Fast and high-fidelity state preparation and measurement in triple-quantum-dot spin qubits

We demonstrate rapid, high-fidelity state preparation and measurement in exchange-only Si/SiGe triple-quantum-dot qubits. Fast measurement integration ($980$ ns) and initialization ($\approx 300$ ns) operations are performed with all-electrical, baseband control. We emphasize a leakage-sensitive joint initialization and measurement metric, developed in the context of exchange-only qubits but applicable more broadly, and report an infidelity of $2.5\pm0.5\times 10^{-3}$. This result is enabled by a high-valley-splitting heterostructure, initialization at the 2-to-3 electron charge boundary, and careful assessment and mitigation of $T_1$ during spin-to-charge conversion. The ultimate fidelity is limited by a number of comparably-important factors, and we identify clear paths towards further improved fidelity and speed. Along with an observed single-qubit randomized benchmarking error rate of $1.7\times 10^{-3}$, this work demonstrates initialization, control, and measurement of Si/SiGe triple-dot qubits at fidelities and durations which are promising for scalable quantum information processing.


I. INTRODUCTION
Spins in semiconductor quantum dots are promising foundational elements for scalable quantum information processing [1][2][3][4][5][6]. This technology leverages the hardearned knowledge and exquisite tools of the semiconductor industry, which routinely mass-produces devices with billions of nanoscale structures. In this work we employ quantum dots which are laterally confined by lithographically-patterned gate electrodes and vertically confined within a high-mobility Si/SiGe heterostructure [7,8]. This construction yields suppressed sensitivity to gate-oxide disorder and noise relative to MOS-based devices [9][10][11]. Additionally, the use of isotopicallyenriched 28 Si permits long spin-coherence times relative to control times [12][13][14]. Rather than form a qubit from an individual electron spin, one can encode a qubit in the collective spin state of three electrons in three quantum dots-the exchange-only qubit (more specifically, a decoherence-free subsystem [DFS] qubit) [15][16][17][18]. These qubits are insensitive to global magnetic noise processes and allow universal control with only baseband electrical pulses, not requiring lasers, large RF circuits, or micromagnets.
High-fidelity single-qubit operations for Si/SiGe exchange-only qubits have been previously demonstrated [19], and we here show high-fidelity state preparation and measurement (SPAM) in a similar device. State preparation and measurement are integral to quantum computing-indeed they are the first and last steps in any algorithm, be it for NISQ, fault-tolerant computing, networking, or sensing applications. A reasonable ambition for SPAM performance is that it maintain fidelities * jzblumoff@hrl.com and durations comparable to those of coherent manipulations, minimizing its likelihood of being a limiting factor in a larger application which may require multiple rounds of initialization and measurement. This establishes concrete goals and forms a natural basis of comparison, and using these criteria we show that exchange-only-qubit SPAM can maintain performance parity.
Our key advancements relative to prior work in PSB/DCS spin qubit measurements-enabling the SPAM performance reported here-include details of the device, the control and amplifier chains, and our voltage biasing protocols. We also employ careful met-arXiv:2112.09801v2 [quant-ph] 28 Jan 2022 rics for device-relevant characterization of SPAM fidelity, and much of this analysis is applicable to measurement modalities other than the PSB/DCS approach. One goal of this work is to provide an updated basis upon which to evaluate the potential of the PSB/DCS approach; whether it is sufficient for high-quality SPAM, or whether more read-out resources will be required for acceptable performance.
Spin qubit initialization also has several approaches, including the use of microwave pumping [46], relaxation [20,47], and measurement-based mechanisms [48], but in light of the desirably-weak interaction of spins with electromagnetic fields, these approaches are often impractically slow. A faster method available in spin systems is to exchange quantum-dot electrons with those from a cold electron reservoir. This contrasts with initialization in other architectures (e.g., superconducting qubits or trapped ion qubits), for which it is impossible or inefficient to deterministically replace the particles hosting the qubit.
This article is organized into the following sections: first we describe the measurement approach used for our devices and quantify some aspects of its performance, paying attention to both fidelity and duration. We then do the same for state preparation. We conclude by discussing our preferred technique for quantifying SPAM performance using a joint metric (F BC , with BC standing for Benchmarking Contrast) and compare the results to other key qubit device measures.

