Experimental error mitigation via symmetry verification in a variational quantum eigensolver
R. Sagastizabal (TU Delft - QCD/DiCarlo Lab, TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft)
Xavi Bonet Monroig (Universiteit Leiden, TU Delft - QuTech Advanced Research Centre, TU Delft - QCD/DiCarlo Lab)
Malay Singh (Kavli institute of nanoscience Delft, Student TU Delft)
M. Adriaan Rol (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab)
C.C. Bultink (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab)
X. Fu (TU Delft - QuTech Advanced Research Centre, FTQC/Bertels Lab, TU Delft - Computer Engineering, Kavli institute of nanoscience Delft)
V. P. Ostroukh (TU Delft - QCD/DiCarlo Lab, Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre)
N. Muthusubramanian (TU Delft - QuTech Advanced Research Centre, TU Delft - QCD/DiCarlo Lab, Kavli institute of nanoscience Delft)
A. Bruno (Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab, TU Delft - QuTech Advanced Research Centre)
M.C. Beekman (Kavli institute of nanoscience Delft, TU Delft - Business Development)
S.N. Haider (TU Delft - Business Development, TNO)
Tom O'Brien (Universiteit Leiden)
Leonardo di Carlo (TU Delft - QCD/DiCarlo Lab, Kavli institute of nanoscience Delft, TU Delft - QN/DiCarlo Lab, TU Delft - QuTech Advanced Research Centre)
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Abstract
Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by applying the recently proposed symmetry verification technique to the experimental estimation of the ground-state energy and ground state of the hydrogen molecule. A finely adjustable exchange interaction between two qubits in a circuit QED processor efficiently prepares variational ansatz states in the single-excitation subspace respecting the parity symmetry of the qubit-mapped Hamiltonian. Symmetry verification improves the energy and state estimates by mitigating the effects of qubit relaxation and residual qubit excitation, which violate the symmetry. A full-density-matrix simulation matching the experiment dissects the contribution of these mechanisms from other calibrated error sources. Enforcing positivity of the measured density matrix via scalable convex optimization correlates the energy and state estimate improvements when using symmetry verification, with interesting implications for determining system properties beyond the ground-state energy.