  An efficient simulator for quantum systems is one of the original goals for
the efforts to develop a quantum computer [1]. In recent years, synthetic
dimension in photonics [2] have emerged as a potentially powerful approach for
simulation that is free from the constraint of geometric dimensionality. Here
we demonstrate a quantum-correlated synthetic crystal, based upon a
coherently-controlled broadband quantum frequency comb produced in a chip-scale
dynamically modulated lithium niobate microresonator. The time-frequency
entanglement inherent with the comb modes significantly extends the
dimensionality of the synthetic space, creating a massive nearly 400 x 400
synthetic lattice with electrically-controlled tunability. With such a system,
we are able to utilize the evolution of quantum correlations between entangled
photons to perform a series of simulations, demonstrating quantum random walks,
Bloch oscillations, and multi-level Rabi oscillations in the time and frequency
correlation space. The device combines the simplicity of monolithic
nanophotonic architecture, high dimensionality of a quantum-correlated
synthetic space, and on-chip coherent control, which opens up an avenue towards
chip-scale implementation of large-scale analog quantum simulation and
computation [1,3,4] in the time-frequency domain.