II. MEASUREMENT
In this work we employ a device fabricated similarly to that of Ref. 19. This device comprises a linear array of six quantum dots and two DCSs, which share a common source but have independent drain leads. Only half of the device is utilized in this work, and a nominally identical device is shown in the electron microscopy inset of Fig. 1. The overlapping gates are formed from aluminum, 60 nm above a 3-nm-wide, 800-ppm 29 Si quantum well [13,49,50].
Singlet-triplet measurement via Pauli spin blockade exploits the fermionic nature of electrons, which are constrained to anti-symmetric wavefunctions. At low magnetic fields, the ground state of two electrons in one dot must correspond to an anti-symmetric spin singlet; higher-energy triplet states which are spin-symmetric require valley and/or orbital excitations to provide overall antisymmetry. Here we notate charge in a set of dots as (n, m); for example (2,0) represents two electrons in dot 1, zero electrons in dot 2, etc. A spin singlet is indicated by S, so "S(2,0)" is the ground state of the (2,0) charge state of a double-dot. In the (2,0) charge state, valley and/or orbital excitations provide a singlet-triplet energy splitting δ ST which can be exploited for both spin initialization and measurement, with the magnitude of that splitting being critical to the fidelity of both opera- Square waves are generated at room temperature, attenuated, and sent into the dilution refrigerator, where they act as a bias between source and drain two-dimensional electron gas (2DEG) leads. These square waves probe the conductance of the DCS (labeled M), which is sensitive to the TQD charge state, and generate a current across a subsequent 20 kΩ sense resistor. This signal is amplified by a two-stage cryogenic HEMT, then demodulated and thresholded at room temperature. Signal adder circuits (dashed contour) enable fast and accurate baseband control of the plunger (blue, "P" & "M") and barrier (pink "T" and "X") gate biases. The adder circuit (simplified in this figure) is described in further detail in appendix A. Note that the source signal attenuation has a low-impedance output.

tions.
In a triple-quantum-dot (TQD) DFS, the encoded-|0 state is given by a spin singlet on two (hereafter "outer") dots, "S(1,1)". The third dot charge-state is omitted for brevity but is singly occupied by an electron which is sometimes referred to as the "gauge spin" and is crucial for exchange-only universal control. This electron need not be initialized into any particular spin state [18,19], but reliable exchange coupling requires that it not be in an excited orbital or valley state. The encoded-|1 state of the DFS qubit is a superposition of triplet-states [T 0,± (1,1)] on the outer dot spins, entangled with this third spin. Since PSB measures whether or not the two outer spins are in a spin singlet or triplet, the preparation and measurements of exchange-only qubits can proceed in the same fashion as in double-quantum-dot singlettriplet qubits [51,52].
Charge-states of the triple-quantum-dot are probed by the electrostatic interaction with a nearby DCS (underneath the "M" gate in the device depicted in Fig. 1). The DCS is biased into the Coulomb blockade regime, where its conductance is highly sensitive to the potential environment and, accordingly, to the charge occupancy of the TQD. We interrogate this conductance by applying a bias between the source and drain 2DEGs connected to this dot, modulated by a square wave at a frequency of about 2 MHz. The resulting DCS drain current flows through a 20 kΩ sense resistor R s , and the generated voltage signal is amplified by a two-stage cryogenic HEMT (Avago ATF-38133) [53,54], shown in Fig. 1. Placing a low-dissipation stage at the still plate (T ≈ 800 mK) before a second stage of amplification (at T ≈ 4 K) allows for reduced added noise while respecting the thermal constraints of the dilution refrigerator. A cold finger locates that 800 mK amplifier in spatial proximity (several cm) to the device chip, minimizing the (bandwidthlimiting) parasitic capacitance C p , which we estimate to be roughly 8 pF from the signal bandwidth. The signal then continues to room temperature where it is digitized and demodulated in software.
We measure the spin state of the device by performing spin-to-charge conversion-detuning the device from an "idle" bias configuration (or "coordinate") of low exchange energy in the (1,1) charge cell towards the (2,0) regime. Because of PSB and the finite singlet-triplet energy splitting, the charge-state level crossing occurs at higher detuning bias for spin triplets than for singlets (see the energy diagram in Fig. 2a.) This sets a "measure window" of bias where the spin states differ in their charge character. At an intermediate bias near one half of the two-electron excited-state splitting, the singlet-triplet degree of freedom and the charge occupancy are maximally correlated, and measurement of charge also yields spin-state information. This is directly evident from spin blockade spectroscopy-histograms of DCS conductance as a function of detuning bias (Fig. 2b) [55].
Near the charge-state transition the bias is ramped in time so as to minimize Landau-Zener processes which might excite the spins into elevated valley-orbit states. This is discussed further in Section III. Due to imperfect signal integrity engineering, with the current design we require a "settling" period of order one to ten µs before the source-drain square waves are applied to maintain consistent measurement results. Generally this delay, rather than integration, dominates the obtainable measurement cadence, but we expect to ameliorate this with further signal chain engineering. Energy level diagram and spin blockade spectroscopy. a, Energy level diagram near the measurement window, shown at zero magnetic field for clarity. Horizontal lines (energy independent of detuning) represent the (1,1) charge state used for exchange and idle operations, while the diagonal lines represent the (2,0) charge state. In this illustration the relevant singlet-triplet splitting δST (and accordingly the region of spin-to-charge conversion) is set by the twoelectron orbital energy (Eo) rather than the excited valley state energy (Ev). b, Spin blockade spectroscopy, showing histograms of DCS current as a function of detuning between the (2,0) and (1,1) charge states. The fully-resolved gap between the singlet and triplet branches is reflective of highlyefficient spin-to-charge conversion.

