Digital Quantum Simulation of Squeezed States via Enhanced Bosonic Encoding and its Demonstration With Superconducting Qubits

Abstract

We present a fully digital approach for simulating single‐mode squeezed states using an enhanced bosonic encoding strategy on a circuit model, and demonstrate it on a superconducting quantum processor through a cloud platform. By mapping up to 2n$2^{n}$ photonic Fock states onto n$n$ qubits, our framework leverages Gray‐code‐based encodings to reduce gate overhead compared to conventional one‐hot or binary mappings. We further optimize resource usage by restricting the simulation to Fock states with even numbers of photons only, effectively doubling the range of photon numbers that can be represented for a given number of qubits. To overcome noise and finite coherence in current hardware, we employ a variational quantum simulation protocol, which adapts shallow, parameterized circuits through iterative optimization. Implemented on the Zuchongzhi‐2 superconducting platform, our method demonstrates squeezed‐state dynamics via a parameter sweep from vacuum state preparation ( r=0$r=0$ ) to squeezing levels that extend beyond the conventional truncation bound of encoded Fock space ( r>1.63$r>1.63$ ). Results of our demonstration, corroborated by quantum state tomography and Wigner‐function analysis, confirm high‐fidelity state preparation and demonstrate the potential of Gray‐code‐inspired techniques for realizing continuous‐variable physics on near‐term, qubit‐based quantum processors.