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One of Dr Koh’s works, "," published in Quantum in 2022, delves into the performance of classical shadows under noisy conditions. It explores the impact of noise on the classical shadows protocol and introduces an unbiased estimator that adapts to noisy conditions. The findings establish upper bounds on the number of samples required for learning the properties of quantum systems when the classical shadow protocol implemented is subject to various noise channels, like depolarizing noise and amplitude damping.

In January 2024, Dr Koh co-authored "," published in npj Quantum Information. The study focuses on the least stringent assumption on the unitary ensemble used in the classical shadow protocol that can still deliver meaningful results. It zeroes in on Pauli-invariant unitary ensembles, which stay invariant when multiplied by Pauli operators. For these ensembles, the authors offer explicit formulas for the reconstruction map and sample complexity bounds, extending to noisy scenarios. This is especially useful for locally scrambled unitary ensembles, where explicit formulas for the reconstruction map and sample complexity bounds are given that circumvent the need to solve an exponential-sized linear system. The findings present a comprehensive framework for classical shadows with Pauli-invariant unitary ensembles, relevant in both noisy and noiseless conditions for states and channels, making it ready for use in near-term quantum devices.

In April 2024, Dr Koh advanced the field even further with "," also published in npj Quantum Information. This study tackles error mitigation in classical shadows of fermionic systems on noisy quantum devices. Estimating fermionic Hamiltonian expectation values is crucial for simulating various physical systems. Classical shadow (CS) algorithms help by cutting down the number of quantum state copies needed, but noise in quantum devices remains a challenge. The proposed error-mitigated CS algorithm assumes gate-independent, time-stationary, and Markovian (GTM) noise. For n-qubit systems, the algorithm efficiently estimates k-particle reduced density matrices under GTM noise with constant fidelities. The proposed algorithm is shown to be robust against noise types like depolarizing, amplitude damping, and X-rotation noise with constant strengths, showing similar scalings to previous CS algorithms for fermions but with better noise resilience. Numerical simulations back up its effectiveness in noisy environments, suggesting its readiness for near-term quantum devices.

These papers have collectively received over 100 citations in two years, reflecting the significant impact of Dr Koh's research. His collaborative efforts and innovative approaches have pushed the field of classical shadows forward, and we look forward to his future contributions.