A. SNR
We now probe the quality of that measurement, starting with the signal to noise ratio (SNR). The experimental routine begins with preparation of a dephased spin state, which is created by waiting at the idle bias for a time longer than the hyperfine-dominated T * 2 . This is followed by the previously-described S2C and charge-state measurement processes, and we histogram the resulting measurement current. We use this routine to explore the obtainable spin SNR as a function of measurement duration and strength (i.e. source-drain bias amplitude) in Fig. 3. As we increase the integration duration from 980 ns to roughly 40 µs, the SNR first improves as we better average away white noise, then saturates as it becomes limited by the 1/f charge noise on the DCS. Similarly, the SNR increases quickly as we increase the source-drain bias amplitude but then decreases after a critical value. This reflects nonlinearity in the DCS con- a, Log-scale histograms of DCS current (data in black), with Gaussian fits indicating singlet (blue) and triplet (red) readout signals, here with a total integration time of 980 ns. Thresholding a distribution with this SNR (6.5) provides a bound on 1 − FBC ≥ 6 × 10 −4 . b, Histograms taken at an integration time of 40 µs and with an additional measurement subtracted, giving an SNR of 15.5. This distribution bounds 1 − FBC > ∼ 5 × 10 −15 , but other limiting effects (such as relaxation during measurement) are evident. c, Histogram SNR as a function of both sourcedrain bias amplitude and integration time. SNR saturates as a function of increasing integration time due to 1/f noise on the DCS potential. SNR increases with bias amplitude, then decreases after a critical point.
ductance, for instance due to excited states. Quantitative predictions for both components of SNR are discussed in detail in appendix B.
We can further look at two extremal cases: the shortest-duration measurement which maintains a "sufficiently high" SNR, and the long-duration measurement with maximized SNR. Fig. 3a depicts a rapid measurement, integrating for only 980 ns. This timescale compares favorably to spin-relaxation T 1 (>10 ms, discussed further in Section II B), quantum-dot dynamicaldecoupling timescales [56], and anticipated two-qubit gate durations [18,19]. In that time we obtain an SNR of 6.5, which limits 1 Alternately we can saturate the high-SNR limit by integrating for 40 µs (and subtracting a reference measurement), as shown in Fig. 3b, which achieves an SNR of 15.5. This SNR yields an exceptionally small theoretical bound on infidelity, but other factors limit fidelity far more strongly. An examination of the histogram of Fig. 3b shows evidence of T 1 (points scattered between the two Gaussian distributions) and additional spurious counts, the latter of which may indicate morepathological noise mechanisms or a probability of populating other charge states. We now go on to discuss those T 1 effects.

