Sebastian Leontica

We embed 1-layer QAOA circuits into the larger class of parameterized Instantaneous Quantum Polynomial circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The use of analytic expressions to find optimal parameters classically makes our protocol robust against barren plateaus and hardware noise. The average overlap with the ground state scales as $\mathcal{O}(2^{-0.31 N})$ with the number of qubits $N$ for random Sherrington-Kirkpatrick (SK) Hamiltonians of up to 29 qubits, a polynomial improvement over 1-layer QAOA. Additionally, we observe that performing variational imaginary time evolution on the manifold approximates low-temperature pseudo-Boltzmann states. Our protocol outperforms 1-layer QAOA on the recently released Quantinuum H2 trapped-ion quantum hardware and emulator, where we obtain an average approximation ratio of $0.985$ across 312 random SK instances of 7 to 32 qubits, from which almost $44\%$ are solved optimally using 4 to 1208 shots per instance.

We investigate the feasibility of observing matter-wave interference of a micron-sized charged particle by putting it into a quantum superposition of states with a distinguishable separation. In the proposed method, an atomic ion is confined in a linear Paul trap along with the massive charged particle so that we can make use of the extensive toolbox of experimental techniques developed to control quantum states of trapped ions, and to manipulate their motions with high fidelity operations. This approach provides a stringent test of the predictions of dynamical reduction models of delocalised quantum superpositions of a particle, reaching macroscopicities of up to $\mathcal{M}=17$.