Sequential Quantum Simulations Using a 3D Superconducting Cavity Circuit-QED System

Quantum simulation is a leading near-term application of quantum processors, enabling exploration of correlated many-body systems beyond classical reach. We investigate a sequential quantum simulation framework to find the many-body ground state of a quantum-critical spin chain implemented in a 3D superconducting cavity within the circuit-QED architecture. The method encodes many-body correlations sequentially by mapping a matrix-product-state representation of the ground state onto the Hilbert space of a single bosonic cavity mode, enabling resource-efficient simulations that preserve entanglement with minimal hardware overhead. We experimentally use a high-coherence 3D cavity coupled to a transmon as a controllable register for constructing and manipulating MPS representations. Using a universal gate set consisting of cavity displacements and number-selective qubit rotations, together with mid-circuit measurement and transmon reset, we realize target unitaries and extract correlation functions corresponding to benchmark quantum states. These results highlight the potential of sequential quantum algorithms and cavity-based circuit-QED systems as powerful and scalable platforms for quantum simulation in near-term devices.