Experimental computations of atomic properties on a superconducting quantum processor

We experimentally compute relativistic and correlation effects in the atomic properties by using a superconducting qubit processor. Specifically, we compute the relativistic ground-state energies and magnetic-dipole hyperfine structure constants for four Li-like atomic systems ranging from very light to moderately heavy to very heavy in terms of nuclear charge. A symmetry-conserving Bravyi-Kitaev transformation is used to reduce the original six-qubit problem to a four-qubit problem, which is experimentally contrived by reducing the hardware requirement by employing a virtual two-qubit gate. It enables the simulation of four-qubit circuits using two physical qubits with additional circuit evaluations. The ground-state wave functions, required for computing atomic properties, are obtained by using quantum state tomography. Our results show that the averaged relative errors for the ground-state energies are <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>≈</a:mo><a:mn>0.3</a:mn><a:mo>±</a:mo><a:mn>1</a:mn><a:mo>%</a:mo></a:mrow></a:math>. However, for the hyperfine structure constants, the mean values of the relative errors are less than <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>15</b:mn><b:mo>%</b:mo></b:mrow></b:math>, with their estimated upper bound of relative errors of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>≈</c:mo><c:mo>±</c:mo><c:mn>10</c:mn><c:mo>%</c:mo></c:mrow></c:math> (with the exception of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>7.2</d:mn><d:mo>±</d:mo><d:mn>47</d:mn><d:mo>%</d:mo></d:mrow></d:math> for neutral <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mmultiscripts><e:mi>Li</e:mi><e:mprescripts/><e:none/><e:mn>7</e:mn></e:mmultiscripts></e:math>). Notably, our results for the hyperfine structure constants exhibit higher sensitivity to errors as compared to energies; a trend which we also confirm through additional numerical simulations. Published by the American Physical Society 2024