One of the most important questions for quantum computers of today is to understand the behaviour and impact of noise. It is crucial to understand whether noisy quantum computers provide any advantage, both for practically relevant problems, or even as proof-of-principle, or whether we ultimately need error-corrected logical qubits to achieve this goal.
In this work, EQUALITY partners from Inria and collaborators, motivated by realistic hardware considerations of the pre-fault-tolerant era, study the impact of uncorrected noise on quantum circuits. The authors first show that any noise `truncates' most quantum circuits to effectively logarithmic depth, in the task of computing Pauli expectation values. They then prove that quantum circuits under any non-unital noise exhibit lack of barren plateaus for cost functions composed of local observables.
By leveraging the effective shallowness, the researchers also design a classical algorithm to estimate Pauli expectation values within inverse-polynomial additive error with high probability over the ensemble. Its runtime is independent of circuit depth, and it operates in polynomial time in the number of qubits for one-dimensional architectures and quasi-polynomial time for higher-dimensional ones.
Taken together, their results showcase that, unless one carefully engineers the circuits to take advantage of the noise, it is unlikely that noisy quantum circuits are preferable over shallow quantum circuits for algorithms that output Pauli expectation value estimates, like many variational quantum machine learning proposals. Moreover, the authors anticipate that their work could provide valuable insights into the fundamental open question about the complexity of sampling from (possibly non-unital) noisy random circuits.
Read the paper by clicking on the link below.
