Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access to quantum hardware remains too limited to meet the demand, simulating quantum circuits on conventional computers satisfies many needs. We advance Schrödinger-style simulation of quantum circuits that is useful standalone and as a building block in layered simulation algorithms, both cases are illustrated in our results. Our algorithmic contributions show how to simulate multiple quantum gates at once, how to avoid floating-point multiplies, how to best use data-level and thread-level parallelism as well as CPU cache, and how to leverage these optimizations by reordering circuit gates. While not described previously, these techniques implemented by us supported published high-performance distributed simulations up to 64 qubits. To show additional impact, we benchmark our simulator against Microsoft, IBM and Google simulators on hard circuits from Google.

As quantum computers grow more capable, simulating them on conventional hardware becomes more challenging yet more attractive since this helps in design and verification. Some quantum algorithms and circuits are amenable to surprisingly efficient simulation, and this makes hard-to-simulate computations particularly valuable. For such circuits, we develop accurate massively-parallel simulation with dramatic speedups over earlier methods on 42- and 45-qubit circuits. We propose two ways to trade circuit fidelity for computational speedups, so as to match the error rate of any quantum computer. Using Google Cloud, we simulate approximate sampling from the output of a circuit with 7 × 8 qubits and depth 42 with fidelity 0.5% at an estimated cost of $35K.