Impact of Classical Control Electronics on Qubit Fidelity

Quantum processors rely on classical electronic controllers to manipulate and read out the state of quantum bits (qubits). As the performance of the quantum processor improves, nonidealities in the classical controller can become the performance bottleneck for the whole quantum computer. To prevent such limitation, this paper presents a systematic study of the impact of the classical electrical signals on the qubit fidelity. All operations, i.e., single-qubit rotations, two-qubit gates, and readout, are considered, in the presence of errors in the control electronics, such as static, dynamic, systematic, and random errors. Although the presented study could be extended to any qubit technology, it currently focuses on single-electron spin qubits, because of several advantages, such as purely electrical control and long coherence times, and for their potential for large-scale integration. As a result of this study, detailed electrical specifications for the classical control electronics for a given qubit fidelity can be derived. We also discuss how qubit fidelity is affected by the limited performance of the general-purpose room-temperature equipment typically employed to control the few qubits available today. Ultimately, we show that tailor-made electronic controllers can achieve significantly lower power, cost, and size, as required to support the scaling up of quantum computers.

Figure 1

(a) A generic model of a spin-qubit quantum processor comprising qubits encoded in the spin of electrons trapped in quantum dots and a charge sensor (e.g., a quantum point contact, QPC). The blue background indicates the two-dimensional electron gas (2DEG) where quantum dots, shown in red, are formed locally. Individual control over the dot potential and the tunnel barriers is assumed, using plunger gates (orange) and barrier gates (green), respectively. Furthermore, each qubit can have a unique Larmor frequency (${\omega }_{0,qi}$). (b) The classical control electronics required for each line type (electron-spin-resonance (ESR) line, plunger gate, and barrier gate) of the quantum processor. The electronic components in the figure are placeholders for the respective functionalities and are grouped by operation, i.e., single-qubit operation, two-qubit operation, and readout. Thus, they do not necessarily correspond to a physical implementation. Arbitrary-waveform generators (AWG) are shown for the envelope and pulse generation.

Figure 2

The amplitude response of the intrinsic qubit filter for (a) frequency noise, (b) wide-band additive noise, and (c) amplitude noise, for various rotation angles $\theta$. The brick-wall approximations are shown with dashed lines.

Figure 3

A typical plot of (a) the phase noise and (b) the resulting frequency-noise PSD of a PLL-based frequency generator. The red line indicates the noise as measured by a phase-noise analyzer, whereas the blue line indicates the part of the noise that is actually phase noise. At high offset frequencies, where the lines diverge, wide-band additive noise shows up in the phase-noise plot, giving rise to a noise floor of around $-150\mathrm{dBc}/\mathrm{Hz}$ in this example.

Figure 4

Qubit-frequency multiplexing: the envelopes, achievable fidelity, and requirements in the case of a rectangular envelope. (a) The rectangular envelope under consideration. (b) The Gaussian envelope under consideration. (c) The infidelity of an identity operation (and the amount of $X$ or $Y$ rotation and $Z$ rotation) on a qubit spaced at ${\omega }_{0,\mathrm{space}}$ from the carrier for a rectangular envelope, along with the Fourier transform of the rectangular envelope. (d) The infidelity of an identity operation (and the amount of $X$ or $Y$ rotation and $Z$ rotation) on a qubit spaced at ${\omega }_{0,\mathrm{space}}$ from the carrier for a Gaussian envelope, obtained by numerical simulation, along with the Fourier transform of the Gaussian envelope. (e) The frequency spacing required to achieve a certain fidelity at given relative signal strength $\beta$, for a rectangular envelope. The upper bound (dashed lines) is given in Eq. (8). (f) The driving tone attenuation $\beta$ required at a certain frequency spacing to achieve a given fidelity, for a rectangular envelope. The lower bound (dashed lines) is given in Eq. (9).

Figure 5

(a) The energy-level diagram of the two-qubit system. An avoided crossing is visible for $|ϵ|=U$ when there is a finite tunnel coupling between the dots. (b) The two-qubit operation speed ${\omega }_{\mathrm{op}}$ [Eq. (11)] versus the interdot tunnel coupling and detuning. A nominal tunnel coupling $t_{0n}$ of 1 GHz is used.

Figure 6

(a) The energy of the stationary states versus the detuning near the avoided crossing. The black dashed lines indicate the states where the left qubit was originally in the $\left|\downarrow \right.⟩$ state. (b) The error probability $1-P_{\mathrm{charge}}$, along with the individual error contributors, at various points of detuning as simulated for various tunnel rates, Larmor frequencies, charging energies, and singlet-triplet energy splittings (each varied over a decade; the resulting plots are overlapping). The obtained probabilities are plotted relative to the optimum, i.e., the lowest error probability at $ϵ=U+E_{\mathrm{ST}}/2$, thereby showing the degradation when moving away from the optimum detuning. (c) The simulated probability $1-P_{\mathrm{charge}}$ versus the singlet-triplet splitting, normalized to the tunnel coupling at $ϵ=U+E_{\mathrm{ST}}/2$, while sweeping either the tunnel coupling or the singlet-triplet energy splitting. (d) A plot of $1-P_{\mathrm{detect}}$ versus SNR in the case of Gaussian-distributed noise. (e) A model of a typical readout chain, showing the sensor, the readout electronics, and the required signal processing for the measurement discrimination. Additional sources modeling the noise are shown in gray.