  Quantum computers allow for direct simulation of the quantum interference and
entanglement used in modern interferometry experiments with applications
ranging from biological sensing to gravitational wave detection. Inspired by
recent developments in quantum sensing at the Laser Interferometer
Gravitational-wave Observatory (LIGO), here we present two quantum circuit
models that demonstrate the role of quantum mechanics and entanglement in
modern precision sensors. We implemented these quantum circuits on IBM quantum
processors, using a single qubit to represent independent photons traveling
through the LIGO interferometer and two entangled qubits to illustrate the
improved sensitivity that LIGO has achieved by using non-classical states of
light. The one-qubit interferometer illustrates how projection noise in the
measurement of independent photons corresponds to phase sensitivity at the
standard quantum limit. In the presence of technical noise on a real quantum
computer, this interferometer achieves the sensitivity of 11\% above the
standard quantum limit. The two-qubit interferometer demonstrates how
entanglement circumvents the limits imposed by the quantum shot noise,
achieving the phase sensitivity 17\% below the standard quantum limit. These
experiments illustrate the role that quantum mechanics plays in setting new
records for precision measurements on platforms like LIGO. The experiments are
broadly accessible, remotely executable activities that are well suited for
introducing undergraduate students to quantum computation, error propagation,
and quantum sensing on real quantum hardware.
