Toward the Speed Limit of High-Fidelity Two-Qubit Gates

At a Glance

Metadata	Details
Publication Date	2022-06-08
Journal	Physical Review Letters
Authors	Swathi S. Hegde, Jingfu Zhang, Dieter Suter
Institutions	TU Dortmund University
Citations	10
Analysis	Full AI Review Included

Technical Documentation: High-Fidelity, Speed-Limit 2-Qubit Gates in NV Diamond

This document analyzes the research paper “Towards the speed limit of high fidelity 2-qubit gates” (arXiv:2205.02324v1) and outlines how 6CCVD’s advanced MPCVD diamond materials and fabrication services can support and accelerate similar quantum computing research.

Executive Summary

This research demonstrates a highly efficient method for implementing fast, high-fidelity 2-qubit gates using a Nitrogen-Vacancy (NV) center in diamond, leveraging the static internal Hamiltonian rather than complex external control fields.

Core Achievement: Implementation of a Controlled Rotation (U_CR) gate by utilizing the free evolution of the system under its internal Hamiltonian, eliminating errors associated with time-dependent control fields.
Speed Limit Attained: The gate operation achieves the quantum speed limit for the given Hamiltonian, resulting in the shortest possible duration.
Qubit System: The register consists of the NV electron spin (Control Qubit) coupled to a nearby ¹³C nuclear spin (Target Qubit) in diamond.
Gate Time: A minimum gate time of $\tau = 4.545$ µs was achieved for a U_CR($\pi$) operation, dictated by the hyperfine coupling strength (A_zx = 0.110 MHz).
Fidelity: High experimental fidelity of 96% was demonstrated for the preparation of a Bell-type state ($\vert\beta\rangle$).
Material Relevance: The success of this room-temperature quantum operation relies fundamentally on the low-strain, high-purity characteristics of the Single Crystal Diamond (SCD) host material.

Technical Specifications

The following hard data points were extracted from the experimental demonstration of the fast 2-qubit gate operation:

Parameter	Value	Unit	Context
Zero Field Splitting (D)	2.870	GHz	Electron spin
Longitudinal Hyperfine Coupling (A_zz)	-0.152	MHz	Electron-¹³C coupling
Transverse Hyperfine Coupling (A_zx)	0.110	MHz	Electron-¹³C coupling
Magnetic Field (B₀)	14.2	mT	Oriented along the NV axis (z-axis)
Electron Larmor Frequency (ν_e)	-400.110	MHz	Includes shift from ¹⁴N coupling
¹³C Larmor Frequency (ν_c)	0.152	MHz	In B₀ = 14.2 mT field
Minimum Gate Time (τ)	4.545	µs	Time required for U_CR($\pi$), reaching quantum speed limit
Bell State Fidelity (Experimental)	96	%	Final state fidelity using full state tomography
Initialization Laser Wavelength	532	nm	Used for electron spin initialization
Initialization Laser Pulse Duration	5	µs	Used for electron spin initialization
MW Pulse Duration (90° pulse)	0.125	µs	Used in Bell state preparation sequence

Key Methodologies

The experiment successfully demonstrated a controlled rotation gate (U_CR($\alpha$)) by leveraging the intrinsic properties of the NV-¹³C system, minimizing external control overhead.

System Selection: A single NV center in diamond was used, consisting of the electron spin (spin-1) coupled to a passive ¹⁴N spin (spin-1) and an active ¹³C nuclear spin (spin-1/2).
Qubit Definition: The 2-qubit system was defined using two electron spin levels ($\text{m}_{\text{s}} = {0, -1}$) as the control qubit and the ¹³C spin as the target qubit.
Hamiltonian Transformation: The secular part of the Hamiltonian was transformed into an interaction frame (H_I) such that the computational basis states are not eigenstates of H_I.
Gate Implementation (Free Evolution): The logical operation (U_CR($\alpha$)) was generated simply by allowing the system to evolve freely under the static internal Hamiltonian for a duration $\tau$.
State Preparation: Initial state preparation ($\vert 00\rangle$) involved a 532 nm laser pulse (5 µs) followed by a state swap operation and a clean-up operation (U_cu) to remove spurious populations.
Measurement: The effect of the U_CR($\alpha$) operation was verified by measuring the diagonal elements of the final density operator in the computational basis, confirming the conditional rotation behavior.

6CCVD Solutions & Capabilities

The successful implementation of high-fidelity, speed-limit quantum gates relies entirely on the quality and precision of the diamond substrate. 6CCVD is uniquely positioned to supply the necessary materials and fabrication services to replicate and scale this research.

Applicable Materials

To replicate or extend this research, the highest quality Single Crystal Diamond (SCD) is required to ensure long coherence times (T₂) and stable NV center formation.

Material Requirement	6CCVD Material Recommendation	Technical Rationale
High Purity & Low Strain	Optical Grade Single Crystal Diamond (SCD)	Essential for minimizing decoherence sources (e.g., residual nitrogen, lattice defects) that limit the qubit coherence time and gate fidelity.
Isotopic Control	High-Purity ¹²C SCD Substrates	While the paper uses natural abundance ¹³C, future scaling requires precise control. 6CCVD can supply SCD with >99.99% ¹²C purity, allowing researchers to isolate specific coupled nuclear spins or control the density of the spin bath.
Qubit Integration	Custom SCD Substrates for Implantation	We provide SCD plates optimized for subsequent ion implantation and annealing processes necessary to create shallow, high-quality NV centers.

Customization Potential

6CCVD’s in-house fabrication capabilities directly address the needs of advanced quantum device engineering:

Custom Dimensions: We supply SCD plates in custom dimensions and thicknesses, ranging from 0.1 µm up to 500 µm. This is critical for integrating the diamond into specific cryogenic or room-temperature quantum setups.
Ultra-Smooth Polishing: The experiment relies on 532 nm laser access for initialization and readout. 6CCVD guarantees Ra < 1 nm polishing for SCD, minimizing optical scattering losses and maximizing photon collection efficiency.
Advanced Metalization: For integrating microwave (MW) antennas or control electrodes necessary for initialization and readout pulses (like the 90° MW pulse mentioned), 6CCVD offers internal metalization services, including deposition of Ti, Pt, Au, Pd, W, and Cu. This allows for the creation of integrated quantum devices on the diamond surface.
Large-Scale Substrates: For future multi-qubit systems, 6CCVD can provide large-area Polycrystalline Diamond (PCD) wafers up to 125 mm in diameter, suitable for hybrid quantum architectures or classical control layers.

Engineering Support

6CCVD’s in-house PhD team specializes in the material science of diamond for quantum applications. We offer consultation on:

Optimizing SCD material specifications (purity, orientation, thickness) to maximize NV center T₂ and T₂* coherence times.
Designing custom metalization stacks and patterns for efficient microwave delivery and magnetic field control in similar NV quantum computing projects.
Selecting the optimal diamond grade for specific operating conditions (e.g., room temperature vs. cryogenic environments).

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

View Original Abstract

Most implementations of quantum gate operations rely on external control fields to drive the evolution of the quantum system. Generating these control fields requires significant efforts to design the suitable control Hamiltonians. Furthermore, any error in the control fields reduces the fidelity of the implemented control operation with respect to the ideal target operation. Achieving sufficiently fast gate operations at low error rates remains therefore a huge challenge. In this Letter, we present a novel approach to overcome this challenge by eliminating, for specific gate operations, the time-dependent control fields entirely. This approach appears useful for maximizing the speed of the gate operation while simultaneously eliminating relevant sources of errors. We present an experimental demonstration of the concept in a single nitrogen-vacancy center in diamond at room temperature.