Programming a Quantum Computer with Quantum Instructions (Part 1): Introduction and construction*

The equivalence between the instructions used to define programs and the input data on which they operate is a basic principle of classical computer architectures and programming. However, in all previous quantum computing models, quantum data are transformed by a set of gates compiled using solely classical information. In this work, we execute a quantum program–density matrix exponentiation (DME)–that uses quantum instructions to process quantum data. Here, a fixed sequence of gates performs an operation that depends on a quantum instruction state. Quantum instructions remove the need for state reconstruction in a broad range of algorithms, enabling exponential speedup. In Part 1, we introduce the DME algorithm and describe our experimental implementation of DME on a quantum processor using a 99.7% fidelity CPHASE gate between two superconducting transmons.