Optimisation of diamond quantum processors
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-09-01 |
| Journal | New Journal of Physics |
| Authors | YunHeng Chen, Sophie Stearn, Scott Vella, Andrew. Horsley, Marcus W. Doherty |
| Institutions | Australian National University |
| Citations | 16 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThe research focuses on developing and simulating optimal control methods for Nitrogen-Vacancy (NV) center diamond quantum processors, aiming for high-speed, high-fidelity operation at ambient conditions.
- Core Value Proposition: A three-step semi-analytical optimal control method was developed to design gate pulses that minimize infidelity caused by random control errors (amplitude, phase, frequency noise).
- Fidelity Achievement: Theoretical single-qubit gate infidelities were demonstrated approaching 10-5, and evidence suggests similar performance (10-6) is achievable for the two-qubit CZ gate.
- Speed Achievement: Optimal gate times were determined to be approximately 1 ”s for both single-qubit and two-qubit CZ operations, achieving 10-6 infidelity.
- Error Mitigation: The optimized control errors (10-5 to 10-6) are reduced below the intrinsic errors introduced by decoherence and hyperfine field misalignment (both typically 10-3 to 10-4).
- Decoherence Limit: The primary performance bottleneck remains the electron spin relaxation time (T1,e â 2.4 ms), which limits nuclear spin coherence and dictates the necessity for faster gates.
- Benchmark Performance: Simulation of Quantum Fourier Transforms (QFT) showed high fidelity (QFT3: 0.964; QFT5: 0.855) with total computation times in the millisecond range (e.g., QFT3 â 0.0031 s).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Operating Temperature | Ambient (Room) | K | Primary operational environment for NV centers. |
| Electron Spin Coherence Time (T2) | â 2.4 | ms | Longest T2 for any solid-state spin at room temperature. |
| Electron Spin Relaxation Time (T1,e) | 1.8 - 2.4 | ms | Limits the nuclear spin qubit coherence time (T2,n). |
| Background Magnetic Field (B0) | 0.62 | T | Static field used for qubit frequency selectivity. |
| Single-Qubit Gate Time (Optimal) | 1 | ”s | Conservative estimate for achieving 10-6 infidelity. |
| Two-Qubit CZ Gate Time (Optimal) | 1 | ”s | Fastest speed demonstrated for 10-6 infidelity. |
| Single-Qubit Infidelity (Control Error) | ~ 10-5 | N/A | Achieved via optimal control, below decoherence limit. |
| Two-Qubit Infidelity (Control Error) | ~ 10-6 | N/A | Theoretically achievable via optimal control. |
| Intrinsic Decoherence Error Magnitude | ~ 10-3 to 10-4 | N/A | Error floor set by T1,e. |
| Hyperfine Misalignment Error Magnitude | ~ 10-3 | N/A | Additional error source for two-qubit gates. |
| Max RF Pulse Amplitude (Single Qubit) | 25 | Mrad/s | Experimental hardware constraint (time domain). |
| Max MW Pulse Amplitude (Two Qubit) | 80 | Mrad/s | Experimental hardware constraint (time domain). |
| QFT3 Total Computation Time | â 0.0031 | s | Simulated time including 500 readout cycles per qubit. |
Key Methodologies
Section titled âKey MethodologiesâThe optimal control method employs a three-step process designed to maximize gate speed and fidelity while ensuring compatibility with physical constraints and feedback optimization routines.
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Quantum Processor Modeling:
- The system Hamiltonian (HI) models nuclear spins (15N, 13C) coupled to the NV electron spin (quantum bus).
- The secular approximation is applied, assuming a strong magnetic field aligned with the NV axis, simplifying the nuclear spin Hamiltonian.
- The computational subspace is defined by the ms = -1 electron spin state.
-
Semi-Analytical Basis Generation (Cross-talk Minimization):
- Control pulses are parameterized in the frequency domain using frequency-shifted sinc functions (Fourier series ansatz).
- The initial step generates a complete basis set that minimizes cross-talk between qubits by satisfying constraints that ensure identity operations on non-target qubits, neglecting time-ordering effects.
-
Linear Combination Optimization (Control Error Minimization):
- The control pulse is constructed as a linear combination of the generated basis functions.
- The linear coefficients are optimized to minimize the average gate infidelity (I) in the presence of random control errors (amplitude, phase, and frequency noise, modeled as Gaussian distributions).
- This step ensures the gate infidelity converges monotonically with increasing basis function size (typically 3 basis functions for single-qubit gates).
-
Time-Ordering Correction (Numerical Refinement):
- For the highest fidelity requirements (approaching 10-5), the effects of time-ordering (neglected in the initial steps) are incorporated via closed-loop optimization or numerical methods (e.g., finite-difference method).
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Decoherence Assessment:
- The performance of the optimized gates is simulated using the Lindblad master equation to account for pure dephasing induced by the electron spin relaxation (T1,e). This confirms that control errors are minimized below the intrinsic decoherence limit.
Commercial Applications
Section titled âCommercial ApplicationsâThe optimization of diamond quantum processors is critical for advancing several quantum technology sectors, particularly those leveraging room-temperature operation.
- Quantum Computing:
- Development of large-scale, fault-tolerant diamond quantum computers.
- Implementation of complex quantum algorithms (e.g., Quantum Fourier Transforms, Shorâs algorithm).
- Building blocks for logical qubits requiring high physical gate fidelities (up to 10-4 for surface code error correction).
- Quantum Sensing and Microscopy:
- Next-generation enhanced quantum sensors and microscopes operating at room temperature.
- Applications in detection of metallo-protein molecules and enhanced signal processing.
- Quantum Information Processing Architectures:
- Promising architecture due to operation in ambient conditions and relatively simple control systems (microwave, RF, off-resonant optical).
- Integration of embedded quantum memories and signal processing capabilities.
- Materials Science Research:
- Quantum simulation of complex systems (e.g., helium hydride cation, topological phase transitions).
View Original Abstract
Abstract Diamond quantum processors consisting of a nitrogen-vacancy centre and surrounding nuclear spins have been the key to significant advancements in room-temperature quantum computing, quantum sensing and microscopy. The optimisation of these processors is crucial for the development of large-scale diamond quantum computers and the next generation of enhanced quantum sensors and microscopes. Here, we present a full model of multi-qubit diamond quantum processors and develop a semi-analytical method for designing gate pulses. This method optimises gate speed and fidelity in the presence of random control errors and is readily compatible with feedback optimisation routines. We theoretically demonstrate infidelities approaching âŒ10 â5 for single-qubit gates and established evidence that this can also be achieved for a two-qubit CZ gate. Consequently, our method reduces the effects of control errors below the errors introduced by hyperfine field misalignment and the unavoidable decoherence that is intrinsic to the processors. Having developed this optimal control, we simulated the performance of a diamond quantum processor by computing quantum Fourier transforms. We find that the simulated diamond quantum processor is able to achieve fast operations with low error probability.