Quantum error mitigation for physical and logical qubits
Sergey Bravyi
APS March Meeting 2022
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless 2-local Hamiltonians H describing a system of n qubits. We give an efficient algorithm that outputs a separable state whose energy is at least λ max /O(log n), where λ max is the maximum eigenvalue of H. We also give a simplified proof of a theorem due to Lieb that establishes the existence of a separable state with energy at least λ max /9. Second, we consider a system of n fermionic modes and traceless Hamiltonians composed of quadratic and quartic fermionic operators. We give an efficient algorithm that outputs a fermionic Gaussian state whose energy is at least λ max /O(n log n). Finally, we show that Gaussian states can vastly outperform Slater determinant states commonly used in the Hartree-Fock method. We give a simple family of Hamiltonians for which Gaussian states and Slater determinants approximate λ max within a fraction 1 − O(n −1 ) and O(n −1 ), respectively.
Sergey Bravyi
APS March Meeting 2022
Robert König, Graeme Smith
Nature Photonics
Sergey Bravyi, Jeongwan Haah
Physical Review A - AMO
Sergey Bravyi, Anirban Chowdhury, et al.
Nature Physics