Gate Sequence Optimization for Quantum State Tomography under Noise

Quantum state tomography (QST) is time consuming even for small systems, thus, the optimal QST measurement scheme is highly relevant. While those optimal schemes are known in some ideal cases, e.g. mutually unbiased bases for non-degenerate measurements [1], often they need to be found numerically. Here, we investigate the effect of noise on the optimal QST measurement sets for two noise models: depolarization and over-under-rotation in two-qubit gates [2]. We apply these noise models to measurements realized by a quantum gate sequences followed by a projection on one state, yielding measurements effectively described by independent rank-1 projectors. This applies e.g. to two spin qubits measured by spin-to-charge conversion. We apply reinforcement learning for optimizing the effective times each quantum gate is switched on in a set of gate sequences. We evaluate the benefit of including noisy two-qubit gates. Even when two-qubit gates are not included, our solution outperforms the popular QST quorum by James et al. [3]. We extend the model by including errors from single-qubit gates and more variance in the gate sequences than necessary for realizing arbitrary projectors aiming at higher noise resilience overall. We test our findings on a quantum computing device.

[1] Wootters, Fields, Ann. Phys. 191, 363 (1989)

[2] Ivanova-Rohling, Rohling, Burkard, arXiv:2203.05677

[3] James et al., Phys. Rev. A 64, 052312 (2001)