Simulating the Mott transition on a noisy digital quantum computer via
Cartan-based fast-forwarding circuits
- URL: http://arxiv.org/abs/2112.05688v1
- Date: Fri, 10 Dec 2021 17:32:15 GMT
- Title: Simulating the Mott transition on a noisy digital quantum computer via
Cartan-based fast-forwarding circuits
- Authors: Thomas Steckmann, Trevor Keen, Alexander F. Kemper, Eugene F.
Dumitrescu, Yan Wang
- Abstract summary: Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model.
Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models.
This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
- Score: 62.73367618671969
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 arbitrary 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.
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