| Metadata | Details |
|---|
| Publication Date | 2023-01-01 |
| Journal | Acta Physica Sinica |
| Authors | Fan Xiong, Yong-Cong Chen, Ping Ao |
| Analysis | Full AI Review Included |
- Core Value Proposition: Developed an optimized quantum control strategy for single qubits operating in a thermal noise environment, achieving sustained high fidelity by actively mitigating decoherence effects.
- Control Mechanism: Utilizes a three-dimensional magnetic dipole field drive, which provides more flexible control over the qubit state trajectory compared to traditional planar field methods.
- Modeling Approach: Qubit dynamics under thermal noise were modeled using the Stochastic Dynamic Structure Decomposition (SDSD) method combined with the Kubo-Einstein Fluctuation-Dissipation Theorem.
- Noiseless Performance: Simulations confirmed that the dipole field control method achieves perfect (100%) fidelity in the absence of environmental noise, successfully avoiding non-adiabatic transitions.
- Optimization Strategy: Monte Carlo optimization was applied to the Fourier components of the driving magnetic field to search for optimal control paths that minimize thermal fluctuation-induced deviations.
- Achievement in Noise: The optimized control maintained extremely high quantum fidelity (up to 0.9996) in a simulated noisy environment (T = 0.1 K), demonstrating the methodâs robustness against thermal decoherence.
| Parameter | Value | Unit | Context |
|---|
| Achieved Fidelity (Noiseless) | 1.00 | N/A | Maximum fidelity achieved in the ideal, noise-free simulation. |
| Achieved Fidelity (Noisy) | 0.9996 | N/A | Highest fidelity achieved after Monte Carlo optimization at T = 0.1 K. |
| Magnetic Field Strength (Bd) | 0.4 | T | Selected magnetic field magnitude for the dipole drive. |
| Characteristic Time Scale (t) | ~10-11 | s | Order of magnitude for evolution time (based on h / (M*Bd) for Bd = 1 T). |
| Normalized Evolution Time (Ts) | 0.5 | N/A | Total time duration used in the numerical simulation (where h=1). |
| Environment Temperature (T) | 0.1 | K | Temperature used for modeling the thermal noise environment. |
| Viscosity Coefficient (etax) | 0.08 | N/A | Normalized viscosity coefficient for the x-direction (used in the friction matrix S). |
| Viscosity Coefficient (etay, etaz) | 0.01 | N/A | Normalized viscosity coefficients for the y and z directions. |
| Fourier Components (N) | 2 | N/A | Number of Fourier components used to approximate and optimize the magnetic field trajectory. |
- Qubit System Definition: The qubit was modeled as a spin-1/2 particle in a magnetic field, with its state represented on the Bloch sphere by the vector $n = (\sin \alpha \cos \beta, \sin \alpha \sin \beta, \cos \alpha)$.
- Dipole Field Control: The control field $B(t)$ was generated by a rotating magnetic dipole moment ($m$), providing three orthogonal field components ($B_x, B_y, B_z$) to drive the qubit dynamics.
- Trajectory Design (Noiseless): Initial and final magnetic field directions were constrained to be parallel to the initial and final qubit states. Smooth, non-adiabatic trajectories for the dipole angles ($\theta, \phi$) were constructed using half-period cosine functions (Equations 12, 13).
- Field Decomposition: The time-dependent magnetic field $B(t)$ was approximated using a Fourier series expansion with a limited number of components ($N=2$) to facilitate optimization (Equation 15).
- Thermal Noise Modeling: Thermal noise $\xi(t)$ was introduced as a Gaussian random field added to the control field $B(t)$. The system dynamics were governed by a stochastic differential equation derived using SDSD and the Kubo-Einstein theorem, incorporating friction (S) and diffusion (D) matrices (Equation 29).
- Fidelity Calculation (Noisy): Quantum fidelity ($f$) was calculated using a modified formula that includes an exponential decay term representing the thermal fluctuation-induced deviation ($X$) from the target state (Equation 34).
- Optimization: The Monte Carlo optimization algorithm was applied to the Fourier coefficients ($B_{j,n}$) of the magnetic field. This process iteratively searched the parameter space to find the optimal control path that maximized the calculated quantum fidelity in the presence of noise.
- Quantum Computing Hardware: Essential for developing robust, fault-tolerant quantum computers, particularly those based on spin qubits (e.g., semiconductor quantum dots) or NV centers, where magnetic control is primary.
- High-Fidelity Quantum Gate Operations: The methodology provides a proven technique for designing highly reliable single-qubit gates, a fundamental requirement for scalable quantum processors.
- Quantum Sensing and Metrology: Applicable to high-precision sensors, such as those utilizing Nitrogen-Vacancy (NV) color centers in diamond, where precise magnetic field control and noise mitigation are critical for sensitivity.
- Cryogenic Control Systems: The optimization techniques are relevant for designing control sequences for superconducting qubits and other cryogenic quantum systems where low-temperature thermal noise remains a limiting factor.
- Advanced Quantum Control Theory: Provides a verified framework for integrating fluctuation-dissipation theorems into stochastic quantum dynamics, useful for developing control protocols for multi-qubit systems and complex environments (e.g., colored noise).
View Original Abstract
Quantum computing is a new way to process quantum information by using superposition and entanglement of the quantum system. Quantum stateâs vast Hilbert space allows it to perform operations that classical computers cannot. The quantum computing has unique advantages in dealing with some complex problems, so it has attracted wide attention. Computing a single qubit is the first of seven fundamental stages needed to achieve a large-scale quantum computer that is universal, scalable and fault-tolerant. In other words, the primary task of quantum computing is the careful preparation and precise regulation of qubits. At present, the physical systems that can be used as qubits include superconducting qubits, semiconductor qubits, ion trap systems and nitrogen-vacancy (NV) color centers. These physical systems have made great progress of decoherence time and scalability. Owing to the vulnerability of qubits, ambient thermal noise can cause quantum decoherence, which greatly affects the fidelity of qubits. Improving the fidelity of qubits is therefore a key step towards large-scale quantum computing. Based on the dipole field driven qubit, the stochastic dynamic structure decomposition method is adopted and the Kubo-Einstein fluctuation-dissipation theorem is used to study the qubit control in a thermal noise environment. The dipole field has components in three directions, not just in one plane, which allows more flexible control of quantum states. Without considering the noise, the quantum state can reach the target state 100%. In the noisy environment, thermal noise will cause the deviation between the actual final state and the target final state caused by thermal fluctuation, which becomes the main factor affecting the quantum fidelity. The influence of thermal noise is related to temperature and the evolution trajectory of quantum state. Therefore, this paper proposes an optimal scheme to improve the qubit fidelity in the thermal noise environment. The feasibility of this method is verified by numerical calculation, which can provide a new solution for further guiding and evaluating the experiment. The scheme is suitable for qubit systems of various physical control fields, such as semiconductor qubits and nitrogen vacancy center qubits. This work may have more applications in the development of quantum manipulation technology and can also be extended to multi-qubit systems, the details of which will appear in the future work.