Fast classical simulation of Harvard/QuEra IQP circuits
Abstract
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 103 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.