Leo Joon Il Moon

Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent robustness of time crystalline order to perturbations in the drive protocol makes DTCs promising for applications in quantum technologies. We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, with improvements of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50kHz range - a challenging frequency regime for sensors based on atomic vapor or electronic spins - and attains a competitive sensitivity. PDTC sensors are resilient to errors in the drive protocol and sample inhomogeneities, and are agnostic to the macroscopic details of the physical platform: the underlying physical principle applies equally to superconducting qubits, neutral atoms, and trapped ions.

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states of Hamiltonians -- is to know how close the algorithm's output solution is to the true ground state, when the true ground state and ground-state energy are unknown. This is especially important in iterative algorithms, such as VQE, where one wants to avoid erroneous early termination. Recent developments in Hamiltonian reconstruction -- the inference of a Hamiltonian given an eigenstate -- give a metric can be used to assess the quality of a variational solution to a Hamiltonian-eigensolving problem. This metric can assess the proximity of the variational solution to the ground state without any knowledge of the true ground state or ground-state energy. In numerical simulations and in demonstrations on a cloud-based trapped-ion quantum computer, we show that for examples of both one-dimensional transverse-field-Ising (11 qubits) and two-dimensional J1-J2 transverse-field-Ising (6 qubits) spin problems, the Hamiltonian-reconstruction distance gives a helpful indication of whether VQE has yet found the ground state or not. Our experiments included cases where the energy plateaus as a function of the VQE iteration, which could have resulted in erroneous early stopping of the VQE algorithm, but where the Hamiltonian-reconstruction distance correctly suggests to continue iterating. We find that the Hamiltonian-reconstruction distance has a useful correlation with the fidelity between the VQE solution and the true ground state. Our work suggests that the Hamiltonian-reconstruction distance may be a useful tool for assessing success in VQE, including on noisy quantum processors in practice.