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<!DOCTYPE html>
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<title>Thomas Steckmann</title>
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<h3>
Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits
</h3>
<p>Thomas Steckmann, Trevor Keen, Alexander F. Kemper, Eugene F. Dumitrescu, Yan Wang</p>
<p>
Abstract:
</p>
<p>
Dynamical mean-field theory (DMFT) maps the local Green’s function of the Hubbard model to that of the Anderson impurity
model and thus gives an approximate solution of the Hubbard model by solving the simpler quantum impurity model. Quantum
and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models by preparing and
evolving the ground state under the impurity Hamiltonian on a quantum computer instead of using intractable classical
algorithms. We propose a highly optimized fast-forwarding quantum circuit to significantly improve quantum algorithms
for the minimal DMFT problem preserving the Mott phase transition. Our Cartan decomposition based algorithm uses a fixed
depth quantum circuit to eliminate time-discretization errors and evolve the initial state over <em>arbitrary</em> times.
Exploiting the structure of the fast-forwarding circuits, we sufficiently reduce the gate cost to simulate the dynamics
of, and extract frequencies from, the Anderson impurity model on noisy quantum hardware and demonstrate the Mott
transition by mapping the phase-diagram of the corresponding impurity problem. Especially near the Mott phase transition
when the quasiparticle resonance frequency converges to zero and evolving the system over long-time scales is necessary,
our method maintains accuracy where Trotter error would otherwise dominate. This work presents the first computation of
the Mott phase transition using noisy digital quantum hardware, made viable by a highly optimized computation in terms
of gate depth, simulation error, and run-time on quantum hardware. The combination of algebraic circuit decompositions
and model specific error mitigation techniques used may have applications extending beyond our use case to solving
correlated electronic phenomena on noisy quantum computers.
</p>
<p>
<a href='https://arxiv.org/abs/2112.05688'>https://arxiv.org/abs/2112.05688</a>
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