Sequential quantum simulation with circuit QED devices

Quantum simulation of many-body systems in materials science and chemistry are promising application areas for quantum computers. However, the limited scale and coherence of near-term quantum processors pose a significant obstacle to realizing this potential. Here, we outline how circuit quantum electrodynamics (cQED) devices, each consisting of a transmon qubit coupled to a long-lived cavity mode, can be used to simulate the ground state of a highly-entangled quantum many-body spin chain. We exploit recently developed methods for implementing quantum operations to sequentially build up a matrix product state (MPS) representation of a many-body state. This approach re-uses the transmon qubit to read out the state of each spin in the chain and exploits the large state space of the cavity as a quantum memory encoding inter-site correlations and entanglement.

We show that analog (pulse-level) control schemes can accurately prepare a known MPS representation of a quantum critical spin chain in significantly less time than digital (gate-based) methods, thereby reducing the exposure to decoherence. We then explore this analog-control approach for the variational preparation of an unknown ground state. Practically, the large state space of the cavity can be used to replace multiple qubits in a qubit-only architecture, and could therefore simplify the design of quantum processors for simulating a wide range of materials, from the Ising model to fractional quantum Hall systems.