Quantum Supremacy Is Both Closer and Farther than It Appears

TL;DR

This paper introduces a new massively-parallel simulation tool for quantum circuits that can match the fidelity of quantum computers, providing insights into the realistic costs and limitations of classical simulation of quantum supremacy tasks.

Contribution

We develop Rollright, a scalable simulation software that enables fidelity-cost tradeoffs and provides a detailed cost analysis for simulating quantum circuits, challenging assumptions about quantum supremacy.

Findings

Achieved massive speedups over prior simulators.

Simulated 7x8 qubits with 0.5% fidelity at $35,184 cost.

Estimated costs for deeper circuits reach one million dollars.

Abstract

As quantum computers improve in the number of qubits and fidelity, the question of when they surpass state-of-the-art classical computation for a well-defined computational task is attracting much attention. The leading candidate task for this milestone entails sampling from the output distribution defined by a random quantum circuit. We develop a massively-parallel simulation tool Rollright that does not require inter-process communication (IPC) or proprietary hardware. We also develop two ways to trade circuit fidelity for computational speedups, so as to match the fidelity of a given quantum computer --- a task previously thought impossible. We report massive speedups for the sampling task over prior software from Microsoft, IBM, Alibaba and Google, as well as supercomputer and GPU-based simulations. By using publicly available Google Cloud Computing, we price such simulations and enable comparisons by total cost across hardware platforms. We simulate approximate sampling from the output of a circuit with 7x8 qubits and depth 1+40+1 by producing one million bitstring probabilities with fidelity 0.5%, at an estimated cost of $35184. The simulation costs scale linearly with fidelity, and using this scaling we estimate that extending circuit depth to 1+48+1 increases costs to one million dollars. Scaling the simulation to 10M bitstring probabilities needed for sampling 1M bitstrings helps comparing simulation to quantum computers. We describe refinements in benchmarks that slow down leading simulators, halving the circuit depth that can be simulated within the same time.