Calculating the many-body density of states on a digital quantum
computer
- URL: http://arxiv.org/abs/2303.13476v1
- Date: Thu, 23 Mar 2023 17:46:28 GMT
- Title: Calculating the many-body density of states on a digital quantum
computer
- Authors: Alessandro Summer, Cecilia Chiaracane, Mark T. Mitchison, and John
Goold
- Abstract summary: We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer.
We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
- Score: 58.720142291102135
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum statistical mechanics allows us to extract thermodynamic information
from a microscopic description of a many-body system. A key step is the
calculation of the density of states, from which the partition function and all
finite-temperature equilibrium thermodynamic quantities can be calculated. In
this work, we devise and implement a quantum algorithm to perform an estimation
of the density of states on a digital quantum computer which is inspired by the
kernel polynomial method. Classically, the kernel polynomial method allows to
sample spectral functions via a Chebyshev polynomial expansion. Our algorithm
computes moments of the expansion on quantum hardware using a combination of
random state preparation for stochastic trace evaluation and a controlled
unitary operator. We use our algorithm to estimate the density of states of a
non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a
controlled register of 18 qubits. This not only represents a state-of-the-art
calculation of thermal properties of a many-body system on quantum hardware,
but also exploits the controlled unitary evolution of a many-qubit register on
an unprecedented scale.
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