B. Relaxation during measurement
As we access larger signal-to-noise ratios, measurement fidelity quickly becomes limited by relaxation during the measurement. This was explored experimentally, and a key result is shown in Fig. 4a. These data were gathered by preparing a dephased qubit state and transitioning to a trial measurement bias, then sweeping the detuning of that bias. For each detuning we apply a typical modulated source-drain bias for a variable amount of time (called "measurement time" in the figure), but do not record a measurement signal. After that time we perform a calibrated measurement at a fixed bias to examine the resulting state, and we show that result as a function of both trial measurement detuning and duration. The detuning axis has an arbitrary offset but is referenced to the SNR at each point (extracted from spin blockade spectroscopy), which serves to demarcate the singlet and triplet charge-state transitions.
The locations of the sharp reductions in T 1 at negative detuning are consistent with anticrossings between the S(1,1) and T − (1,1) states, given our 1.5 mT applied magnetic field. We can estimate the bound on measurement fidelity imposed by finite SNR and T 1 , as shown in Fig. 4b 2 . Combining those two effects, we can locate the bias for optimal contrast-which, notably, is not the bias at which SNR is maximized. Importantly, we see T 1 decay times of over 20 ms within biases that yield high SNR, which compares favorably to our achievable measurement rates of µs order. We additionally performed the same experimental sequence and analysis but with the amplitude of the source-drain bias as the independent variable, and discuss that result in appendix C. That measurement shows that large source-drain bias can induce T 1 , and accordingly a compromise must be made in choosing that amplitude.
The rich T 1 behavior displayed in Fig. 4a involves a complex interplay of microscopic semiconductor physics. One extrinsic relaxation pathway is via cotunneling with the electron bath, but this can typically be exponentially suppressed by increasing the relevant tunnel barrier. The intrinsic decay channels within the device require both charge-transition and spin-flip mechanisms. Charge decay proceeds via electron-phonon coupling or electromagnetic interactions with the gate, bath, or charge noise 2 Relaxation during measurement yields a bound a, In color, the resulting singlet probability after trial measurements at swept bias (x axis) and duration (left vertical axis). In gray, the fit 1/e times at each bias point. In blue, the SNR as a function of bias, extrapolated from a fit of spin blockade spectroscopy (right vertical axis). b, Calculating the limits on FBC that result both from finite SNR and from relaxation during measurement. Combining those sources, we see clearly that the maximum fidelity measurement bias does not coincide with maximal SNR for this choice of measurement parameters. sources, which can have different densities of states and hence differing dependence on detuning. Microscopically, singlet and triplet states can couple to each other via nuclear hyperfine interaction with 29 Si and 73 Ge atoms, as well as the spin-orbit interaction present in Si/SiGe quantum wells. T 1 "hot spots" can appear at detuning biases where excited singlet and triplet states anticross, leading to strong spin mixing and rapid charge decay, as observed experimentally in Fig. 4a. In appendix D we address how these features are expected to connect with the "measure window" energy spectrum.

III. STATE PREPARATION
We initialize the spin state by biasing fully into the (2,0) charge configuration, maximizing the energy splitting between the triplet states and the ground-state singlet. At thermal equilibrium, we expect to preferentially populate the encoded-|0 (singlet) state. Waiting for relaxation to equilibrium is impractical, as singlet-triplet decay rates (1/T 1 ) can be quite long due to the necessity for spin relaxation [57,58]. Instead, as previously mentioned, we speed up the process by exchanging electrons with a cold reservoir-here a 2DEG which also serves as the drain for the DCS current. Typically initialization is achieved by biasing the outermost dot to the vicinity of the (2,0)-(1,0) charge boundary where the chemical potential of the (1,0) charge state lies between that of the S(2,0) and T(2,0) states (as shown empirically in Fig. 5a and schematically in Fig. 5b). This enables bathdot tunneling to more rapidly equilibrate or "flush" to the ground state. We sweep the duration of this flush period and choose a duration at which the triplet population stabilizes. In this work, we exploit the (2,0)-(3,0) charge boundary [rather than (1,0)-(2,0)], seen on the right side of Fig. 5b, which to our knowledge has not been previously discussed for this purpose. Initialization is completed by transitioning back to the idle bias via a ramped trajectory. First, we change the bias quickly from the initialization charge boundary to an "entry" point just outside the (2,0)-(1,1) boundary. Then we ramp slowly-with ramping times of order 10-100 ns-into and through the PSB coordinate, ending at a second entry point just inside the (1,1) charge cell. This is designed so as to move through the anti-crossing without triggering a Landau-Zener transition. Then, we jump quickly from that point to idle, minimizing the time spent at low-exchange regions where magnetic dephasing is more rapid. To return from idle to measurement, we repeat latter half of this process in reverse. The optimal choices of ramp times and the entry coordinates balance many factors, and are a subject for future study.

