Mid-circuit logic executed in the qubit layer of a quantum processor

Abstract

Practical quantum computers need to continuously exchange data between classical and quantum subsystems during a computation. Mid-circuit measurements of a qubits state are transferred to the classical electronics layer, and their outcome can inform feedforward operations that close the loop back to the quantum layer. These operations are crucial for fault-tolerant quantum computers, but the quantum-classical loop must be completed before the qubits decohere, presenting a substantial engineering challenge for full-scale systems comprising millions of qubits. Here we perform the first mid-circuit measurements in a system of silicon spin qubits, and show that feedforward operations can be performed without needing to route information to the classical layer. This in-layer approach leverages a backaction-driven control technique that has previously been considered a source of error. We benchmark our in-layer strategy, together with the standard FPGA-enabled approach, and analyse the performance of both methods using gate set tomography. Our results provide the first step towards moving resource-intensive classical processing into the quantum layer, an advance that could solve key engineering challenges, and drastically reduce the power budget of future quantum computers.

Figures (10)

• Figure 1: Characterization of charge-induced backaction.a, Schematic of qubit layout and process of charge-induced Larmor (qubit) frequency shift. The translucent qubit symbols denote the configuration of the system in the nominal ($N_\text{A2}$,$N_\text{A1}$,$N_\text{D1}$,$N_\text{D2}$)=(3,5,5,3) charge configuration. The solid qubit symbols denote the ($N_\text{A2}$,$N_\text{A1}$,$N_\text{D1}$,$N_\text{D2}$)=(4,4,5,3) charge configuration and the corresponding Stark-shift and exchange-rate modulation of the data qubit pair. b, Phase accumulation of D1 (blue) and D2 (red) over time $t_\text{m}$ while in an ($N_\text{A2}$,$N_\text{A1}$)=(4,4) charge configuration. The corresponding Stark shift is indicated by linear fit (solid lines), with values of $f_\mathrm{c}^\mathrm{D1} = 11.8 \pm 0.4kHz$ and $f_\mathrm{c}^\mathrm{D2} = 4.9 \pm 0.6kHz$. The yellow shaded region denotes the time $t_\text{m}$ at which D1 accumulates $\theta_\mathrm{c}^\mathrm{D1} = \pi$. c, Schematic diagram of the Ramsey-style measurement used to characterize the performance of the MCMs (gold, green and grey boxes) in d. From left to right: A1 and D1 are prepared to the equator with $\sqrt{X}$ gates. A1 is measured in the Z basis (via PSB with A2) and a unitary phase $\theta_\mathrm{m}$ is applied on D1 conditional on the A1 measurment outcome due to charge-induced Stark shift (gold box). The A1 measurement result is detected by sensor $\text{S}_\text{A}$ and transmitted through an analogue-to-digital converter (ADC) to an FPGA (grey box). The FPGA executes a feedforward operation conditional on the measurement result registered (green box). $\varphi$ is swept between 0 and $2\pi$ so that the data qubit phase and coherence can be extracted with the Z($\varphi$) -- $\sqrt{X}$ -- Z-measurement operation. d, Coherence vs. phase-accumulation time of D1 for three MCM methods: phase-accumulation mode (teal), phase-accumulation with FPGA-enabled phase correction (turquoise) and phase-echoed mode (navy). The vertical axis is the Bloch length on the XY-plane averaged over 500 shots. The grey curve is a fit of the XY-plane Bloch length in the $T_2^\mathrm{Hahn}$ experiment, representing the upper limit that D1 coherence can achieve if the charge-induced phase accumulation is not present or is successfully suppressed. The yellow shaded region corresponds to the shaded region in b), where $\theta_\mathrm{c}=\pi$. Here this causes a complete loss of visibility.
• Figure 1: Full experimental setup schematic. See Methods for further information on hardware and experimental setup.
