Simulating the Electronic Structure of Spin Defects on Quantum Computers

At a Glance

Metadata	Details
Publication Date	2022-03-10
Journal	PRX Quantum
Authors	Benchen Huang, Marco Govoni, Giulia Galli
Institutions	Argonne National Laboratory, University of Chicago
Citations	40
Analysis	Full AI Review Included

Technical Documentation & Analysis: Quantum Simulation of Spin Defects in Diamond

This document analyzes the research paper “Simulating the electronic structure of spin defects on quantum computers,” focusing on the implications for the physical realization of diamond-based quantum technologies, specifically the Nitrogen Vacancy (NV-) center. As an expert material scientist at 6CCVD, this analysis connects the theoretical requirements of high-fidelity spin qubits to our advanced MPCVD diamond manufacturing capabilities.

Executive Summary

This research successfully demonstrates a hybrid classical/quantum computational protocol for accurately simulating the electronic structure of critical solid-state spin defects, validating key methodologies for future quantum technology development.

Core Achievement: First-time calculation of excited state energies for the Nitrogen Vacancy (NV-) center in diamond and the Double Vacancy (VV) in 4H-SiC using a hybrid Variational Quantum Eigensolver (VQE) and Quantum Subspace Expansion (QSE) approach.
Methodological Innovation: Employed Quantum Defect Embedding Theory (QDET) to efficiently model localized electronic excitations within large periodic crystal supercells (216 atoms for diamond).
Noise Mitigation Success: Developed and implemented Zero-Noise Extrapolation (ZNE) via exponential block replication, significantly reducing hardware noise errors (down to ~0.002 eV for NV- ground state).
Hardware Validation: Calculations were performed on a real Near-Intermediate Scale Quantum (NISQ) computer (IBM ibmq_casablanca), proving the feasibility of simulating complex material properties on current quantum architectures.
Material Relevance: The high accuracy achieved in simulating NV- electronic states is crucial for the physical engineering and optimization of high-coherence diamond quantum sensors and communication devices.
6CCVD Value Proposition: Replicating and advancing this research requires ultra-high purity, low-strain Single Crystal Diamond (SCD) substrates, which 6CCVD provides with industry-leading control over purity, thickness, and surface finish (Ra < 1 nm).

Technical Specifications

The following hard data points were extracted from the research paper detailing the computational models and performance metrics.

Parameter	Value	Unit	Context
Target Spin Defect 1	NV<sup>-</sup> center	N/A	Qubit in diamond
Target Spin Defect 2	Double Vacancy (VV)	N/A	Qubit in 4H-SiC
Diamond Supercell Size	216	atoms	Used for hybrid DFT calculation
SiC Supercell Size	200	atoms	Used for hybrid DFT calculation
Kinetic Energy Cutoff	50	Ry	Plane-wave pseudopotential method
NV<sup>-</sup> Active Space Model	(4e, 3o)	N/A	Minimum model for QDET
VV Active Space Model	(6e, 4o)	N/A	Minimum model for QDET
VQE Error (No ZNE, Case b)	~0.02	eV	Ground state error on noisy hardware
NV<sup>-</sup> VQE Error (ZNE)	~0.002	eV	Error relative to noiseless simulator
VV VQE Error (ZNE)	~0.005	eV	Error relative to noiseless simulator
Measurement Standard Deviation (σ)	~3	meV	Noise limit with 50 repetitions
NV<sup>-</sup> <sup>3</sup>A<sub>2</sub> → <sup>1</sup>E Excitation (FCI)	0.512	eV	Reference excitation energy
VV <sup>3</sup>A<sub>2</sub> → <sup>1</sup>E Excitation (FCI)	0.378	eV	Reference excitation energy

Key Methodologies

The computational protocol relies on a sophisticated hybrid classical/quantum workflow to accurately model the electronic structure of the spin defects:

