Latest research progress of Tencent quantum computing：High efficiency superconducting qubit initialization scheme

When we use classical calculators, we often press a reset key before starting a new calculation, and some calculators will make a crisp "reset". Quantum computers also need to "reset" or "initialize" before performing a calculation. In 2000, one of the five general standards for constructing quantum computers (i.e. divinenzo criteria [1]) proposed by physicist divinenzo is "the ability to initialize quantum states". As the starting point of the whole quantum circuit, efficient initialization is very important for subsequent gate operation and reading. Moreover, because qubits are easily polluted by environmental noise, preparing a clean initial state for quantum computing is also a challenging topic.

In addition to the preparation of pure initial states, there is a problem similar to the memory overflow of classical computers in superconducting quantum computing. In the commonly used transmon superconducting qubits, the | 0 > and | 1 > states are represented by the ground state and the first excited state of the system. However, due to the small energy level anharmonicity, the energy is easy to leak out of the computational subspace formed by these two states and enter the high energy level. This leakage will not only increase the computational error rate, but also cause coherent error propagation, which makes most current quantum error correction schemes ineffective. In order to improve the calculation success rate and ensure the success of error correction code, we also need to reset some target bits with high fidelity, fast and without affecting the reset of surrounding bits. For these practical needs, researchers have developed many schemes for the initialization of superconducting qubits, but these schemes still have their own advantages and disadvantages, and there is still much room for improvement compared with other quantum computing systems. To solve this bottleneck problem, the relevant teams of Tencent quantum lab have proposed an efficient scheme to initialize superconducting qubits. Its highlights include: 1) the initialization speed and fidelity are better than those proposed in the past; 2) Initialization has little impact on the surrounding bits and strong scalability; 3) It can be used for initialization of higher energy levels; 4) There is no need to introduce auxiliary system, which has strong compatibility with the existing system and wide applicability.

This parameter initialization scheme has the following advantages:
Fast speed and high fidelity
As summarized in Fig. 3, among the publicly reported superconducting qubit initialization schemes, our scheme (red dot) has obvious advantages in speed and fidelity. The schemes summarized in Figure 3 are divided into two categories: one is the feedback method based on pre measurement (diamond), and the other is the method without feedback (square and circle). There are two characteristic time points in the non feedback scheme: the first lowest point and the stable time point waiting for 5 / 𝜅, which are distinguished by square and circle respectively. 1 / 𝜅 is the characteristic dissipation time of the resonator. After waiting for 5 / 𝜅, the system dissipates 0.007 photons. It can be approximately considered that the photons in the resonator have been attenuated, so it is called the stable time point. In our scheme, the initialization time required for the first lowest point is 34ns and the corresponding fidelity is 99.92%, which can be applied to the fields of state transmission and quantum simulation [8]. This characteristic point has advantages in speed, but because there are still excited photons in the resonator, it needs to wait for dissipation, so it is not possible to operate the gate immediately. As mentioned earlier, in order to avoid the influence of residual photons on bit frequency, it is necessary to wait another 5 / 𝜅 for the photons to decay completely. The overall initialization time is 284 ns (34 + 5 / 𝜅, 1 / 𝜅 = 50ns), and the corresponding fidelity is 99.86%. It can be seen that different characteristic time points have their own advantages and disadvantages in speed and scope of application, which need to be selected as appropriate in practical application.

 summary of different initialization schemes: initial time and fidelity (red is the work) [4-5, 9-14]

It has little impact on the surrounding bits and is suitable for multi bit system
As mentioned earlier, the biggest defect of the scheme [5] to realize bit cooling by changing the bit frequency and resonating with a high loss reading cavity is crosstalk. The driving applied by this scheme of changing frequency has a great impact on the surrounding bits, and additional calibration of the surrounding bits is required, which affects the overall efficiency. One advantage of the proposed parameter initialization is that the applied drive is a simple single frequency or dual frequency sinusoidal drive, which has little effect on the surrounding bits. Through a series of randomized benchmarking, we studied the influence of bits around the parameter initialization process on the fidelity of single bit gate, as shown in Figure 4. During the initialization of the first bit Q1, the single bit gate fidelity of the other two bits Q2 and Q3 decreased by only 0.07% and 0.03% respectively, indicating that parameter initialization has little impact on the surrounding bits. Therefore, the initialization of qubits and the gate operation of surrounding bits can be carried out at the same time, which greatly enhances the scalability of the initialization scheme: when the number of bits increases, the bit initialization of adjacent bits that are not affected will significantly improve the mobility and computational efficiency of the quantum algorithm.

Influence of initialization process of calibration parameters on surrounding bits in random benchmark

It can be applied to the initialization of highly excited states
The model described above only considers the two-level system composed of the ground state | g > and the first excited state | E >. However, in actual bit manipulation, such as the common CZ double bit gate operation, the bit may be excited to a higher energy level, such as the second excited state | f >. This high-energy leakage will reduce the fidelity of the bit gate [5]. Therefore, an efficient initialization scheme that can combine | E > and | f > states at the same time will have wider practical value. For highly excited states, we further extend the two tone parametric initialization scheme, which can apply parametric modulation of two frequencies to bits at the same time. These two frequencies can be finely adjusted to establish a connection channel between a higher bit level and the reading resonator. As shown in Figure 5, we prepare the system to | E >, | f > states respectively. Under dual frequency modulation, both initial states can reach 99.23% initialization fidelity within 1000 ns. If some quantum algorithms, especially when intermediate measurement is required, have strict requirements for leakage accumulation, we can use dual frequency initialization for high-energy level to reduce the error of high-energy level leakage.

Dual frequency initialization shall be used for high-energy excitation, and the first excited state and the second excited state shall be initialized at the same time

Link：https://www.nature.com/articles/s41467-021-26205-y