Symmetry-Assisted Preparation of Entangled Many-Body States on a Quantum Computer

Nuclear shell-model simulation in digital quantum computers

The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus. This work paves the way for quantum computing shell-model studies across the nuclear chart and our quantum resource quantification may be used in configuration-interaction calculations of other fermionic systems.

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.