A. Initialization fidelity
After tunneling to and from the bath, at equilibrium we expect to populate the ground-state singlet state with probability given by the partition function where β = 1/(k B T e ) (here, the effective electron temperature T e ≈ 220 mK, measured from tunneling linewidth as a function of mixing chamber temperature), E v is the excited valley state energy in the outermost dot (≈250 µeV, measured with detuning axis pulsed spectroscopy [59]), E o is the two-electron orbital excited state energy (≈160 µeV, measured with spin blockade spectroscopy), and we neglect higher excited valley-orbital states (assuming their contributions are negligible at sufficiently low temperatures). The factors of three and hour come from the respective degeneracies of the excited valley and orbital states. Zeeman splittings of the polarized triplet states are also neglected in this equation as they are small at the low and moderate magnetic fields at which we typically operate exchange-only qubits (here, 1.5 mT). We have also neglected the third electron, which we estimate to be separable from the outer-dot initialization, and may eventually reach an equilibrium set by its own (one-electron) excited-state energy. It is possible to end in the wrong charge state during this process, so for example the partition function in Eq. 3 can be extended to account for (1,0) occupation as well (if initializing at that charge boundary), though empirically this is not a common outcome.

B. Initialization speed
This speed of this initialization process benefits from the fact that tunneling between the outer dot and bath depends exponentially on the height of the insulating tunnel barrier. Pulsing the voltage bias on the relevant barrier gate strongly and quickly modulates that potential. In practice, we observe a speed limit enforced by two main mechanisms: orbital suppression and waveform stability. First, depressing the barrier height can distort and desymmetrize the quantum dot confining potential, which decreases the orbital excited-state energy [60] and limits the ultimate obtainable fidelity (Eq. 3). In principle, this effect could be countered by shaping the potential further with appropriate pulses on other nearby gate electrodes. Second, the stability of the bias waveform strongly influences this process. Ideally, when sweeping the initialization bias and duration (Fig. 6), we expect the resulting population to be strongly bias-dependent Sweeping initialization bias and duration. Sweeping the outer-dot plunger gate bias across the (2,0)-(3,0) boundary and sweeping time. This population is the thresholded result of a spin-state measurement immediately after bath-exchange following preparation of a dephased state. The populations are not monotonic in duration, which is indicative of the bias waveforms settling in time. While our highspeed adder circuit (appendix A) attempts to provide a flat response, not all non-idealities are accounted for. This settling limits the minimum initialization time in this case to roughly 300 ns to reach an asymptotic population of 6×10 −4 . P1 biases differ from Fig. 5a because additional (pulsed) tunnelbarrier bias has been introduced and that T gate has a nontrivial cross-capacitance to the first dot potential. This result is degraded from the Boltzmann distribution prediction for initialization fidelity alone (Eq. 3, ≈5×10 −4 ), due to measurement and mapping errors. and to change monotonically with time. In contrast, we believe the observed non-monotonic signal is a signature of bias drift. This effect limits us to a minimum duration of roughly 300 ns to reach the asymptotic population; however this limitation should be reduced with improved engineering for signal integrity. We note also that a wider initialization bias window (resulting from larger excitedstate splittings) should also reduce the sensitivity to this drift.
We find that using the alternate (2,0)-(3,0) "initialization window" leads to the same asymptotic singlet population but often more than an order of magnitude more quickly. Several factors likely contribute to this operational improvement; for one, the increased dot plunger (P) gate voltage required at this boundary decreases the effective tunnel barrier. Second, the increased bias-space width of this initialization window (evident in Fig. 5) likely mitigates the effects of waveform drift. Finally, the spin and charge character of the multi-electron states also play an important role. For instance, it can be shown from the relevant Clebsch-Gordan coefficients that the tunneling transition rate between an N -electron state of total spin S i and an N + 1 state with spin S j is weighted by a factor [61] As a result, while both the one-and three-electron ground states have total spin S = 1/2 at typical magnetic fields, the single-electron state has a three-times larger tunneling rate to the triplets compared to singlets where both are energetically available, whereas the opposite is true for the three-electron ground state, which has a three-times larger tunneling rate for singlets compared to triplets. Details of the three-electron excitation spectrum may also play a role and depend sensitively on the confining electrostatics as well as valley mixing; quantifying the effects of these states on the initialization process is an interesting area for further study.