• Figure 2: X-basis mid-circuit measurements and correctionsa, Experimental circuit for b-f. The MCM tested comprises an X-basis CNOT (yellow box), an ancilla qubit measurement (gold box), an ancilla readout via sensor (grey box) and a classical controller/FPGA block (green box). We change the input D1 state by sweeping $\varphi$ between $0-2\pi$. The output D1 state is measured in the X-basis. b, D1 input state, measured by deactivating the MCM. The probability of $\ket{-}$ measurement is plotted vs. $\varphi$ (blue trace), as well as the data sensor output (blue histogram) and D1 state classification threshold (dashed line). c, MCM performed on D1, using the phase-accumulation readout (upwards arrow) with FPGA-enabled phase correction, with read time $t_m =$ 20µs. The conditional phase operations are $\phi_0 = \{-0.05\pi,0.37\pi\}$. The ancilla sensor output (gold histogram) and A1 state classification threshold (dashed line) is plotted. d, MCM performed on D1 using the phase-echoed readout method (backwards arrow). No phase correction is applied to the data qubit following readout. e, FPGA-enabled feedforward $Z(\pi)$ performed on D1. The FPGA conditionally executes a Z($\pi$) on D1 if the MCM of D1 is $\ket{+}$ (indicated by an A1 readout of $\ket{0}$). To do this, we set $\phi_{\pi} = \{-0.05\pi, 1.37\pi\}$. This operation corrects D1 to $\ket{-}$ irrespective of the the input state. f, In-layer feedforward $Z(\pi)$ performed on D1. Read time is set to $t_m =$ 42µs so that the CDS phase induces a Z($\pi$) when A1 is projected in $\ket{0}$, relative to when it is projected to $\ket{1}$. A fixed phase rotation of $\phi_r = -0.04\pi$ is used to correct for the residual phase error. The sensor is turned off, resulting in an indistinguishable ancilla readout, demonstrating this is not controlled via the sensor output and FPGA. D1 $\ket{X}$ projection traces (blue) in c-f are normalized to the D1 $T_2^\textrm{Hahn}$ visibility of the corresponding $t_m$ used for readout. Data qubit sensor $\text{S}_\text{D}$ output in b is indicative of $\text{S}_\text{D}$ outputs for c-f.
• Figure 2: Basic device operation.a, Charge stability diagrams of the isolated quantum dots as a function of P1, P2 and J1 (sensing A1-A2 transitions), P3, P4 and J3 (sensing D1-D2 transitions), and P2, P3 and J2 (sensing A1-D1 transitions) respectively. PSB readout is performed towards the (4,4) charge transitions for both (A1,A2) and (D1,D2) pairs of dots. Single qubit ESR control is performed at $V_\text{ctrl}$ where $\Delta V_\text{J1}=\Delta V_\text{J2}=\Delta V_\text{J3}=-100$mV to suppress exchange interaction. D1 and D2 are held at the $V_\text{ctrl}$ detuning and $\Delta V_\text{J2}=\Delta V_\text{J3}=-100$mV when the MCM is performed. b, A closer view of the Pauli-spin blockade window in the (A1,A2) pair (left) and (D1,D2) pair (right). Colorscale corresponds to the SET signal difference between an odd and even parity state being measured. The PSB region appears as non-zero (yellow) region. (A1,A2) plot is the $\text{S}_\text{A}$ signal, and the (D1,D2) plot is the $\text{S}_\text{D}$ signal. c, Sequentially-driven Rabi oscillations on pairs of uncoupled qubits. The array is initialised in $\ket{\text{A2},\text{A1},\text{D1},\text{D2}}=\ket{1111}$. After ESR pulses are applied a parity measurement is performed in the (A1,A2) dots and (D1,D2) dots using PSB regions in b. Left(right) plot corresponds to thresholded signal from $\text{S}_\text{A}$($\text{S}_\text{D}$).
• Figure 3: Tomographic analysis of the MCMs and feedforward operations.a, Estimated quantum instrument of Z-basis MCM using phase-accumulation readout with FPGA-enabled phase correction ($t_\text{m}=10$ µs). Fidelity estimate $F = 0.834\pm 0.013$. b, Quantum instrument estimate of Z-basis MCM using phase-echoed readout ($t_\text{m}=10$ µs). $F = 0.838\pm 0.013$. c, Quantum instrument estimate of X-basis MCM using phase-accumulation readout with FPGA-enabled phase correction ($t_\text{m}=10$ µs). $F = 0.793\pm 0.015$. d, Quantum instrument estimate of X-basis MCM using phase-echoed readout ($t_\text{m}=10$ µs). $F = 0.790\pm 0.015$. e, Quantum instrument estimate of X-basis MCM with Z($\pi$) feedforward operation using FPGA-enabled conditional operations ($t_\text{m}=10$ µs). $F = 0.801\pm 0.015$. f, Quantum instrument estimate of X-basis MCM with Z($\pi$) feedforward operation using CDS control, i.e. in-layer feedforward operation. ($t_\text{m}=42$ µs). $F = 0.592\pm 0.012$. All the matrices here are Pauli transfer matrices of the intended operation conditional on the outcome of the MCM labelled as $Q_0$ and $Q_1$, referring to even and odd readout outcomes respectively. g, Dependence of coherence and charge fidelity as a function of total measurement time (reference time + read time = 2$t_\text{m}$). This is equivalent to total $t_\text{wait}$ in $\text{T}_2^\text{Hahn}$ experiment. h, Hamiltonian and stochastic error channels for X-basis MCM with FPGA-enabled feedforward Z($\pi$) operation ($t_\text{m}=10$ µs). i, Comparison of pure readout errors for the Z-basis MCM, X-basis MCM, and feedforward Z($\pi$) operations. j, Comparison of dephasing errors in X-basis MCM and feedforward Z($\pi$) operations.