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6CCVD Research

Efficient Implementation of a Quantum Algorithm in a Single Nitrogen-Vacancy Center of Diamond

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-07-14
JournalPhysical Review Letters
AuthorsJingfu Zhang, Swathi S. Hegde, Dieter Suter
InstitutionsTU Dortmund University
Citations54
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research demonstrates the highly efficient implementation of Grover’s quantum search algorithm within a single Nitrogen Vacancy (NV) center in diamond, utilizing a hybrid 2-qubit register.

  • High Control Efficiency: The entire quantum search was implemented using only 4 Microwave (MW) pulses, a significant reduction in control cost compared to previous methods.
  • Indirect Control Success: Gate operations targeting the nuclear spin (the slower qubit) were achieved solely through MW pulses applied to the electron spin, leveraging anisotropic hyperfine interaction and free precession. This avoids slow radio-frequency (RF) control.
  • Quantum Speedup Demonstrated: The experiment achieved target state populations ranging from 0.76 to 0.87, confirming the quadratic speedup of Grover’s algorithm over the classical search probability (0.25).
  • High Fidelity: A final state fidelity of F|11) = 0.85 ± 0.03 was measured at room temperature, validating the effectiveness of the Optimal Control (OC) pulse sequences.
  • Scalability Confirmed: Numerical simulations show that the indirect control scheme is scalable up to 5 qubits (1 electron + 4 13C nuclear spins), with CNOT-like gate durations remaining short (16-18 ”s).
  • Robustness: Pulse sequences were optimized using a genetic algorithm to be robust against observed fluctuations in the MW Rabi frequency (up to 0.03 MHz variation).

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Qubit SystemHybrid 2-QubitN/AElectron spin (Qubit 1) and 13C nuclear spin (Qubit 2).
Diamond Purity (12C)99.995%Used to minimize decoherence effects.
Substitutional Nitrogen< 10ppbUsed to minimize decoherence effects.
Operating TemperatureRoomTemperatureExperiment performed without cryogenic cooling.
Static Magnetic Field (B)14.8mTAligned along the NV symmetry axis (z-axis).
Zero-Field Splitting (D)2.87GHzElectron spin property.
13C Hyperfine (Azz)-0.152MHzRelevant tensor component.
13C Hyperfine (Azx)0.110MHzRelevant tensor component.
Control Pulses (Search)4MW pulsesTotal required for the complete Grover’s search operation.
Target State Population0.76 to 0.87(Probability)Experimental success probability across four target states.
Final State Fidelity (F|11))0.85 ± 0.03(Unitless)Measured fidelity after search completion.
Electron Spin T2*~35”sMeasured from ESR Free Induction Decay (FID).
Electron Spin T2 (DD)~1msMeasured using dynamical decoupling sequence.
5-Qubit CNOT Duration16 - 18”sSimulated gate duration for 1 electron + 4 13C spins.
MW Rabi Frequency (w1/2π)0.48 to 0.52MHzRange used for robust pulse sequence optimization.

Key Methodologies

Section titled “Key Methodologies”

The experiment relied on a combination of optical, microwave, and computational control techniques to achieve high-fidelity quantum algorithm implementation:

  1. NV Center Setup: A home-built confocal microscope was used for optical addressing. A 532 nm continuous wave laser (0.5 mW) was used for initialization and detection.
  2. Qubit Initialization: The electron spin was initialized into the ms = 0 state using a 4 ”s laser pulse. The 13C nuclear spin was subsequently polarized using a combination of MW and laser pulses to achieve the pure state |00).
  3. Indirect Quantum Control: All necessary unitary operations (including the Oracle and Diffusion steps) were implemented using only rectangular MW pulses resonant with the electron spin transitions (ms = 0 ↔ ms = -1).
  4. Optimal Control (OC) Theory: A genetic algorithm was employed to optimize the pulse sequence parameters (durations, phases, and delays) to maximize the theoretical fidelity (Fg) between the generated operation (U) and the target unitary operation (Utarget).
  5. Robustness Optimization: The OC optimization was performed over a range of Rabi frequencies (0.48-0.52 MHz) to ensure the resulting pulse sequences were robust against experimental fluctuations in MW power.
  6. State Measurement: Quantum State Tomography (QST) was performed on the output state (|Κ)out) to reconstruct the full density matrix (ρexp) and determine the final populations and fidelities.
  7. Scalability Simulation: Numerical simulations were conducted by generalizing the Hamiltonian to include up to four additional 13C nuclear spins, demonstrating the feasibility of controlled-Rz(π) gates in larger hybrid systems.

Commercial Applications

Section titled “Commercial Applications”

The demonstrated technology, focusing on efficient quantum control in solid-state NV centers, has direct implications for several high-tech sectors:

  • Solid-State Quantum Computing: NV centers serve as leading candidates for room-temperature quantum processors, particularly for hybrid architectures combining fast electron qubits and long-coherence nuclear qubits.
  • Quantum Algorithm Acceleration: The successful implementation of Grover’s search validates the use of NV systems for accelerating computationally hard problems, such as database searching, machine learning optimization, and logistics planning.
  • High-Fidelity Quantum Control Systems: The use of Optimal Control (OC) theory provides a blueprint for designing highly efficient and robust pulse sequences, applicable to controlling other solid-state qubits (e.g., silicon carbide defects, superconducting circuits).
  • Quantum Sensing and Metrology: The underlying NV platform, characterized by long nuclear spin coherence, is critical for developing ultra-sensitive quantum sensors for magnetic fields, temperature, and pressure.
  • Advanced Diamond Materials: The requirement for ultra-high purity diamond (99.995% 12C, low nitrogen) drives demand for specialized material fabrication techniques necessary for next-generation quantum hardware.
View Original Abstract

Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen-vacancy (NV) center in diamond, are among the most promising systems to implement quantum computing, provided the control of the different types of qubits can be efficiently implemented. In the case of the NV center, the anisotropic hyperfine interaction allows one to control the nuclear spins indirectly, through gate operations targeting the electron spin, combined with free precession. Here, we demonstrate that this approach allows one to implement a full quantum algorithm, using the example of Grover’s quantum search in a single NV center, whose electron is coupled to a carbon nuclear spin.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2000 - Quantum Computation and Quantum Information
  2. 2008 - Quantum Computing: A Short Course from Theory to Experiment

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