Researchers at the University of New Mexico have developed a new algorithm accurately simulating the behaviour of noisy quantum computers. Shravan and colleagues present a polynomial-time classical algorithm capable of sampling output distributions from instantaneous quantum polynomial (IQP) circuits affected by amplitude-damping noise. The algorithm addresses a key gap in the field, as most existing simulation techniques rely on specific types of noise or inherent randomness, whereas this one functions effectively with non-unital noise and without requiring randomness. Efficient simulation of these circuits, generated by arbitrary local gates with sufficient depth, is a vital step towards validating quantum computations and developing strong error mitigation strategies for near-term quantum devices. Polynomial time simulation of amplitude-damped instantaneous quantum polynomial circuits overcomes existing limitations Circuits previously requiring a depth exceeding Ω(log(n)) for classical simulation are now efficiently sampled in polynomial time. The breakthrough applies to amplitude-damped instantaneous quantum polynomial (IQP) circuits, a class specifically designed to challenge classical computers and benchmark quantum supremacy. These circuits are constructed using Clifford gates and a non-Clifford gate, typically a Hadamard gate applied to a specific qubit, creating a computational basis state that is difficult for classical computers to represent efficiently. Previous methods struggled with circuits beyond this logarithmic depth or relied on specific noise conditions, such as unital noise where the trace of the noise operator is preserved, meaning the overall probability remains constant. Researchers have developed a classical algorithm capable of simulating quantum circuits previously considered beyond reach, utilising arbitrary ‘l-local diagonal gates’, meaning gates acting on a limited number of qubits at a time. Diagonal gates, in this context, represent operations that preserve the diagonal elements of the density matrix, simplifying the simulation process. This expands the scope of verifiable quantum computation and offers a new tool for developing error mitigation techniques, enabling the