Mitigating many-body quantum crosstalk with tensor-network robust control

TL;DR

It is shown that many-body robust control can be utilized to suppress unwanted couplings during multi-qubit gate operations and state preparation and pave the way for more reliable operations on near-term quantum processors.

Abstract

Quantum crosstalk poses a major challenge to scaling up quantum computations as its strength is typically unknown and its effect accumulates exponentially as system size grows. Here, we show that many-body robust control can be utilized to suppress unwanted couplings during multi-qubit gate operations and state preparation. By combining tensor network simulations with the GRAPE algorithm, and leveraging an efficient random sampling over noise ensembles, our method overcomes the exponential scaling of the Hilbert space. We demonstrate its effectiveness for designing control solutions for high-fidelity implementations of parallel X gates and parallel CNOT on a chain of 50 qubits, and for realizing a 30-qubit GHZ state and the ground state of a 20-qubit Heisenberg model. In the presence of many-body quantum crosstalk due to parasitic interaction between neighboring qubits, robust control results in order-of magnitude improvement in fidelity for large system sizes. These findings pave the way for more reliable operations on near-term quantum processors.

Figures (5)

• Figure 1: Illustration of a qubit chain with tunable coupling and permanent parasitic interaction. Each qubit is controlled by a single-qubit drive.
• Figure 2: Ensemble-averaged infidelity for the parallel $X$ gate (diamonds) and parallel CNOT gate (circles). Results are shown for control solutions optimized without robustness (open symbols) and with robustness against quantum crosstalk at 5% of the main energy scale (solid symbols). Without robustness, the average infidelity increases rapidly with system size, approaching 0.5 at $n=50$. In contrast, robust optimization suppresses the infidelity by nearly three orders of magnitude for the parallel $X$ gate and by approximately two orders of magnitude for the parallel CNOT. The maximum MPO bond size during optimization is $D_{\text{max}}=20$, and the pulse duration is independent of system size.
• Figure 3: The pulses optimized with robustness for a chain of $n=50$ qubits. Panels (a,b) show the pulses for the parallel $X$ gate, and panels (c,d) show those for the parallel CNOT. Time is given in units of $\tau_{\pi}$ and $\tau_g=2\pi/g$, and amplitudes are shown in units of $\Omega_{\pi}$ and $g$, respectively. For each case, all 50 control pulses on the X-quadrature (top) and Y-quadrature (bottom) are displayed, with each pulse shown as a row of color-coded amplitudes. The resulting many-body gate infidelities are approximately $5.0\times 10^{-3}$ for the parallel $X$ gate and $2.7\times 10^{-2}$ for the parallel CNOT, despite parasitic interaction at 5% of the main energy scales.
• Figure 4: Ensemble-averaged infidelity for the preparation of the GHZ state (diamonds) and the Heisenberg ground state (circles). Results are shown for control solutions optimized without robustness (open symbols) and with robustness against parasitic interactions at $5\%$ of the interaction strength $g$ (solid symbols). Without robustness, the infidelity increases exponentially with system size before saturating near unity. Robust optimization keeps the infidelity below $0.1$ for the GHZ state at $n=30$ and below $0.15$ for the Heisenberg ground state at $n=20$. The maximum bond size during optimization is $D_{\text{max}}=10$ for the GHZ state and $D_{\text{max}}=20$ for the Heisenberg ground state.
• Figure 5: The pulses optimized with robustness for the preparation of the GHZ state with $n=30$ qubits (a,b) and the Heisenberg ground state with $n=20$ qubits (c,d). Pulse amplitudes, shown in units of $g$, are color-coded as functions of time in units of the interaction timescale $\tau_g = 2\pi/g$. Pulses on the $X$-quadrature ($Y$-quadrature) are shown in the top (bottom) panels, with each row corresponding to a single qubit. The resulting state infidelities are approximately $0.1$ for the GHZ state and $0.15$ for the Heisenberg ground state despite parasitic interactions at $5\%$ of the main interaction strength.