First-Principles Electronic Structure (DFT/Hybrid-DFT):
- Determine the mean-field electronic structure of the full periodic solid (supercell) using Density Functional Theory (DFT) or hybrid-DFT.
- Identify a localized set of single-particle orbitals around the defect site.
Quantum Defect Embedding Theory (QDET):
- Define an effective Hamiltonian (Heff) in second quantization for the small active space (e.g., 4 electrons, 3 orbitals for NV-).
- This step incorporates correlation effects from the surrounding host lattice (diamond).
Qubit Hamiltonian Transformation:
- Map the fermionic Heff onto a qubit Hamiltonian (Hq) using transformations like Jordan-Wigner, Bravyi-Kitaev, or parity mapping.
Ground State Calculation (VQE):
- Use the Variational Quantum Eigensolver (VQE) algorithm, employing the Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz, to variationally minimize the energy expectation value on the quantum computer.
Excited State Calculation (QSE):
- Compute excited state energies using the Quantum Subspace Expansion (QSE) method, starting from the optimized VQE ground state.
Error Mitigation Techniques:
- Post-Selection: Apply constraints on measurement outcomes to discard “unphysical states” that do not conserve the correct number of electrons.
- Zero-Noise Extrapolation (ZNE): Artificially amplify the circuit noise using exponential block replication and extrapolate the results back to the zero-noise limit (n → 0) to improve accuracy.

6CCVD Solutions & Capabilities

The successful simulation of the NV- center’s electronic structure highlights the critical need for high-quality diamond substrates for the physical realization of quantum devices. 6CCVD is uniquely positioned to supply the materials required to turn these computational results into functional quantum hardware.

Applicable Materials for NV- Center Implementation

The NV- center is the gold standard for solid-state qubits, demanding exceptional material purity and crystalline perfection to maximize spin coherence time (T2).

6CCVD Material Solution	Description & Relevance to Quantum Research
Optical Grade Single Crystal Diamond (SCD)	Ultra-high purity SCD, essential for minimizing background paramagnetic impurities (e.g., substitutional nitrogen P1 centers) that limit T<sub>2</sub>.
Low-Strain SCD Wafers	SCD material grown under optimized conditions to minimize internal strain, critical for maintaining the spectral stability and coherence of the NV<sup>-</sup> spin state.
Controlled Nitrogen Doping (SCD)	Precise control over nitrogen incorporation during MPCVD growth, allowing researchers to engineer the density of NV precursors for optimal qubit density.
Polycrystalline Diamond (PCD) Substrates	Available for large-area applications (up to 125 mm diameter) where thermal management or robust mechanical properties are prioritized over single-crystal coherence.

Customization Potential for Quantum Device Integration

The transition from simulation to physical device requires precise material engineering, a core capability of 6CCVD.

Custom Dimensions and Thickness: We provide SCD plates and wafers with thicknesses ranging from 0.1 µm to 500 µm, allowing researchers to optimize the proximity of NV centers to the surface for sensing applications or integration into photonic structures.
Large-Area PCD: For scaling up quantum sensing arrays or thermal management layers, 6CCVD offers PCD wafers up to 125 mm in diameter.
Ultra-Smooth Polishing: Achieving high-fidelity optical coupling and low surface noise requires exceptional surface quality. We guarantee Ra < 1 nm polishing for SCD and Ra < 5 nm for inch-size PCD.
Integrated Metalization Services: Quantum device fabrication often requires contact pads or microwave striplines. 6CCVD offers in-house deposition of critical metals, including Au, Pt, Pd, Ti, W, and Cu, tailored to specific device layouts.

Engineering Support & Global Logistics

6CCVD provides comprehensive support to accelerate quantum materials research:

Defect Engineering Consultation: 6CCVD’s in-house PhD team specializes in MPCVD growth parameters necessary for controlled defect creation (e.g., nitrogen incorporation, subsequent irradiation/annealing protocols) for similar spin defect and quantum sensing projects.
Material Selection Guidance: We assist researchers in selecting the optimal diamond grade (SCD vs. PCD, doping level, orientation) to match the specific requirements derived from computational studies like the one analyzed.
Global Supply Chain: We ensure reliable, timely delivery of custom diamond materials worldwide, offering DDU (Delivery Duty Unpaid) as default and DDP (Delivery Duty Paid) options for seamless international procurement.

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

View Original Abstract

We present calculations of both the ground-and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol. We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H Si C, which are of interest for the realization of quantum technologies. We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation. We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation. We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground-and excited-state properties of spin defects.

Tech Support

Original Source

DOI: https://doi.org/10.1103/prxquantum.3.010339