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Lee-Yang (LY) zeros, points on the complex plane of physical parameters wherethe partition function goes to zero, have found diverse applications acrossmultiple disciplines like statistical physics, protein folding, percolation,complex networks etc. However, experimental extraction of the complete set ofLY zeros for general asymmetrical classical systems remains a crucial challengeto put those applications into practice. Here, we propose a qubit-based methodto simulate an asymmetrical classical Ising system, enabling the exploration ofLY zeros at arbitrary values of physical parameters like temperature, internalcouplings etc. Without assuming system symmetry, the full set of LY zeros formsan algebraic variety in a higher-dimensional complex plane. To determine thisvariety, we pro ject it into sets representing magnitudes (amoeba ) and phases(coamoeba ) of LY zeros. Our approach uses a probe qubit to initialize thesystem and to extract LY zeros without assuming any control over the systemqubits. This is particularly important as controlling system qubits can getintractable with the increasing complexity of the system. Initializing thesystem at an amoeba point, coamoeba points are sampled by measuring probe qubitdynamics. Iterative sampling yields the entire algebraic variety. Experimentaldemonstration of the protocol is achieved through a three-qubit NMR register.This work expands the horizon of quantum simulation to domains whereidentifying LY zeros in general classical systems is pivotal. Moreover, byextracting abstract mathematical objects like amoeba and coamoeba for a givenpolynomial, our study integrates pure mathematical concepts into the realm ofquantum simulations.

Observing Algebraic Variety of Lee-Yang Zeros in Asymmetrical Systems via a Quantum Probe