IV. JOINT SPAM FIDELITY & BUDGET
A. Quantifying SPAM performance In this section we move on from the mechanics of individual SPAM operations to focus on the quantification of their performance. Measurement SNR and T 1 both contribute to SPAM infidelity and are useful diagnostic quantities, but tell only part of the story. We can probe initialization fidelity by performing a measurement directly after initialization (as in Fig. 6) however we do not consider this quantity to be a reliable summary metric of initialization quality, nor of integrated SPAM quality. Among other concerns, it can be gamed by biased measurement error, it doesn't include any errors in "mapping" when biasing to and from the idle point, and it does not guarantee what fraction of the population will exhibit proper qubit evolution. The last criterion is generally relevant due to the possibility of leakage outside of the qubit space, the effects of which vary widely between physical-qubit implementations. One plausible alternative metric is the ultimate contrast that can be observed in exchange oscillations (appendix E), but this is also degraded by charge noise and other decoherence mechanisms whose infidelity is better associated with coherent manipulation.
Instead, we emphasize an integrated preparation and measurement metric (first presented in Ref. 19 and reproduced mathematically in appendix F) that avoids the previously mentioned flaws while providing several other benefits. This measure, dubbed F BC for Benchmarking Contrast, probes the fundamental concern of imperfect preparation and measurement: what fraction of the time do we obtain the correct result after an arbitrary qubit evolution, independent of the fidelity of that evolution. F BC is derived from "blind" randomized benchmarking, a method originally designed to detect leakage out of the computational space during coherent manipulation of exchange-only qubits. In this procedure an ordinary randomized benchmarking experiment (with sequences that compile to the identity) is executed along with a second benchmarking experiment, whose sequences are instead engineered to compile to a population-inverting gate. To assess SPAM performance, we evaluate the contrast of these fit curves at zero Clifford operations, which attempts to subtract any contrast loss due to imperfect qubit rotations.
F BC transposes randomized benchmarking's typical objective-measuring Clifford fidelity independently of SPAM performance. This measure differs from assignment fidelity 3 , which might be quite coarsely approximated by the same curves evaluated at 0.5 Clifford operations. Importantly for exchange-only qubits, we find F BC to be more robust than assignment fidelity in the presence of leakage, though that import depends on the qubit physical implementation. F BC also implicitly disallows the use of different processes for preparation or measurement of |0 and |1 which may boost assignment fidelity at the expense of operational utility. We note that this metric is essentially universal, and allows fair comparison between diverse physical implementations of qubits. One final desirable feature of F BC as a "summary" metric is its resilience to manipulation, or being increased at the expense of the fidelity of other qubit operations. Any tradeoffs between SPAM and single-qubit errors are readily apparent in this extraction.
Blind randomized benchmarking for the device described in this work is shown in Fig. 7a. These data indicate a per-Clifford error of 1.7×10 −3 and F BC of 2.5(5)×10 −3 . This latter estimate is highly consistent with the visible contrast of exchange oscillations (appendix E).

B. Compiled budget & missing error
To understand this SPAM performance, we can consider three components: initialization, measurement, and mapping. Initialization quality is foremost bound by the magnitude of the 2e and 1e excited state energies relative to the effective electron temperature T e (Eq. 3). Measurement performance can be determined from a trio of "active" factors: signal amplitude, noise amplitude, and relaxation during measurement-the latter of which was discussed in Section II B and the former two in appendix B. These three factors are tightly interrelated and sometimes in tension, so that overall optimization is often a balancing act between them. Mapping errors, which occur in the transitions from initialization to the idle bias and from the idle bias to the measurement bias, can reasonably be grouped with one of the above or considered as a separate category, but should be included in any operationally-representative integrated SPAM metric. These errors are further discussed in appendix G.
Here we consider and assemble the effects of those components into a budget for F BC , shown in table I.
This budget leaves roughly 1×10 −3 infidelity unexplained relative to the observed 1 − F BC = 2.5 × 10 −3 . We hypothesize that the missing fidelity is attributable to probabilistically initializing with the gauge electron in an excited state. During these events, the exchange rate on one control axis will exhibit a different voltage dependence (J(V )) than occurs when the gauge electron is in its ground state. As a result, Clifford operations composed of pulses calibrated for the J(V ) mapping of the ground state quickly scramble the spin-state when that electron is excited, resulting in an apparent SPAM error. This effect, sometimes described as "dual exchange frequencies," has been reported in other works [9], where the Fourier transform of time-domain exchange oscillations clearly shows two peaks. For the present device under study, we are unable to observe a clear second peak in the spectra of exchange evolution on either exchange axis, however it is unclear whether this experiment has sufficient resolution to differentiate a second frequency at the 1×10 −3 level. Development of a better method to quantify such population is an important area for future work.
Though the energy of the gauge electrons first excitedstate was not measured, as a one-electron property we can reasonably associate its first excited state with the valley degree of freedom. Assuming equilibrium statistics in a Boltzmann distribution, the missing infidelity implies an excited valley-state energy of roughly 130 µeV, a value which is consistent with the measured valley splitting distribution for this heterostructure [59]. We note that this population would not be evident in initialization metrics which did not require fairly measuring qubit evolution, pointing again to the importance of the use of blind randomized benchmarking as a fair SPAM fidelity metric.

