Toward the Speed Limit of High-Fidelity Two-Qubit Gates

At a Glance

Metadata	Details
Publication Date	2022-06-08
Journal	Physical Review Letters
Authors	Swathi S. Hegde, Jingfu Zhang, Dieter Suter
Institutions	TU Dortmund University
Citations	10
Analysis	Full AI Review Included

Executive Summary

This research introduces a highly efficient, high-fidelity 2-qubit gate operation that achieves the theoretical quantum speed limit by eliminating time-dependent external control fields.

Core Innovation: The Conditional Rotation (U_CR) gate is implemented solely through free evolution under the static internal Hamiltonian, removing the need for complex microwave (MW) pulse sequences during the gate operation.
Speed Maximization: The gate duration (4.545 µs for a π rotation) is limited only by the intrinsic hyperfine coupling (A_zx) of the system, achieving the fastest possible time (the quantum speed limit).
Error Mitigation: By eliminating time-dependent control fields, the gate is inherently robust against errors arising from control field imperfections, noise, and timing jitter.
System Used: A single Nitrogen-Vacancy (NV) center in diamond, utilizing the electron spin (control qubit) and a coupled ¹³C nuclear spin (target qubit) at room temperature.
Performance: Demonstrated high experimental state fidelities, achieving 96% for Bell-type state preparation and >0.99 for checks of the conditional rotation operation.
Impact: This methodology significantly reduces control overhead and execution time, improving the overall efficiency of multi-gate quantum circuits for sensing and computing protocols.

Technical Specifications

Parameter	Value	Unit	Context
Quantum Speed Limit Gate Time (U_CR(π))	4.545	µs	Duration of free evolution for π rotation.
Operating Temperature	Room	Temperature	Experimental environment (NV center in diamond).
Electron Zero Field Splitting (D)	2.870	GHz	Static Hamiltonian parameter.
¹³C Longitudinal Hyperfine Coupling (A_zz)	-0.152	MHz	Coupling between electron and ¹³C.
¹³C Transverse Hyperfine Coupling (A_zx)	0.110	MHz	Parameter determining the gate speed (τ = α / 2πA_zx).
External Magnetic Field (B₀)	14.2	mT	Applied along the NV axis (z-axis).
Electron Larmor Frequency (v_e)	-400.110	MHz	Includes shift from ¹⁴N coupling.
Bell State Preparation Fidelity (F)	96	%	Fidelity relative to the ideal Bell-type state.
CR Operation Fidelity (Control Qubit 1)	>0.99	N/A	Experimental fidelity check (Fig. 3d).
Initialization Laser Wavelength	532	nm	Used for electron spin initialization and readout.
Initialization Laser Pulse Duration	5	µs	Used for electron spin reset.
Initialization Laser Power	~0.5	mW	Used during initialization/readout.

Key Methodologies

The experiment relies on engineering the computational basis states such that they are not all eigenstates of the system Hamiltonian, allowing conditional evolution without external fields.

System Selection and Alignment: A single NV center in diamond is used, coupling the electron spin (S=1) to a nearby ¹³C nuclear spin (I=1/2). A static magnetic field (B₀ = 14.2 mT) is applied along the NV axis (z-axis).
Qubit Definition: The control qubit is defined by two electron spin levels (m_s = 0 and m_s = -1). The target qubit is the ¹³C nuclear spin.
Basis State Engineering: The computational basis states are chosen such that states |00> and |01> are eigenstates of the system Hamiltonian (and thus do not evolve), while states |10> and |11> are superpositions of eigenstates (and thus evolve conditionally).
Initialization and Purification: The system is initialized to a starting state (e.g., |00>) using a 532 nm laser pulse and subsequent electron-nuclear spin swap operations. A clean-up operation (U_cu), consisting of MW pulses, is applied to selectively move spurious populations (e.g., |01>) out of the computational subspace (to m_s = +1) for high polarization.
Gate Implementation (Free Evolution): The Conditional Rotation gate (U_CR(α)) is executed by simply waiting for a duration τ under the influence of the internal Hamiltonian (H_I). For a π rotation, the duration is set precisely to τ = 4.545 µs, determined by the transverse hyperfine coupling A_zx.
Readout Procedure: State populations are measured by counting photons during a final laser pulse. Since the laser only measures the m_s = 0 ground state population, additional inversion pulses (U₁₈₀) and clean-up operations (V_cu) are incorporated into the readout sequence to measure specific diagonal elements (e.g., P_|11>).

Commercial Applications

This technology, focused on high-speed, robust quantum gates in solid-state systems, is highly relevant to the development of practical quantum hardware.

Quantum Computing (Solid-State Qubits): Provides a method for implementing fundamental 2-qubit gates (like CNOT or conditional rotations) at the physical speed limit, drastically reducing the execution time of quantum algorithms in diamond-based quantum processors.
Quantum Sensing and Metrology: Efficient, high-fidelity gates are crucial for preparing entangled states (like Bell states) used in quantum sensors based on NV centers, improving sensitivity and coherence time utilization.
NV Center Technology: Advances the control and manipulation capabilities of NV centers, which are leading candidates for room-temperature quantum registers and memory elements.
Fault-Tolerant Quantum Systems: The inherent robustness against control field errors makes this gate design valuable for building more reliable quantum circuits, reducing the overhead required for error correction.
Hybrid Quantum Systems: Applicable to other hybrid qubit architectures where a fast, robust gate between two coupled spins (e.g., electron-nuclear or electron-photon) is required.

View Original Abstract

Most implementations of quantum gate operations rely on external control fields to drive the evolution of the quantum system. Generating these control fields requires significant efforts to design the suitable control Hamiltonians. Furthermore, any error in the control fields reduces the fidelity of the implemented control operation with respect to the ideal target operation. Achieving sufficiently fast gate operations at low error rates remains therefore a huge challenge. In this Letter, we present a novel approach to overcome this challenge by eliminating, for specific gate operations, the time-dependent control fields entirely. This approach appears useful for maximizing the speed of the gate operation while simultaneously eliminating relevant sources of errors. We present an experimental demonstration of the concept in a single nitrogen-vacancy center in diamond at room temperature.

Toward the Speed Limit of High-Fidelity Two-Qubit Gates

At a Glance

Executive Summary

Technical Specifications

Key Methodologies

Commercial Applications

Tech Support

Original Source

References

Toward the Speed Limit of High-Fidelity Two-Qubit Gates

At a Glance

Executive Summary

Technical Specifications

Key Methodologies

Commercial Applications

Tech Support

Original Source

References

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