Fast classical simulation of Harvard/QuEra IQP circuits

Establishing an advantage for (white-box) computations by a quantum computer against its classical counterpart is currently a key goal for the quantum computation community. A quantum advantage is achieved once a certain computational capability of a quantum computer is so complex that it can no longer be reproduced by classical means, and as such, the quantum advantage can be seen as a continued negotiation between classical simulations and quantum computational experiments. A recent publication (Bluvstein et al., Nature 626:58-65, 2024) introduces a type of Instantaneous Quantum Polynomial-Time (IQP) computation complemented by a $48$-qubit (logical) experimental demonstration using quantum hardware. The authors state that the ``simulation of such logical circuits is challenging'' and project the simulation time to grow rapidly with the number of CNOT layers added, see Figure 5d/bottom therein. However, we report a classical simulation algorithm that takes only $0.00257947$ seconds to compute an amplitude for the $48$-qubit computation, which is roughly $10^3$ times faster than that reported by the original authors. Our algorithm is furthermore not subject to a significant decline in performance due to the additional CNOT layers. We simulated these types of IQP computations for up to $96$ qubits, taking an average of $4.16629$ seconds to compute a single amplitude, and estimated that a $192$-qubit simulation should be tractable for computations relying on Tensor Processing Units.