The tantalizing promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here, we report using a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 ∼ 10^16. Measurements from repeated experiments sample the corresponding probability distribution, which we verify using classical simulations. While our processor takes about 200 seconds to sample one instance of a quantum circuit 1 million times, a s...