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6CCVD Research

Efficient Quantum Gates for Individual Nuclear Spin Qubits by Indirect Control

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-06-02
JournalPhysical Review Letters
AuthorsSwathi S. Hegde, Jingfu Zhang, Dieter Suter
InstitutionsTU Dortmund University
Citations45
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research demonstrates a highly efficient method for implementing universal quantum gates on individual nuclear spin qubits within a Nitrogen Vacancy (NV) center in diamond using Indirect Control (IC).

  • Core Innovation: Realization of robust quantum gates (Hadamard UH, Controlled-NOT UCNOT) on a weakly coupled 13C nuclear spin by applying control fields only to the electron spin.
  • Efficiency and Overhead: The scheme uses minimal control overhead, requiring only 2-3 short Microwave (MW) pulses and optimized delays, significantly reducing complexity compared to previous IC methods.
  • Speed Advantage: Gate operation times (e.g., UCNOT ≈ 14.3 ”s) are shorter than the electron spin coherence time (T2* ≈ 20 ”s), eliminating the need for complex Dynamical Decoupling (DD) sequences during gate operation.
  • Fidelity: Numerical optimization achieved high theoretical gate fidelities (UH > 96%, UCNOT > 97%), demonstrating robustness against MW pulse amplitude fluctuations.
  • Scalability: The method is applicable to weakly coupled, remote nuclear spins (distance r ≈ 0.89 nm), addressing a major challenge in scaling up NV-based quantum registers.
  • Universal Control: The demonstrated UH and UCNOT gates form a universal set necessary for complex quantum algorithms.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Quantum SystemNV CenterN/AElectron (Spin-1), 14N (Spin-1), 13C (Spin-1/2)
Operating TemperatureRoomTemperatureExperimental condition
External Magnetic Field (B0)14.8mTAligned along NV axis (z-direction)
Electron Zero Field Splitting (D)2.87GHzIntrinsic NV property
Electron Coherence Time (T2*)~20”sMinimum requirement for the 2-qubit system
MW Pulse Rabi Frequency (ω1/2π)0.5MHzUsed for selective subspace control
Hadamard Gate Duration (UH)3.78”sTotal sequence time (Ti + ti)
CNOT Gate Duration (UCNOT)14.28”sTotal sequence time (Ti + ti)
Theoretical Gate Fidelity (UH)>96%Optimized for robustness
Experimental State Fidelity (UCNOT)~80%Estimated from P0↓ measurement
Electron-13C Distance (r)0.89nmCalculated from hyperfine tensor
13C Larmor Frequency (vc)0.158MHzIn 14.8 mT field
13C Hyperfine Coupling (Azz)-0.152MHzCoupling strength
Scalability Test (6-Qubit System)22-28”sTotal duration for controlled-controlled rotations
Scalability Control Overhead4MW pulsesRequired for controlled-controlled rotations (n=6)

Key Methodologies

Section titled “Key Methodologies”

The experiment utilized Indirect Control (IC) on a single NV center in a 12C enriched diamond sample:

  1. System Setup: Experiments were conducted at room temperature with a 14.8 mT magnetic field aligned along the NV axis (z-direction).
  2. Electron Initialization: The electron spin was initialized to the |0> state using a 532 nm laser pulse (5 ”s duration).
  3. Nuclear Spin Initialization: The 13C nuclear spin was initialized to a pure state (|↑>) using a separate Indirect Control method.
  4. Subspace Selection: All gate operations were confined to the mN = 1 subspace of the 14N spin. This was achieved by using MW pulses (Rabi frequency 0.5 MHz) resonant with the electron ESR transition 0 ↔ -1, which selectively addresses the desired subspace.
  5. Gate Implementation (IC): Quantum gates (UH, UCNOT) were constructed using sequences consisting only of short MW pulses applied to the electron spin, interleaved with free evolution delays (Ti) under the electron-nuclear hyperfine coupling.
  6. Numerical Optimization: Pulse parameters (durations ti, delays Ti, phases φi) were optimized using a genetic algorithm to maximize the gate fidelity (F), ensuring robustness against ±4% fluctuations in the MW pulse amplitude.
  7. State Detection: The final state was analyzed using partial tomography via Free Induction Decay (FID) measurements. The electron state (ms = 0 population) was measured using a 400 ns laser readout pulse.

Commercial Applications

Section titled “Commercial Applications”

The demonstrated efficient control over remote nuclear spins in solid-state systems is critical for advancing several quantum technologies:

  • Scalable Quantum Computing: NV centers are a leading solid-state architecture. This IC scheme enables fast, high-fidelity control over multiple remote 13C qubits, which is essential for scaling up quantum registers beyond nearest-neighbor interactions.
  • Quantum Memory: Nuclear spins, particularly those weakly coupled (remote), possess extremely long coherence times (T2). The ability to quickly and coherently transfer information between the fast electron control qubit and the long-lived nuclear memory qubit is vital for quantum repeaters and storage nodes.
  • Quantum Simulation: The technique provides a robust method for coherent manipulation of multi-qubit systems, enabling high-fidelity quantum simulation of complex spin dynamics.
  • Quantum Sensing: NV centers are used for high-resolution magnetic and electric field sensing. Improved control over the coupled nuclear spins enhances the sensitivity and coherence of these sensors.
  • Solid-State Qubit Architectures: The methodology is broadly applicable to other hybrid spin systems where a fast control qubit (like an electron) is coupled to slower memory qubits (like nuclear spins), such as quantum dots or other defect centers.
View Original Abstract

Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme for circumventing this problem by indirect control: we apply a small number of short pulses only to the electron and let the full system undergo free evolution under the hyperfine coupling between the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system, including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin as the target qubit. The durations of these gates are shorter than the electron coherence time, and thus additional operations to extend the system coherence time are not needed. Our demonstration serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems, such as nitrogen vacancy centers in diamond. Our scheme is still applicable when the nuclear spins are only weakly coupled to the electron.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2002 - Quantum Computation and Quantum Information
  2. 2008 - Quantum Computing: A Short Course from Theory to Experiment

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