Estimates the canonical partition function of a Hamiltonian by interpolating Trotter error, replacing the quantum walk with generalized quantum signal processing on a Trotterized evolution operator.
All you need is Trotter
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abstract
The work here enables linear cost-scaling with evolution time $t$ while keeping ${\rm polylog} (1/\epsilon)$ scaling and no extra block-encoding qubits, where $\epsilon$ is the algorithmic error. This is achieved through product formulas, stable interpolation (Chebyshev), and to calculate the needed fractional queries, cardinal sine interpolation is used.
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Canonical Partition Function on a Quantum Computer through Trotter Interpolation
Estimates the canonical partition function of a Hamiltonian by interpolating Trotter error, replacing the quantum walk with generalized quantum signal processing on a Trotterized evolution operator.