Noise-Resilient Quantum Computing with a Nitrogen-Vacancy Center and Nuclear Spins

At a Glance

Metadata	Details
Publication Date	2016-09-20
Journal	Physical Review Letters
Authors	J. Casanova, Z.-Y. Wang, Martin B. Plenio
Institutions	Universität Ulm
Citations	50
Analysis	Full AI Review Included

Noise-Resilient Quantum Computing in Diamond: Technical Analysis and 6CCVD Solutions

Executive Summary

This paper demonstrates a robust protocol for implementing high-fidelity quantum gates in solid-state registers utilizing Nitrogen-Vacancy (NV) centers coupled to surrounding nuclear spins (specifically Carbon-13, ¹³C) in diamond. The key findings and technical value proposition are summarized below:

High-Fidelity Quantum Control: Achieved single- and two-qubit gate fidelities consistently exceeding 99% (up to 0.9984), validating the noise-resilient protocol.
Decoupling Strategy: Successfully utilized Dynamical Decoupling (specifically AXY-8 sequences and tailored microwave/RF control fields) to suppress both environmental decoherence of the electron spin and unwanted internuclear interactions ($H_{nn}$).
Scalability for Quantum Memory: The protocol is applicable even to weakly coupled, distant spins, positioning ¹³C nuclear ensembles in high-purity Single Crystal Diamond (SCD) as robust, scalable quantum memories with long coherence times.
Material Specification Focus: Successful replication requires high-purity SCD with controlled isotopic composition, particularly minimized ¹⁴N impurities (to reduce detuning errors) and precise ¹³C natural or enriched abundance (to form the qubit register and control the noise bath).
Rapid Gate Operation: Gates were achieved on the order of hundreds of microseconds (t₁ = 480 µs, t₂ = 1.6 ms), demonstrating feasibility for circuit-based quantum algorithms and DQC1 computation.
Noise Resilience Confirmed: Simulations, including a bath of 200 unused ¹³C nuclei (radius ≈ 4.7 nm) under strong error conditions (5% Rabi error, $\Lambda = 2\pi \times 2$ MHz), showed minimal degradation of gate coherence ($L$ remained above 0.9936).

Technical Specifications

Parameter	Value	Unit	Context
Zero Field Splitting ($D$)	$2\pi \times 2.87$	GHz	Intrinsic property of the NV center
Static Magnetic Field ($B_z$)	≥ 0.1, up to 2	T	Required for resonance branch separation
Electron Spin Flip Time ($\tau_R$)	12.5	ns	Corresponding to the Rabi Frequency ($\Omega$)
Decoupling Field Constant ($\Delta$)	$2\pi \times 100$	kHz	Used in simulations, corresponds to $B_d \sim 0.1$ T
Nuclear Distance ($r_0$)	1.54	Å	Minimum ¹³C-¹³C distance in diamond lattice
NV Operating Temperature	$\sim 4$	K	Required for long electron spin $T_1$ (many seconds)
Entangling Gate Time ($t_1$)	480	µs	Gate: exp(-$i\frac{\pi}{2}\sigma_z I_x$) using 800 pulses
Two-Qubit Gate Time ($t_2$)	1.6	ms	Gate: exp(-$i\frac{\pi}{2} \sigma_z I_x^2$) using 2800 pulses
High Fidelity Range ($F_{-/+}$)	0.9911 - 0.9984	Dimensionless	Fidelity of tested single and two-qubit gates (Spin 1)
Strong Error Condition ($\Lambda$)	$2\pi \times 2$	MHz	Detuning error tested (1 K temp shift is $2\pi \times 70$ kHz)
Minimum Sample Volume	10 $\mu$m x 10 $\mu$m x 10	nm	Layer size required to contain one sample (0.01 ppm NV)
Coherence ($L$) with Bath	0.9936	Dimensionless	Averaged coherence over 10 samples including 200 bath ¹³C atoms
Maximum Allowed Hyperfine ($	A_j^{\perp}	$)	< $2\pi \times 45$

Key Methodologies

The core protocol relies on the combination of continuous wave (CW) microwave/RF fields and pulsed dynamic decoupling sequences to achieve selective quantum control and noise mitigation.

