Programming a quantum computer with quantum instructions

TL;DR

This paper introduces a method to execute quantum instructions directly on quantum data using density matrix exponentiation, enabling more efficient quantum algorithms and overcoming classical instruction-data limitations.

Contribution

It presents a novel approach for implementing quantum instructions on quantum data, maintaining instruction-data symmetry in quantum computing models.

Findings

Achieved 99.7% fidelity in controlled-phase gate implementation.

Demonstrated algorithmic fidelity over 90% at circuit depths >70.

Enabled exponential speedup for key quantum algorithms.

Abstract

The equivalence between the instructions used to define programs and the input data on which the instructions operate is a basic principle of classical computer architectures and programming. Replacing classical data with quantum states enables fundamentally new computational capabilities with scaling advantages for many applications, and numerous models have been proposed for realizing quantum computation. However, within each of these models, the quantum data are transformed by a set of gates that are compiled using solely classical information. Conventional quantum computing models thus break the instruction-data symmetry: classical instructions and quantum data are not directly interchangeable. In this work, we use a density matrix exponentiation protocol to execute quantum instructions on quantum data. In this approach, a fixed sequence of classically-defined gates performs an operation that uniquely depends on an auxiliary quantum instruction state. Our demonstration relies on a 99.7% fidelity controlled-phase gate implemented using two tunable superconducting transmon qubits, which enables an algorithmic fidelity surpassing 90% at circuit depths exceeding 70. The utilization of quantum instructions obviates the need for costly tomographic state reconstruction and recompilation, thereby enabling exponential speedup for a broad range of algorithms, including quantum principal component analysis, the measurement of entanglement spectra, and universal quantum emulation.