Jaewon Jung

Figure 1 The 28Si quantum dot device and spin manipulation. (a) Scanning electron microscopy image of a semiconductor quantum dot device with a cobalt micromagnet. The device has an overlaid structure consisting of the screening gate (pink), the accumulation and plunger gates (green), and the barrier gates (blue). it is designed to form a linear five-qubit array. We focused on the leftmost dot (an orange circle in the image) of the linear array as a qubit. By adjusting the plunger gate voltage Vp, we can confine a single electron in the quantum dot. The yellow circle indicates the sensor dot (SD) based on the radio-frequency single-electron transistor (rf-SET). An LC-tank circuit with an inductor L = 1200 nH and a parasitic capacitance Cp ~ 1 pF enables charge sensing via radio-frequency reflectometry. For the qubit operation, we apply a microwave pulse of Vscreen to the screening gate to induce spin resonance. The thin black arrows indicate the x-z plane and the bold arrow with Bext denotes the external magnetic field. (b) illustrates the simple schematic of a single electron spin qubit operation and Rabi chevron pattern. The resonance frequency is 14.6564 GHz at Bext = 439.7 mT.

Figure 2 Schematic of noise amplification methods. (a) An example of the original quantum circuit U is illustrated. The quantum circuit U is composed of the quantum gates G1, G2, ..., GN. The square enveloped pulse shape on the gate block G1 is a schematic of a microwave pulse during spin manipulation. (b), (c), and (d) represent the noise amplification methods that are used in zero-noise extrapolation (ZNE). (b) By adjusting the microwave parameter, we can stretch the gate length of the circuit U', which behaves like the original quantum circuit U. (c) shows the local folding case. The gate Gi is mapped to Gi → Gi (Gi†Gi)n since Gi†Gi equals the identity. (d) shows the global folding case. It is similar to the local folding, but the entire circuit U is mapped to U → U(U†U)n. In (c) and (d), the gray shaded area indicates the identity insertion part that extends the quantum circuit intentionally.

Figure 3 Standard Clifford randomized benchmarking with ZNE. (a)-(c) Probability of measuring a ground state with respect to identity equivalent Clifford sequences for each circuit depth. The color density plots represent the histograms of bootstrapping results of 100 samples for each data point. The noise amplification methods used are (a) global folding and (b) local folding, with corresponding nth-order Richardson extrapolation. (c) The pulse-stretching method is used for the noise amplification, with linear extrapolation results.

Figure 4 Quantum state tomography result of two different prepared states: (a) |-Y⟩ and (b) |X⟩. (a)-(b) Comparison of experimental and ideal values of expectation values for each Pauli operator. The ideal values are shown as the open boxes. Raw data without any mitigation, data with readout error mitigation (REM), and data with both REM and ZNE are depicted as red, green, and blue squares, respectively. (c) Quantum state tomography sequence for ZNE method. The global folding method is used for the ZNE application. The number of shots for the amplification factor n = 0 is three times that for n = 1. (d) State fidelities of raw data (FRaw), REM only (FREM only), and REM and ZNE (FREM+ZNE) with different prepared states. In both cases, the state fidelities are successfully increased through each error mitigating step.

Figure 5 Model violation box plot in gate set tomography (GST). Each box has a loglikelihood ratio (LLR) 2Δ log⁡L values from 36 different sets of circuits with corresponding germ circuits. Germ means the short gate sets and Length means the circuit depth. If the model is Markovian, 2Δ log⁡L is a χ_k^2 random variable where k is 61, 137, 254, 417, 585 each for L = 1, 2, 4, 8, 16. The color of each box indicates the degree of the model violation. The gray color indicates that the model violation is within the expected values, on the other hand, the red color represents a significant model violation where it appears at the probability of 5 % when the gate sequences are Markovian.