Error-mitigated photonic variational quantum eigensolver using a single-photon ququart

Abstract

Variational quantum algorithms, a representative class of modern quantum algorithms, provide practical uses of near-term quantum processors. The size of the problem that can be encoded and solved on a quantum processor is limited by the dimension of the Hilbert space associated with the processor. One common approach for increasing the system dimension is to utilize a larger number of quantum systems. Here, we adopt an alternative approach to utilize multiple degrees of freedom of individual quantum systems to experimentally resource-efficiently increase the Hilbert space. We report experimental implementation of the variational quantum eigensolver (VQE) using four-dimensional photonic quantum states of single photons. The four-dimensional quantum states are implemented by utilizing polarization and path degrees of freedom of a single photon. Our photonic VQE is equipped with a quantum error mitigation protocol that efficiently reduces the effects of Pauli noise in the quantum processing unit. We apply our photonic VQE to estimate the ground state energy of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">H</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>−</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> cation. Simulation and experimental results demonstrate that our experimental resource-efficient photonic VQE can accurately estimate the bond dissociation curve, even in the presence of large noise in the quantum processing unit. We also discuss further possible resource-efficient enhancement of the Hilbert space in photonic quantum processors. Our results propose that photonic systems utilizing multiple degrees of freedom can provide a resource-efficient avenue to implement practical near-term quantum processors.