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