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Quantum interface between a transmon qubit and spins of nitrogen-vacancy centers

MetadataDetails
Publication Date2017-12-01
JournalPhysical review. A/Physical review, A
AuthorsYaowen Hu, Yipu Song, Luming Duan
InstitutionsUniversity of Michigan, Tsinghua University
Citations12
AnalysisFull AI Review Included

Quantum Interface Hybrid Systems: Transmon Qubits and NV Centers in Diamond

Section titled “Quantum Interface Hybrid Systems: Transmon Qubits and NV Centers in Diamond”

Technical Analysis and Material Solutions from 6CCVD

This document analyzes the research paper detailing a hybrid quantum system coupling transmon superconducting qubits directly to nitrogen-vacancy (NV) centers in diamond. This architecture provides a promising pathway for large-scale quantum computing by combining the long coherence times of NV spins (memory) with the fast control capabilities of transmon qubits (processor).


The proposed hybrid system establishes a highly efficient quantum interface by directly coupling a transmon qubit to NV center spins in a diamond chip.

  • 1000x Coupling Enhancement: The direct coupling strength between the transmon and an individual NV spin ($2\pi \times 8\ kHz$) is estimated to be three orders of magnitude larger than that achieved via a conventional cavity-single NV coupling.
  • Low-Density Advantage: This large coupling rate greatly reduces the required density of NV centers, enabling the use of low-density ensembles (e.g., $5 \times 10^{16}\ \text{cm}^{-3}$) while still achieving the strong coupling regime ($g_{t-ens} = 15\ \text{MHz}$).
  • Efficient Quantum Memory: The system facilitates the use of NV spin ensembles as robust quantum memory, leveraging their long coherence time ($\sim 2\ \text{ms}$) to store states transferred from the fast transmon qubit ($\text{T}_1 \sim 10 - 100\ \mu\text{s}$).
  • Feasible Quantum Operations: The architecture supports crucial quantum operations, including SWAP gates for state transfer and Quantum Non-Demolition (QND) measurement of the spin ensemble state via dispersive readout of the transmon.
  • Virtual Exchange Bus: The transmon acts as a high-rate virtual bus, enabling coherent information transfer between distant spins, which is significantly more efficient than direct spin-spin interaction.
  • Material Requirement: Success hinges on integrating high-quality diamond chips, controlling NV density, and precision alignment near superconducting Josephson Junction (JJ) circuits.

ParameterValueUnitContext
NV Center Zero Field Splitting ($\omega_+$)2.88GHzTransition between $m_s=0$ and $m_s=\pm 1$ states.
Required Magnetic Field ($B_{NV}$)$\sim 10$mGUsed to tune Transmon frequency to resonance (2.88 GHz).
Transmon Transition Frequency (Example)3.7 (tuned to 2.88)GHzDouble-JJ Transmon.
Junction Resistance ($R_n$)15kΩCharacteristic resistance of the Josephson Junction.
Charging Energy ($E_c$)92MHzTransmon design parameter.
Transmon Critical Current ($I_c$)500nAUsed for single-spin coupling strength calculation.
Single Spin Coupling Strength ($g_{ts}$)$2\pi \times 8$kHzDirect coupling to single-JJ Transmon (at $0.1\ \mu\text{m}$ distance).
NV Ensemble Density ($n$)$5 \times 10^{16}$$\text{cm}^{-3}$Low-density required for $1\ \text{MHz}$ strong coupling regime.
Diamond Crystal Size ($L_N$)$\sim 4$$\mu\text{m}$Required size to achieve $1\ \text{MHz}$ collective coupling at low density.
Transmon Relaxation Time ($\text{T}_1$)$10 - 100$$\mu\text{s}$Typical coherence time for the transmon qubit.
NV Center Coherence Time$\sim 2$msLong coherence time used for quantum memory.
Collective Coupling Rate ($g_{t-ens}$)15MHzTypical strong coupling strength to the spin ensemble.
Dispersive Frequency Shift ($2\chi$)$\approx 1.15$MHzUsed to distinguish spin ensemble states via transmon readout.

The experiment relies on precision fabrication and operation of a superconducting circuit integrated directly with a high-quality diamond substrate containing NV centers.

