Cost-effective scalable quantum error mitigation for tiled Ansätze

TL;DR

This work tackles the challenge of quantum error mitigation in noisy intermediate-scale quantum devices by combining M0 with a locality-based tiling strategy. By decomposing the full assignment matrix into per-tile matrices for tiled Ansätze such as tUPS, the authors achieve a constant, system-size-independent overhead for noise characterization while retaining mitigation effectiveness. Across molecular systems from LiH to benzene (4–12 qubits), tiled M0 yields substantial energy accuracy improvements in noisy simulations and, in several cases, in hardware experiments, though hardware drift can limit gains for longer runs. The approach promises scalable, cost-efficient mitigation for near-term quantum chemistry on NISQ devices and sets the stage for further drift-robust refinements as hardware improves.

Abstract

We introduce a cost-effective quantum error mitigation technique that builds on the recent Ansatz-based gate and readout error mitigation method (M0). The technique, tiled M0, leverages the unique structure of tiled Ansätze (e.g., tUPS, QNP, hardware-efficient circuits) to apply a locality approximation to M0 that results in an exponential reduction in the QPU cost of the noise characterization. We validate the technique for molecular ground state energy calculations with the tUPS Ansatz on LiH, molecular hydrogen, water, butadiene, and benzene ($4-12$ qubits), demonstrating little to no loss in accuracy compared to M0 in noisy simulations. We also show the performance of the technique in quantum experiments, highlighting its potential use in near-term applications.

Figures (4)

• Figure 1: The tUPS Ansatz with two layers for an $8$-qubit system. Each tile (labelled $t_i$) consists of gates that correspond to single and double electronic excitations. Three variational parameters are associated with every tile. The input qubit register is initialized to the desired reference state.
• Figure 2: Average results from energy calculations with the tUPS Ansatz on LiH and H2. We refer to Table \ref{['shots_tabel']} for the number of shots used. Each quantum experiment and noisy simulation was repeated $5$ times. The noise model used for the simulations was imported from ibm_fez. Note that for both LiH and $\ce{H2}$, a single layer is sufficient to reach the ground state energy, but the addition of more layers serves to introduce more noise, allowing for the viability of tiled M0 to be tested.
• Figure 3: Average results from energy calculations with the tUPS Ansatz on butadiene and H2O. We refer to Table \ref{['shots_tabel']} for the number of shots used. Each quantum experiment and noisy simulation was repeated $5$ times for butadiene. For H2O, the quantum experiments and noisy simulations were repeated $3$ and $5$ times, respectively. The noise model used for the simulations was imported from ibm_fez.
• Figure 4: Average results from energy calculations with the tUPS Ansatz on benzene. We refer to Table \ref{['shots_tabel']} for the number of shots used. Each quantum experiment and noisy simulation was repeated $3$ and $5$ times, respectively. The noise model used for the simulations was imported from ibm_fez.