Updates to figures and referee revisions

README.md

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 # Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer
 
-Thomas Steckmann, Trevor Keen, Alexander F. Kemper, Eugene F. Dumitrescu, Yan Wang
+Thomas Steckmann, Trevor Keen, Efekan Kokcu,    Alexander F. Kemper, Eugene F. Dumitrescu, Yan Wang
 
 [arXiv:2112.05688](https://arxiv.org/abs/2112.05688)
 
 *Abstract:*
 
-Dynamical mean-field theory (DMFT) maps the local Greens function of the Hubbard modelto that of the Anderson impurity model and thus gives an approximate solution of the Hubbardmodel by solving the simpler quantum impurity model. Quantum and hybrid quantum-classicalalgorithms have been proposed to efficiently solve impurity models by preparing and evolving theground state under the impurity Hamiltonian on a quantum computer instead of using intractableclassical algorithms. We propose a highly optimized fast-forwarding quantum circuit to significantlyimprove 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 overarbitrarytimes. By exploiting the structure ofthe fast-forwarding circuits we reduce the gate count (77 CNOTs after optimization), simulate thedynamics, and extract frequencies from the Anderson impurity model on noisy quantum hardware.We then demonstrate the Mott transition by mapping the phase-diagram of the correspondingimpurity problem.  Especially near the Mott phase transition when the quasiparticle resonancefrequency converges to zero and evolving the system over long-time scales is necessary, our methodmaintains accuracy where Trotter error would otherwise dominate.  This work presents the firstcomputation of the Mott phase transition using noisy digital quantum hardware, made viable by ahighly optimized computation in terms of gate depth, simulation error, and run-time on quantumhardware. The combination of algebraic circuit decompositions and model specific error mitigationtechniques used may have applications extending beyond our use case to solving correlated electronicphenomena on noisy quantum computers.
+Dynamical mean-field theory (DMFT) maps the local Greens 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. By exploiting the structure of the fast-forwarding circuits we reduce the gate count (77 CNOTs after optimization), simulate the dynamics, and extract frequencies from the Anderson impurity model on noisy quantum hardware.We then 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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