Perturbative description of high-
Tc superconductivity in the Hubbard model via unitary transformation and classical spins
A unitary transformation is applied to the Hubbard model, which maps the Hubbard interaction to a single particle term. The resulting Hamiltonian consists of unconstrained fermions, which is then mapped to a Hamiltonian of spinless fermions coupled to pseudospins. The fermions are integrated out using second order perturbation theory in
1/U, resulting in an effective spin Hamiltonian. An order parameter is identified, stabilizing d-wave superconductivity. The groundstate energy of classical spin configurations is minimized at a finite value of this order parameter after a critical chemical potential, resulting in d-wave superconductivity at non-zero doping. This suggests, that the onset of high-
Tc superconductivity is governed by the groundstate of a classical spin system.
Abstract Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermionic problem in the qubits of a quantum computer. In this work, we introduce "treespilation," a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings previously introduced by some of the authors. We use this technique to minimise the number of CNOT gates required to simulate chemical groundstates found numerically using the ADAPT-VQE algorithm. We observe significant reductions, up to 74%, in CNOT counts on full connectivity and for limited qubit connectivity-type devices such as IBM Eagle and Google Sycamore, we observe similar reductions in CNOT counts. In many instances, the reductions achieved on these limited connectivity devices even surpass the initial full connectivity CNOT count.