Operating two exchange-only qubits in parallel

Abstract

Semiconductors are among the most promising platforms to implement large-scale quantum computers, as advanced manufacturing techniques allow fabrication of large quantum dot arrays. Various qubit encodings can be used to store and manipulate quantum information on these quantum dot arrays. Regardless of qubit encoding, precise control over the exchange interaction between electrons confined in quantum dots in the array is critical. Furthermore, it is necessary to execute high-fidelity quantum operations concurrently to make full use of the limited coherence of individual qubits. Here, we demonstrate the parallel operation of two exchange-only qubits, consisting of six quantum dots in a linear arrangement. Using randomized benchmarking techniques, we show that issuing pulses on the five barrier gates to modulate exchange interactions in a maximally parallel way maintains the quality of qubit control relative to sequential operation. The techniques developed to perform parallel exchange pulses can be readily adapted to other quantum-dot based encodings. Moreover, we show the first experimental demonstrations of an iSWAP gate and of a charge-locking Pauli spin blockade readout method. The results are validated using cross-entropy benchmarking, a technique useful for performance characterization of larger quantum computing systems; here it is used for the first time on a quantum system based on semiconductor technology.

Figures (12)

• Figure 1: Device and experimental pulse sequencesa) Typical pulse sequence used in this work (left) and the Tunnel Falls device (right). The scanning electron microscope image of a device similar to the one used in this work indicates the position of quantum dots (QD) used to form qubits (blue) and charge sensors (yellow), as well as regions of accumulated two-dimensional electron gas (green). The exchange-only qubits Q$_1$ and Q$_2$ are encoded on the six QDs (dashed lines). Voltage pulses applied sequentially (orange box) or in parallel (green box) to the electrodes dynamically control the exchange coupling strength between QDs, allowing for exchange-only qubit operations. b) Charge-locking readout sequence employed in all measurements presented in the paper (time axis not to scale). First, (I) we ramp QD$_4$-QD$_5$ to the PSB readout window in 21.84ns, (II) subsequently allow a 3.64ns projection time before pulsing Q$_2$ to its PSB readout window, (III, optional) before reducing the tunnel coupling between QDs involved in readout. We repeat these steps for QD$_8$-QD$_9$ in (IV), (V), and (VI). Then, (VII) the signal for QD$_4$-QD$_5$ is integrated for 18µs. Next, (VIII) we integrate the QD$_8$-QD$_9$ signal for 18µs before ramping both qubits to their manipulation position in 21.84ns each in (IX) and (X). c) Quantum State Tomography (QST) of the $\ket{00}$ state. We initialize by post-selection using the PSB readout sequence, and measure a fidelity of $86.4 \pm 1.4 \%$.
• Figure 1: Exchange quality factor vs $N_{osc}$a) Exchange oscillations measured for QD$_8$-QD$_9$. b-e) Zoom-in on the exchange oscillations with sinusoidal fits to extract the momentary frequency. We note that the frequency increases with increasing pulse length, which can be correlated with the final settling of the barrier electrode voltage. For qubit control, only the total angular evolution during the exchange pulse is relevant. Overlap with transients from previously issued pulses can be accounted for with additional calibrations such as pulse-domain pre-distortions. It is, however, difficult to reliably extract quality factors for exchange oscillations at a fixed frequency. f) When fitting the data with a decaying sinusoid, we extract a quality factor of 21.5 at 49.856MHz. Ignoring the steadily rising frequency, we also fit the envelope of the decaying oscillation to extract $N_{osc}$ of 33.7 weinstein2023universal.
• Figure 2: Simultaneous exchange pulsinga) Exchange fingerprint for the double dot QD$_7$-QD$_8$, measured with 8 consecutive exchange pulses of 10.92ns, each followed by a 10.92ns pulse buffer. b) Exchange fingerprint for the double dot QD$_7$-QD$_8$, measured in the same manner as a), while also simultaneously applying a voltage $v'B_6$ on the B$_6$ electrode to emulate an exchange pulse between QD$_5$-QD$_6$. c) Linecuts along the dashed lines of the fingerprints in a) and b), illustrating the change in the exchange coupling due to simultaneous pulsing. d) Qualitative diagram of potential landscape during simultaneous exchange pulses on electrodes B$_6$ and B$_8$ under different barrier-barrier compensation schemes: ideal compensation (black), no compensation (orange) and next-nearest barrier compensation (blue). Using next-nearest barrier compensation, the impact of simultaneous pulses on the potential landscape, and therefore the resulting exchange couplings, is suppressed. e) Change in the linecut of the QD$_7$-QD$_8$ fingerprint at -10mV detuning as a function of the pulse amplitude applied to B$_6$ without barrier-barrier compensation. f) Same measurement as in e), but with barrier-barrier compensation enabled. The B$_6$ amplitude dependence of the fingerprint linecut is suppressed.
• Figure 2: Double quantum-dot characterizationa,f,k,p,u) Charge stability diagrams for a) QD$_4$-QD$_5$ in (1,3) charge configuration, f) for QD$_5$-QD$_6$ in (3,1), k) for QD$_6$-QD$_7$ in (1,1), p) for QD$_7$-QD$_8$ in (1,3), and u) for QD$_8$-QD$_9$ in (3,1). b,g,l,q,v) Exchange fingerprints for b) QD$_4$-QD$_5$ with four 10.92ns pulses, g) for QD$_5$-QD$_6$ with four 10.92ns pulses, l) for QD$_6$-QD$_7$ with eight 10.92ns pulses, q) for QD$_7$-QD$_8$ with eight 10.92ns pulses, and v) for QD$_8$-QD$_9$ with eight 10.92ns pulses. c,h,m,r,w) Calibrated exchange coupling tunability for c) QD$_4$-QD$_5$, h) for QD$_5$-QD$_6$, m) for QD$_6$-QD$_7$, r) for QD$_7$-QD$_8$, and w) for QD$_8$-QD$_9$. d,i,n,s,x) Measurement of exchange oscillations for d) QD$_4$-QD$_5$, i) for QD$_5$-QD$_6$, n) for QD$_6$-QD$_7$, s) for QD$_7$-QD$_8$, and x) QD$_8$-QD$_9$. e,j,o,t,y) Singlet lifetime measurement for d) QD$_4$-QD$_5$, i) for QD$_5$-QD$_6$, n) for QD$_6$-QD$_7$, s) for QD$_7$-QD$_8$, and x) for QD$_8$-QD$_9$.
• Figure 3: Individual vs simultaneous single-qubit gatesa,b) Blind randomized benchmarking of Q$_1$ with both qubits initialized. We measure an average Clifford fidelity of $99.84 \pm 0.02\%$ including $0.08 \pm 0.02\%$ leakage error. The error bar is calculated as a standard deviation to the mean on 5 measurement repetitions. c,d) Blind RB of Q$_2$, measured similarly to Q$_1$. We measure $99.41 \pm 0.03\%$ average Clifford gate fidelity including $0.13 \pm 0.02\%$ leakage error. e) Simultaneous blind RB of Q$_1$ and Q$_2$. The two qubits perform different Clifford sequences with the same number of gates at the same time. We measure $99.77 \pm 0.02\%$ (including $0.11 \pm 0.04\%$ leakage error) and $99.36 \pm 0.03\%$ (including $0.16 \pm 0.03\%$ leakage error) average Clifford gate fidelity for f) Q$_1$ and g) Q$_2$, respectively. This constitutes a $0.05-0.07\%$ reduction in fidelity compared to individual blind RB for both qubits.