V. CONCLUSION
By our preferred, conservative metric, we have demonstrated preparation and measurement in exchange-only qubits with 1 − F BC =2.5(5)×10 −3 . These are obtained using only baseband control electronics, using a measurement integration time of 980 ns, an initialization duration of roughly 300 ns, and a charge-transition ramp time of 100 ns. We present a budget which explains ≈60% of the observed error, and hypothesize that the remaining error is due to thermal excited states of the gauge electron.
Priorities for improving initialization performance are obtaining larger excited-state energies and suppressing the effective electron temperature, which should yield both improved singlet and gauge electron preparation. Initialization may be accelerated by achieving more stable voltage waveforms. Related signal integrity engineering is also key to reducing the "settling" period, which presently dominates the possible measurement cadence. Other paths to improved PSB/DCS measurement performance include lower-noise amplification with lower parasitic capacitances, further exploration of "latching" [62][63][64] and "avalanche" [65] approaches, and improved T 1 decay rates. T 1 effects can likely be reduced by further decreasing charge and magnetic noise, which are already desiderata for improved coherent manipulation. This may also require using smaller source-drain biases, further emphasizing the need for improvements in signal and noise amplitudes.
Importantly, we conclude that high-fidelity and rapid SPAM (maintaining performance parity with coherent manipulation) is achievable in spin qubits using only simple electronics and components with high flexibility in temperature and magnetic field. Routes to even further improvement without addition of other components are clear.

VI. ACKNOWLEDGMENTS
The authors gratefully acknowledge the important contributions of Andrey Kiselev, Matthew Reed, Laura de Lorenzo, Emily Pritchett, Cody Jones, and Ed Chen, and support in figure preparation from John Carpenter. Room temperature high speed adder circuit. This circuit allows high-bandwidth but baseband control, combining inputs both from NI AWGs and custom lownoise DACs. Together with the fridge components shown in Fig. 1 (attenuation, bias tee and low-pass filter), this forms the full signal chain, providing the benefits discussed in the text. R fine and Rcoarse are highly-stable potentiometers that allow for balancing the attenuation of the high-frequency and low-frequency signal paths.
The budget for measurement noise is dominated by three effectively white noise sources of comparable magnitude (input-referred HEMT noise, sense-resistor Johnson noise, DCS current shot noise) and by the noise on the DCS potential. In our measurement chain configuration, the former three sources each generate a noise spectral density of roughly 200-300 pV/ √ Hz. The quantum dot charge noise spectrum is typically of the form A 2 /f , with effective gate-referred voltage spectral density A ≈ 5 µV/ √ Hz at 1 Hz. The effect of this noise source on readout depends on how the DCS is operated. In particular, two extreme choices are to bias the DCS gate voltage to maximize either the transconductance G m (peak of the derivative of conductance with respect to M voltage) or the conductance (the conventional Coulomb blockade peak point). The former maximizes the signal when the magnitude of the charge-dependent potential shift at the DCS (appendix B 2) is small compared to the width of the Coulomb peak, and we can approximate the effect of the DCS-potential noise as a linear shift of the conductance. The latter maximizes the signal when the magnitude of the charge-dependent potential shift is much larger than the width of the Coulomb peak and the state-dependent conductance difference is maximal. In this case, we are insensitive to DCS potential noise to first order. From these two extrema it is evident that the DCS bias that maximizes signal may not be the correct bias to maximize SNR, particularly in the 1/f -dominated long-integration regime.
To predict the ultimate expected noise amplitude we integrate the white noise sources with the filter function appropriate for our square-wave modulated measurement tone, yielding a current noise of σ 2 SD . We account for the charge noise in a conservative analysis, taking the smallshift approximation such that, to first order, the output measured current is modulated by G m d(t), where d(t) is the (noisy) potential shift. If we add that to the previous analysis, assume d(t) has a power-spectral density given by A 2 /f , and account for our averaging scheme when incorporating an (approximately instantaneously) subsequent reference measurement, the total histogram variance can be expressed as This sets an upper bound on the effects of DCS charge noise on measurement histograms. For relevant measurement parameters, we predict σ I ≈ 5pA at long duration, which is in line with observed values (e.g. Fig. 3b, though note in that figure the current values for referenced measurements have been divided by a factor of 4 for inconsequential implementation details.) As subtracting a reference measurement increases the white noise contribution, it is only preferable when the noise is dominated by 1/f or other slow processes. This can occur either because the 1/f contribution is generally large or because one seeks the highest possible SNR and is willing to average long enough to reduce the white noise contribution. Even in such a regime, performing a reference measurement for every experimental query is unlikely to be optimal.

