, 1 ¹⁴N qutrit, 2 ¹³C qubits)
Spectral Resolution (NMR)	~70	Hz	Corresponding to ~10 ppm resolution
Maximum Unambiguously Resolved Field (B_ac)	2.2	µT	Achieved using QFT$^+$ phase estimation
Dynamic Range (DR)	~84	√Hz	Improved by 4.2x over single-qubit Ramsey
¹³C Hyperfine Coupling (A_zz)	414, 90	kHz	For the two specific ¹³C ancillary qubits
QFT Time Overhead	~300	µs	Additional time required for QFT implementation
Polishing Requirement (SCD)	Ra < 1	nm	Required for high-fidelity quantum gate operations

Key Methodologies

The experiment utilized a complex hybrid quantum register and advanced correlation spectroscopy protocols enabled by high-quality diamond material.

Material Platform: Single Nitrogen-Vacancy (NV) center electron spin in ultra-pure Single Crystal Diamond (SCD) served as the sensor. The memory register consisted of three nearby nuclear spins (one ¹⁴N qutrit and two ¹³C qubits).
Initialization: The sensor was initialized to the |0〉 state. The register spins were prepared in a superposition state using local Hadamard and generalized Chrestenson gates.
Phase Encoding: The electron spin was entangled with the nuclear register via CNOT gates. The system then acquired a phase (Φ) during an interrogation time (τ) under the effective Hamiltonian, converting the external signal (e.g., AC magnetic field) into a phase shift.
Quantum Fourier Transform (QFT): The acquired phase state was mapped to a bit representation (population basis) using the QFT algorithm, implemented using optimized conditional non-local rotational gates to maintain high fidelity.
Correlation Protocol: The measurement involved two phase acquisition steps separated by a long correlation time (T_c), encoding the net relative phase (ΔΦ = Φ₁ - Φ₂) into the nuclear register.
Readout: The inverse QFT (QFT$^+$) was applied to convert the phase difference (ΔΦ) into the computational basis (I_z) for single-shot readout, ensuring unambiguous signal estimation across the full 2π range.

6CCVD Solutions & Capabilities

This research highlights the critical need for high-quality, customized diamond substrates and advanced fabrication techniques. 6CCVD is uniquely positioned to supply the materials and services required to replicate and scale this cutting-edge quantum sensing technology.

Requirement from Research Paper	6CCVD Solution & Capability	Technical Advantage
Ultra-High Purity Diamond Host (Required for T₂ = 430 µs)	Optical Grade Single Crystal Diamond (SCD)	Our MPCVD SCD material offers extremely low defect density and minimal strain, maximizing NV electron spin coherence time (T₂) and enabling operation at the Standard Quantum Limit (SQL).
Controlled Nuclear Spin Register (Specific ¹⁴N and ¹³C isolation)	Custom Isotope Control	6CCVD provides SCD substrates with tailored nitrogen concentration (for NV creation) and controlled ¹³C abundance (e.g., depleted or enriched ¹³C) to optimize the density, isolation, and coupling of ancillary nuclear qubits for scalable quantum registers.
Large Area Substrates for Scaling (Future multi-qubit arrays)	Large Format SCD/PCD Plates	We supply SCD plates up to 10x10mm and Polycrystalline Diamond (PCD) wafers up to 125mm in diameter, facilitating the scaling of multi-qubit registers and integration into commercial quantum devices.
High-Fidelity Qubit Control (Requires smooth, low-defect surfaces)	Precision Polishing (Ra < 1 nm)	Our SCD surfaces are polished to an atomic level (Ra < 1 nm), minimizing surface defects and reducing decoherence pathways critical for maintaining the fidelity of complex quantum gate operations (e.g., QFT).
RF/Microwave Delivery Structures (Required for AC field sensing and control pulses)	Custom Metalization Services	6CCVD offers internal metalization capabilities, including deposition of Au, Pt, Pd, Ti, W, and Cu. This is essential for fabricating high-quality microwave striplines and RF antennas directly onto the diamond surface for precise control of the NV center and nuclear spins.
Custom Dimensions and Integration	Custom Dimensions & Laser Cutting	We provide custom plate/wafer dimensions and thicknesses (SCD/PCD from 0.1 µm to 500 µm, substrates up to 10 mm), along with precision laser cutting services, ensuring seamless integration into existing experimental setups.

Engineering Support: 6CCVD’s in-house PhD team specializes in MPCVD growth and material characterization for quantum applications. We offer expert consultation on material selection, defect engineering, and surface preparation necessary for high dynamic range nanoscale NMR and QFT-based quantum sensing projects.

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

Tech Support

Original Source

DOI: https://doi.org/10.1038/s41534-021-00463-6