System Preparation:
- Establish a Single Crystal Diamond (SCD) substrate containing an isolated NV center (electron spin qubit) coupled to a controllable cluster of nearby ¹³C nuclear spins (memory qubits).
- Apply a strong static magnetic field ($B_z$) parallel to the NV axis to define the spin quantization axis and split the energy branches.
Hamiltonian Manipulation & Decoupling:
- Apply a microwave field tuned to the NV center’s electron spin.
- Utilize a radio frequency (RF) field containing a decoupling component ($B_d$) and a control component ($B_c$).
- Employ AXY-8 Pulse Sequences (time-symmetric or anti-symmetric) to generate an effective Hamiltonian ($H_{eff}$) that selectively addresses specific nuclear spins.
Noise Suppression via Magic-Angle Condition:
- The RF decoupling field is carefully oriented to satisfy the magic-angle condition (derived from Lee-Goldburg decoupling).
- This condition ensures that the Hamiltonian component describing internuclear coupling ($H_{nn}$) is suppressed by a factor proportional to $|A_j^{\perp}/2\Delta|$, enabling robust isolation of the qubits.
Selective Gate Implementation:
- Tune the microwave field outside the nuclear resonance band (${\omega_j}$) to achieve protected single-qubit rotations.
- Tune the microwave field inside the resonance band and use tailored symmetric/anti-symmetric sequences to generate entangling two-qubit gates (electron-nuclear coupling) with arbitrarily tunable coefficients $f_s/f_a$.
Fidelity Measurement:
- Gate performance is confirmed using detailed numerical simulations accounting for experimental imperfections, including detuning errors ($\Lambda$) and Rabi frequency errors (RFE).

6CCVD Solutions & Capabilities

6CCVD provides the specialized diamond material and fabrication support necessary to replicate, optimize, and scale this high-fidelity quantum computing research.

Applicable Materials

To achieve the long coherence times ($T_1$ in seconds) and precise spin cluster environment demonstrated in the paper, high-purity materials with controlled isotopic content are essential:

Optical Grade Single Crystal Diamond (SCD): Required as the base material for the NV centers. Our SCD offers extreme purity, minimizing $T_1$ limiting defects.
Low Nitrogen (N) Content: The paper notes $\Lambda$ errors due to imperfect ¹⁴N polarization. 6CCVD guarantees ultra-low residual Nitrogen concentration, ensuring minimal electronic noise.
Controlled ¹³C Isotopic Purity: The experiment relies on natural (1.1%) or specifically controlled ¹³C concentration (0.27% used for noise bath simulations). 6CCVD offers custom isotopic control, allowing researchers to specify the exact percentage of ¹³C required, enabling precise tailoring of the qubit register density and the nuclear spin bath.

Customization Potential

The requirements of this advanced research necessitate materials and device architecture far beyond standard commercial off-the-shelf offerings. 6CCVD is uniquely equipped to meet these demands:

Custom Requirement	6CCVD Capability	Research Relevance
Thin Film Growth/Slab Fabrication	SCD thickness control from 0.1 µm to 500 µm. Allows for the creation of ultra-thin layers (down to 10 nm thick required for efficient sample selection) necessary for maximizing NV coupling efficiency.	Facilitates the high-density NV creation and imaging required for spin cluster selection.
High Precision Dimensions	Custom laser cutting and polishing on plates/wafers up to 125 mm (PCD) and inch-size SCD.	Allows for fabrication of millimeter-scale chips housing the $10~\mu$m $\times 10~\mu$m testing areas used in the simulation models.
Surface Quality	SCD Polishing: Ra < 1 nm. PCD Polishing: Ra < 5 nm.	Critical for NV center research, ensuring minimal scattering losses for the necessary optical fields and microwave delivery structures.
Custom Metalization	In-house deposition of Au, Pt, Pd, Ti, W, Cu.	Essential for defining the microwave/RF striplines (e.g., gold or platinum) used to deliver the precise AXY-8 pulses and RF decoupling fields ($B_d \sim 0.1$ T) with nanometer accuracy.

Engineering Support

This research involves complex dynamic decoupling protocols and precise material-spin interaction tuning. 6CCVD’s in-house PhD material scientists and technical engineers can assist researchers by:

Material Selection and Synthesis: Consulting on optimal ¹³C isotopic doping levels and NV incorporation strategies to maximize qubit density while maintaining low background noise.
Device Integration: Providing guidance on surface preparation and metalization schemes required to integrate microwave delivery circuits capable of generating the high-frequency pulsed fields necessary for the AXY-8 sequences.
Scaling and Robustness: Assisting with material scaling challenges required for transitioning from $10~\mu$m scale laboratory samples to robust, larger-area quantum processors utilizing noise-resilient protocols demonstrated here.

Call to Action: For custom specifications or material consultation related to quantum computing, dynamic decoupling, or solid-state spin registers, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Selective control of qubits in a quantum register for the purposes of quantum information processing represents a critical challenge for dense spin ensembles in solid-state systems. Here we present a protocol that achieves a complete set of selective electron-nuclear gates and single nuclear rotations in such an ensemble in diamond facilitated by a nearby nitrogen-vacancy (NV) center. The protocol suppresses internuclear interactions as well as unwanted coupling between the NV center and other spins of the ensemble to achieve quantum gate fidelities well exceeding 99%. Notably, our method can be applied to weakly coupled, distant spins representing a scalable procedure that exploits the exceptional properties of nuclear spins in diamond as robust quantum memories.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevlett.117.130502