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Exact magnetic field control of nitrogen-vacancy center spin for realizing fast quantum logic gates

MetadataDetails
Publication Date2015-11-30
JournalPhysical Review B
AuthorsWenqi Fang, Bang‐Gui Liu
InstitutionsChinese Academy of Sciences, Institute of Physics
Citations2
AnalysisFull AI Review Included

Technical Documentation & Analysis: Ultra-Fast NV Center Quantum Gates

Section titled “Technical Documentation & Analysis: Ultra-Fast NV Center Quantum Gates”

This research demonstrates a powerful theoretical framework for achieving ultra-fast, high-fidelity quantum logic gates using the negatively charged Nitrogen-Vacancy (NV) center spin in diamond, controlled solely by time-dependent magnetic fields.

  • Core Achievement: Realization of typical quantum logic gates (Phase Shift, Pauli-X, Hadamard) in the nanosecond (ns) regime, significantly faster than previous mechanical or geometric approaches.
  • Methodology: Derivation of the exact evolution operator for the three-level NV spin system by mapping it onto a solvable time-dependent quantum two-level system.
  • Speed Metrics: Gate durations range from 1.1 ns (π/2 phase shift) to 5.3 ns (Pauli-X initialization step), enabling rapid quantum computation cycles.
  • Fidelity Advantage: The approach relies only on controlling magnetic field strength, eliminating timing inaccuracies associated with microwave pulses or rotating wave approximations, promising extremely high theoretical fidelity.
  • Material Requirement: Successful implementation requires high-purity, low-strain Single Crystal Diamond (SCD) to maintain the long coherence times necessary for reliable NV center spin manipulation.
  • 6CCVD Value Proposition: 6CCVD provides the necessary Optical Grade SCD substrates, custom dimensions, and advanced polishing (Ra < 1 nm) required to support the fabrication and integration of these high-speed quantum devices.

The following hard data points were extracted from the analysis of the NV center Hamiltonian and gate performance:

ParameterValueUnitContext
Zero-Field Splitting (D)2.87GHzNV Center Spin Triplet
Electron Gyromagnetic Ratio (Îł)2.8MHz/GUsed in Hamiltonian H
Qubit Basis
Initialization Magnetic Field (B1(Tf) Range)450 to 740,000GRequired field strength for arbitrary qubit initialization
π/2 Phase Shift Gate Time (TG)1.1nsFastest gate duration
π/2 Phase Shift Static Field (h1)888GTime-independent magnetic field component
π Phase Shift Gate Time (TG)1.6ns
Pauli-X Gate Time (TG)2.7nsTotal time for two-step process (U0(π/2, T)U0†(0, T))
Hadamard Gate Time (TG)1.4 or 3.8nsDepending on implementation method (with or without intermediate
Required Fidelity ControlMagnetic Field Strength OnlySimplifies control and maximizes theoretical fidelity

The realization of fast quantum logic gates relies on precise theoretical control of the NV center spin Hamiltonian under time-dependent magnetic fields B(t).

  1. Hamiltonian Definition: The NV center spin Hamiltonian (H) is defined in the Sz representation, incorporating the zero-field splitting (D) and the time-dependent Zeeman term (γS · B(t)).
  2. Basis Transformation: A unitary transform (S1) is applied to change the basis from the standard (| + 1>, |0>, |-1>) to the stable qubit basis (|±>, |0>), where |±> = (| + 1> ± |-1>)/√2.
  3. Special Magnetic Field Application: A time-dependent magnetic field B(t) = (αB1, ÎČB1, 0) is applied, where α and ÎČ are adjustable parameters (α2 + ÎČ2 = 1).
  4. Block Diagonalization: A second unitary transform (S2) is used to transform the Hamiltonian (H0) into a block-diagonal matrix (Ht), separating the |0> state from the |±> qubit subspace.
  5. Exact Evolution Operator Construction: The 2x2 block (Ht2) governing the qubit subspace is mapped onto a solvable time-dependent quantum two-level system. The exact evolution operator (Ut) is constructed using analytical solutions derived from the specified time-dependent function χ(t).
  6. Qubit Initialization and Gating: The derived Ut is used to prepare arbitrary qubit states from the starting |0> state and to construct the required unitary operations for ultra-fast quantum logic gates.

6CCVD is uniquely positioned to supply the high-specification diamond materials required to replicate and advance this research into practical quantum devices. The ultra-fast gate times achieved here necessitate diamond substrates with exceptional purity and minimal internal strain.

To achieve the high fidelity and long coherence times required for nanosecond-scale NV center manipulation, researchers need the highest quality diamond.

  • Primary Material: Optical Grade Single Crystal Diamond (SCD).
    • Purity: Ultra-low nitrogen concentration (< 1 ppb) is critical for minimizing decoherence and maximizing the NV center spin coherence time (T2).
    • Strain: Low internal strain is essential to prevent unwanted splitting or shifting of the spin levels, which would compromise the exact magnetic field control demonstrated in this paper.
  • Alternative/Future Material: Polycrystalline Diamond (PCD) or Boron-Doped Diamond (BDD) may be applicable for integrated magnetic field sensors or electrodes, leveraging 6CCVD’s large-area capabilities.

The integration of NV centers into high-field magnetic systems often requires non-standard material specifications. 6CCVD offers full customization to meet these precise engineering needs.

Requirement from Research6CCVD CapabilityTechnical Specification
Substrate Size & IntegrationCustom Dimensions & Large AreaPlates/wafers up to 125 mm (PCD) and custom SCD sizes for integration into complex magnetic setups.
Depth ControlPrecise Thickness ControlSCD wafers available from 0.1 ”m to 500 ”m thickness, allowing optimization for surface-near NV creation or bulk applications.
Surface QualityAdvanced PolishingSCD surfaces polished to Ra < 1 nm, minimizing surface defects that can introduce noise or reduce NV stability.
Hybrid Control SchemesCustom Metalization ServicesInternal capability to deposit thin films (e.g., Ti/Pt/Au, W, Cu) for creating on-chip microwave antennas or electrodes, supporting future hybrid magnetic/RF control schemes.

6CCVD’s in-house team of PhD material scientists and engineers specializes in optimizing diamond properties for quantum applications. We offer comprehensive support for projects focused on NV Center Quantum Computing and Sensing.

We assist researchers in:

  • Selecting the optimal SCD grade based on target coherence times (T2).
  • Determining ideal substrate thickness and orientation for specific magnetic field geometries.
  • Developing custom metalization recipes for integrated quantum circuits.

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

View Original Abstract

The negatively charged nitrogen-vacancy (NV) center spin in diamond can be used to realize quantum computation and to sense magnetic fields. Its spin triplet consists of three levels labeled with its spin z-components of +1, 0, and -1. Without external field, the +1 and -1 states are degenerate and higher than the 0 state due to the zero-field splitting. By taking the symmetrical and anti-symmetrical superpositions of the +1 and -1 states as our qubit basis, we obtain exact evolution operator of the NV center spin under time-dependent magnetic field by mapping the three-level system on time-dependent quantum two-level systems with exact analytical solutions. With our exact evolution operator of the NV center spin including three levels, we show that arbitrary qubits can be prepared from the starting 0 state and arbitrary rapid quantum logic gates of these qubits can be realized with magnetic fields. In addition, it is made clear that the typical quantum logic gates can be accomplished within a few nanoseconds and the fidelity can be very high because only magnetic field strength needs to be controlled in this approach. These results should be useful to realizing quantum computing with the NV center spin systems in diamond and exploring other effects and applications.