Abstract
Density matrix exponentiation (DME) is a general technique for using a quantum state to enact the quantum operation on a target system. It was first proposed in the context of quantum machine learning, but has since been shown to have broad applications in quantum metrology and computation. No experimental demonstration of DME has been performed thus far due to its demanding circuit depths and the need to efficiently generate multiple identical copies of during the finite lifetime of the target system. In this work, we describe the first demonstration of the DME algorithm, which we accomplish using a superconducting quantum processor. Our demonstration relies on a 99.7% fidelity controlled-phase gate implemented using two tunable superconducting transmon qubits. We achieve a fidelity surpassing 90% at circuit depths exceeding 70 when comparing the output of the circuit executed on our quantum processor to a simulation assuming perfect operations and measurements.
- Received 1 March 2021
- Revised 1 October 2021
- Accepted 4 November 2021
DOI:https://doi.org/10.1103/PhysRevX.12.011005
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers hold the potential to outperform classical supercomputers at certain tasks. To implement algorithms on a quantum computer, programmers use conventional computers and hardware to create a set of classical control signals that implement a desired quantum algorithm. However, feeding the quantum information forward requires an inefficient conversion: extraction of quantum information, conversion to classical control signals, and reinjection of those signals into the system to implement quantum operations. Here, we demonstrate a more natively quantum strategy to programming quantum computers.
Our approach uses the density matrix exponentiation (DME) protocol, a general technique for using a quantum state to enact a quantum operation. It can be thought of as a subroutine with which programmers can turn multiple copies of a quantum state into instructions for next steps in a quantum algorithm.
We implement DME using two qubits in a superconducting quantum processor. Our implementation relies on a high-fidelity two-qubit gate and a novel technique called quantum measurement emulation to approximately reset a known quantum state. These developments enable us to demonstrate the DME protocol for the first time on a small-scale quantum processor and benchmark its performance.
While DME was originally proposed in the context of a specific quantum machine-learning algorithm, it may also represent a fundamentally different approach to quantum programming. It allows the possibility of encoding quantum algorithms directly into quantum states and executing those algorithms on other quantum states, enabling a new class of efficient quantum algorithms.
