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Quantum statistical mechanics allows us to extract thermodynamic informationfrom a microscopic description of a many-body system. A key step is thecalculation of the density of states, from which the partition function and allfinite-temperature equilibrium thermodynamic quantities can be calculated. Inthis work, we devise and implement a quantum algorithm to perform an estimationof the density of states on a digital quantum computer which is inspired by thekernel polynomial method. Classically, the kernel polynomial method allows tosample spectral functions via a Chebyshev polynomial expansion. Our algorithmcomputes moments of the expansion on quantum hardware using a combination ofrandom state preparation for stochastic trace evaluation and a controlledunitary operator. We use our algorithm to estimate the density of states of anon-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for acontrolled register of 18 qubits. This not only represents a state-of-the-artcalculation of thermal properties of a many-body system on quantum hardware,but also exploits the controlled unitary evolution of a many-qubit register onan unprecedented scale.

Calculating the many-body density of states on a digital quantum computer