Ground State

Robert Raussendorf

J. D. Fan, Y. M. Malozovsky

We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations and the pairing condensate. We calculate the contribution of particle-hole excitation to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the superconducting ground state. In contrast, for the repulsive interaction the particle-hole excitations are just to renormalize the ground state energy. Thus, in the case of repulsive interaction the condensate of bound pairs would lead to the real superconducting ground state of the system as shown.

Kazuto Oshima

Abstract We propose a procedure to extract a true ground state from an approximate ground state by using quantum entanglement. We use plural ancilla qubits with hierarchical structure, intending to gradually improve the precision of the approximation. We demonstrate the procedure for quantum systems with a few qubits that derive from the (1+1)-dimensional Schwinger model by classically emulated digital quantum simulation. Although we use for simplicity an approximate ground state prepared by adiabatic quantum computation, our procedure is applicable to any approximate ground state that is a superposition of a true ground state and excited states. Our procedure is applicable for an $N$-qubits Hamiltonian with a nondegenerate ground state.

Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert

Yuping Mao, Chang Chen, Jiaxing Feng +2 more

The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground state as the stabilizer ground state which has the highest fidelity with the true ground state. This is useful in quantum simulation contexts as it allows for a Clifford circuit approximation of a ground state that can be further refined towards the true ground state. We show how the optimal stabilizer ground state may be evaluated. We show applications of this state in the context of measurement-based deterministic imaginary time evolution (MITE), which converges to the ground state with high efficiency. By classically selecting the optimal stabilizer generator group and employing the stabilizer tableaux formalism, the method prepares the corresponding stabilizer ground state with maximal fidelity. The identification and refinement of this generator group are performed using a genetic algorithm tailored to the structure of the target Hamiltonian. The complexity analysis further demonstrates that algorithm's quantum resource cost scales polynomially with system size, highlighting its high efficiency and potential quantum advantage.

Peter Mittelstaedt