Persistence of Entangled States and High Fidelity Quantum Gate Operations in Si/SiGe Spin Qubits at High Temperature

Abstract

We characterize single- and two-qubit operations in a SiGe quantum dot array, from the perspective of its quantum information processing capabilities. The analysis includes rigorous randomized benchmarking of single- and two-qubit gates, SPAM characterization, and Bell's state tomography, which are all basic functionality required for universal quantum computation. To assess compatibility with integrated cryogenic electronics, we evaluate qubit performance at 350 mK, 500 mK, and 750 mK, with high fidelity single and two qubit operations. The highest temperature, 750 mK, falls within the realistic thermal budget for practical integrated cryogenic electronics and represents the highest operating temperature reported for this qubit platform.

Figures (10)

• Figure 1: (a) Scanning electron micrograph of a 6-quantum dot device nominally identical to the one measured. (b) On the left: histogram of the charge sensor signal as a function of the detuning $\epsilon$, scanning perpendicularly to interdot charge transition. The red dashed line identifies the readout point, where parity readout is enabled. Parity readout is used for a state filter (SF; on the right), which discards antiparallel spin states. (c) Even to odd parity flip probability. The pulse on the interdot barrier activates the exchange coupling, exhibiting the typical spin funnel shape (for more details on this experiment see Petta2005). (d) Demonstration of CROT gate. Following a double initialization stage, as explained in main text, a CROT is applied on target qubit $Q_0$ with control qubit $Q_1$. We show the percentage of singlets measured with and without a $\pi$ rotation on the control qubit $Q_1$. The virtual barrier amplitude is approximately 420mV, as indicated by dashed line in (c). (e) Initialization and readout of two qubit state. We apply an additional state filtering (SF3) followed by a CROT operation for the two-qubit readout. This allows to distinguish between two states with same parity, as shown in the schematics. By applying an additional X rotation on control $Q_1$ before the readout stage, SF3, we can map odd states into even states, thus enabling the readout of odd states. All state filterings here refer to the same quantum process.
• Figure 2: Free evolution coherence $T_2^*$ times measurements with the Ramsey protocol at three different temperatures. We add a waiting time-dependent phase shift to the last $\pi/2$ pulse with 1 MHz artificial detuning to highlight the decay envelope. (a), (b) Ramsey interference fringes for $Q_0$ and $Q_1$ at $350mK$ (blue); (c), (d) at $500mK$ (orange); (e), (f) at $750mK$ (red). $T_2^*$ dephasing times are extracted by fitting the envelopes of the Ramsey experiment data, indicated by black dashed lines.
• Figure 3: Clifford randomized benchmarking for both qubits at temperatures of 350mK (blue, $\blacktriangledown$), 500mK (orange, $\bullet$), and 750mK (red, $\blacktriangle$). Each datapoint represents an average return probability after applying 15 random Clifford sequences per Clifford depth. Fidelity data is given in the figures and summarised in Table \ref{['tab:performance_summary']}.
• Figure 4: Benchmarking $CZ$ gate fidelities using ICRB at three different temperatures: 350mK (blue); 500mK (orange); 750mK (red). The left and right columns show results for, respectively, the reference and interleaved benchmarking sequences for $P_1$, $P_2$, $P_3$. Each datapoint represents an average return probability after applying 10 random Clifford sequences per Clifford depth. The extracted fidelities are summarised in Table \ref{['tab:performance_summary']}.
• Figure 5: (a)--(c) Reconstructed via tomography density matrices for the Bell state $\frac{1}{\sqrt{2}}(\ket{00} + \ket{11})$, (d)--(f) corresponding SPAM-corrected density matrices, and (g)--(i) measured SPAM matrices. The vertical axis represents the real component, color indicates phase. The black wireframe for the Bell state results indicates where the real component would be ideally. The columns from left to right represent the results for the temperatures $T=350mK$ ((a),(d),(g)), 500mK ((b), (e), (h)), and 750mK ((c), (f), (i)), respectively. Fidelity and concurrence values before and after SPAM correction are given in Table \ref{['tab:performance_summary']}.