  1. Material Integration: A diamond chip (crystal size $L_N \approx 4\ \mu\text{m}$ to $20\ \mu\text{m}$ scale) containing low-density NV ensembles is placed directly over the superconducting Transmon loop, located inside a coplanar waveguide (CPW) cavity.
  2. Transmon Design: A double-Josephson junction (double-JJ) transmon is utilized. This design allows the transmon’s transition frequency ($\omega_t$) to be finely tuned via external magnetic flux ($\Phi$) to be resonant (2.88 GHz) with the NV spin ensemble.
  3. Direct Magnetic Coupling: The transmon current generates a magnetic field ($B$) that is proportional to the transmon displacement operator ($\tau_x$). This field couples directly to the magnetic dipole moment ($\mu$) of the electron spins in the NV centers ($H_{\text{int}} = -\mu \cdot B$).
  4. Ensemble Coupling Enhancement: The collective coupling rate ($g_{t-ens}$) is enhanced by a factor of $\sqrt{N}$ by utilizing an ensemble of $N$ near-resonant NV spins, allowing strong coupling ($g_{t-ens} \gg \text{decoherence rate}$) even with low spin density.
  5. Quantum State Transfer (SWAP): A resonant interaction ($\Delta_{t-ens} = 0$) between the transmon and the NV ensemble facilitates a SWAP gate operation. This transfers the quantum state from the transmon (processor) to the NV ensemble (memory) in a fixed interaction time $t = \pi/(2g_{t-ens})$.
  6. Quantum Non-Demolition (QND) Readout: The state of the NV ensemble is read out dispersively in the off-resonant regime ($g_{t-ens} \ll \Delta_{t-ens}$). The resulting shift in the transmon frequency ($2\chi \approx 1.15\ \text{MHz}$) is detected by probing the transmon state through the superconducting cavity.

6CCVD is uniquely positioned to supply the advanced diamond materials and precision engineering services required to replicate and advance this cutting-edge hybrid quantum architecture. The success of this design relies critically on controlling NV concentration and ensuring ultra-smooth integration surfaces.

The research necessitates highly controlled, high-purity diamond material. 6CCVD recommends:

  • Optical Grade Single Crystal Diamond (SCD): Required for achieving the necessary long coherence times ($\sim 2\ \text{ms}$) and minimal inhomogeneous broadening, essential for NV center performance as quantum memory.
  • Controlled NV Doping: The experiment explicitly demands a low density of NV centers ($5 \times 10^{16}\ \text{cm}^{-3}$). 6CCVD provides:
    • Low-Nitrogen Precursors: SCD growth using carefully controlled nitrogen incorporation to achieve specific, low-target NV densities.
    • Post-Processing Substrates: Ultra-pure SCD material optimized for subsequent ion implantation and annealing procedures (by the client) to precisely control NV location near the transmon interface (e.g., $0.1\ \mu\text{m}$ depth).

The integration requires a highly specific diamond chip geometry and interface quality to maximize coupling efficiency and minimize decoherence.

Experimental Requirement6CCVD CapabilityValue Proposition
Crystal Dimensions ($L_N$)Custom Plates/Wafers up to 125mm (PCD) or precision-cut SCD samples.We can provide large starting wafers for multiple device fabrication, or precision-cut/laser-machined chips (e.g., $4\ \mu\text{m}$ to $20\ \mu\text{m}$ scale) for direct device integration.
Interface QualityUltra-Polishing: $\text{Ra} < 1\ \text{nm}$ (SCD).Crucial for clean, low-loss deposition of the superconducting Transmon circuit directly onto the diamond surface. Minimizes spurious charge noise affecting transmon coherence.
Integration LayersCustom Metalization: Au, Pt, Pd, Ti, W, Cu (Internal capability).We can provide diamond substrates pre-metalized with adhesion and barrier layers (e.g., Ti/Au) optimized for subsequent superconducting circuit deposition by the client, ensuring robust circuit integration.
Thickness ControlSCD thickness control from $0.1\ \mu\text{m}$ up to $500\ \mu\text{m}$.Precise control over substrate thickness is vital for maintaining microwave cavity modes and thermal management in cryogenic setups.

This research demonstrates a crucial step toward scalable, fault-tolerant quantum computing leveraging the unique properties of MPCVD diamond. 6CCVD’s in-house PhD team specializes in CVD material science and high-purity growth optimization. We can assist researchers and engineers with material selection, orientation matching, and post-growth processing strategies (e.g., surface termination/polishing) required for similar Hybrid Superconducting Qubit/NV Center projects. We ensure that the diamond substrate is engineered to meet the stringent demands of strong coupling and long coherence times at cryogenic temperatures.

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

View Original Abstract

Hybrid quantum circuits combining advantages of each individual system have\nprovided a promising platform for quantum information processing. Here we\npropose an experimental scheme to directly couple a transmon qubit to an\nindividual spin in the nitrogen-vacancy (NV) center, with a coupling strength\nthree orders of magnitude larger than that for a single spin coupled to a\nmicrowave cavity. This direct coupling between the transmon and the NV center\ncould be utilized to make a transmon bus, leading to a coherently virtual\nexchange among different single spins. Furthermore, we demonstrate that, by\ncoupling a transmon to a low-density NV ensemble, a SWAP operation between the\ntransmon and NV ensemble is feasible and a quantum non-demolition measurement\non the state of NV ensemble can be realized on the cavity-transmon-NV-ensemble\nhybrid system. Moreover, on this system, a virtual coupling can be achieved\nbetween the cavity and NV ensemble, which is much larger in magnitude than the\ndirect coupling between the cavity and the NV ensemble. The photon state in\ncavity can be thus stored into NV spins more efficiently through this virtual\ncoupling.\n