Signal amplitude
We can estimate the magnitude of the HEMT-inputreferred voltage signal as a product of five factors: 1. the spin-to-charge conversion efficiency, 2. the inter-charge-state DCS potential shift, 3. the DCS transconductance G m , 4. the maximum applicable source-drain bias, and 5. the value of the sense resistor.
The spin-to-charge conversion efficiency describes how effectively the spin states correspond to different charge states at the measurement bias, and approaches unity when the two-electron excited-state splitting is larger than the singlet-or triplet-selective charge transition widths. That width can be reduced by decreasing the effective electron temperature and tunnel coupling, but it is also sensitive to charge noise (see the supplemental material of [55]). In practice, we find an excited-state splitting of roughly 100 µeV is sufficient to push this term near unity at typical operating electron temperature and tunnel coupling. The magnitude of the potential shift is a straightforward calculation from the device geometry and Coulomb's law, accounting for the effects of image charges due to the electrostatic environment. The transconductance around a Coulomb peak is a wellstudied question, depending on tunneling rates of the DCS tunnel barriers and the effective electron temperature [66,67].
The maximum applicable source bias is limited by two factors. First (as noted in Section II A) nonlinearity in the DCS causes the conductance to decrease after a critical value. Second, we also observe that at sufficiently large source-drain bias, the spin relaxation lifetime begins to decrease, discussed in appendix C. The voltage signal can be linearly increased with high-resistance sense resistors, but at the expense of increased Johnson and shot noise. Additionally, due to parasitic capacitance, the accessible measurement frequency decreases quickly, limiting the ability to mitigate low-frequency noise.

Appendix C: T1 vs Source-Drain Bias Amplitude
We have also explored the effect of measurement-biasdriven T 1 decay using the experiment discussed in Section II B. Fig. 9 shows that T 1 decreases strongly when T1 as a function of applied measurement bias. The decay rate increases after a certain bias amplitude of energy comparable to the singlet-triplet splitting. We also provide a cubic guide to the eye, which appears to track the asymptotic behavior.
we bias beyond roughly 75 µV, a value suggestively close in correspondence to the S-T splitting at the middle of the measurement window, e.g., equal to the gap at that detuning between the ground (2,0) state and the lowest (1,1) excited triplet state. These observations show similarities to other reports in the literature [68,69]. The onset value and the nonlinear scaling with bias are potentially indicative of enhanced relaxation due to phonons generated by the enhanced dissipation of the DCS. Further work is needed to understand the microscopic underpinnings of this effect. 8×10 −4 , respectively, with the difference reflecting mapping error due to that additional bias trajectory.
While mapping errors could be reduced by engineering devices with, e.g. longer singlet-triplet dephasing time T * 2 or better signal integrity, they can also be limited somewhat by careful pulse design. Landau-Zener transitions occur when gate voltages jump between SPAM and idle configurations too quickly, such that the ground state cannot adiabatically move between the (2,0) to (1,1) charge configurations. Such transitions are most likely when the charge states are near an anti-crossing, as they are during initialization and measurement, and as such can be suppressed by ramping slowly to and from the SPAM configurations. On the other hand, magnetic dephasing is in some ways a symptom of ramping too slowly. Near the charge boundary, the same large singlet-triplet energy splitting that enables SPAM suppresses dephasing between the logical states. Close to idle, the energy splitting is much smaller, and dephasing is more significant. Consequently, long-duration ramps deep within the (1,1) charge cell unnecessarily accumulate dephasing error. We employ a two-step approach to ramping (as noted in Section III) to minimize both types of error.