Quantum Simulation of the Polaron-Molecule Transition on a NISQ Device

TL;DR

This work tackles the challenge of simulating strongly correlated fermions by formulating a unified Hamiltonian that blends Fermi-polaron and BEC-BCS crossover physics and mapping it onto a gate-based quantum processor via the Jordan-Wigner transformation. The authors implement real-time dynamics and spectroscopy using a first-order Trotter-Suzuki decomposition and a Ramsey interferometry protocol, validating results against exact classical benchmarks and executing experiments on BSC-CNS hardware. Key contributions include a continuous framework linking polaron and molecular regimes through an effective interaction $g_{\rm eff}$, a discretized extended Hubbard representation, and a Ramsey-based spectroscopy that reveals a polaron-to-molecule transition with a linear energy scaling $E \propto U_{\rm imp}$ in the strong-coupling limit. They also demonstrate error mitigation (ZNE, readout correction) and discuss scalability, proposing higher-order Trotterization and variational quantum time-evolution as avenues to tackle larger Fermi seas and longer evolutions, underscoring the practical impact of digital quantum simulations for complex many-body phenomena.

Abstract

The simulation of strongly correlated fermionic systems remains one of the most significant challenges in computational physics due to the exponential growth of the Hilbert space and the fermionic sign problem. In this work, we present a digital quantum simulation framework to explore the Fermi polaron and the Bose-Einstein Condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover. We develop a unified Hamiltonian formalism that bridges pairing superfluidity and impurity physics, mapping the system onto a gate-based quantum processor via the Jordan-Wigner transformation. Using a first-order Trotter-Suzuki decomposition, we implement a Ramsey interferometry protocol to extract the real-time dynamics and spectral response of the system. Our results demonstrate a smooth transition from a dressed quasiparticle (polaron) regime to a stable molecular bound state, characterized by a linear energy renormalization in the strong-coupling limit. We validate our simulation against exact classical benchmarks and report successful execution on the Barcelona Supercomputing Center quantum hardware. Despite the inherent noise of the quantum hardware, the hybrid variational approach shows remarkable resilience, accurately capturing the bifurcation of the spectral density

Figures (8)

• Figure 1: Quantum circuit implementing the Ramsey interferometry protocol. The ancilla (qubit 0) controls the differential time-evolution. Qubit 1 encodes the impurity, while qubits 2 and 3 represent the bath modes. The use of controlled-MultiRZ gates minimizes depth.
• Figure 2: Algorithmic validation of the quantum simulation against the exact classical solution (ED) for $U_{imp}=2.5J$. The blue dots represent the data obtained via the statevector simulator, showing nearly perfect agreement with the theoretical curve (red line). This overlap confirms the correctness of the Jordan-Wigner mapping and the first-order Trotter-Suzuki decomposition.
• Figure 3: Validation of the quantum simulation executed on the BSC QBlue cluster with $N=1000$ shots (blue dots) compared to the exact theoretical prediction (red dashed line). The fluctuations around the curve represent the intrinsic statistical uncertainties.
• Figure 4: Temporal evolution of the real part of the overlap function $S(t)$. The sustained oscillation confirms the coherent nature of the polaron state in this finite-size system.
• Figure 5: Spectral density obtained via FFT. The peak position corresponds to the renormalized polaron energy $E_{pol}$.