@article{steckmann_keen_kokcu_kemper_dumitrescu_wang_2023, title={Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer}, volume={5}, ISSN={["2643-1564"]}, url={https://doi.org/10.1103/PhysRevResearch.5.023198}, DOI={10.1103/PhysRevResearch.5.023198}, abstractNote={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 from the solution of 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 that is assumed to have the scalability and accuracy far beyond the current state-of-the-art quantum hardware. As a proof of principle demonstration targeting the Anderson impurity model we close the DMFT loop with current noisy hardware. With a highly optimized fast-forwarding quantum circuit and a noise resilient spectral analysis we observe a Mott phase transition. Based on a Cartan decomposition, our algorithm gives a fixed depth, fast-forwarding, quantum circuit that can evolve the initial state over arbitrarily long times without time-discretization errors typical of other product decomposition formulas such as Trotter decomposition. By exploiting the structure of the fast-forwarding circuits we reduce the gate count (to 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 full metal-insulator phase-diagram. Near the Mott phase transition, our method maintains accuracy where Trotter error would otherwise dominate due to the long-time evolution required to resolve quasiparticle resonance frequency extremely close to zero. 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 runtime on quantum hardware.}, number={2}, journal={PHYSICAL REVIEW RESEARCH}, author={Steckmann, Thomas and Keen, Trevor and Kokcu, Efekan and Kemper, Alexander F. and Dumitrescu, Eugene F. and Wang, Yan}, year={2023}, month={Jun} }
 @article{camps_kokcou_bassman_de jong_kemper_van beeumen_2022, title={AN ALGEBRAIC QUANTUM CIRCUIT COMPRESSION ALGORITHM FOR HAMILTONIAN SIMULATION}, volume={43}, ISSN={["1095-7162"]}, DOI={10.1137/21M1439298}, abstractNote={Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in terms of chip size and error rates. Shallow quantum circuits with uncomplicated topologies are essential for successful applications in the NISQ era. Based on matrix analysis, we derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The depth of the compressed circuits is independent of simulation time and grows linearly with the number of spins. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $\mathcal{O}(10^3)$ spins. The resulting quantum circuits have a simple nearest-neighbor topology, which makes them ideally suited for NISQ devices.}, number={3}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Camps, Daan and Kokcou, Efekan and Bassman, Lindsay and De Jong, Wibe A. and Kemper, Alexander E. and Van Beeumen, Roel}, year={2022}, pages={1084–1108} }
 @article{kokcu_camps_bassman_freericks_jong_van beeumen_kemper_2022, title={Algebraic compression of quantum circuits for Hamiltonian evolution}, volume={105}, ISSN={["2469-9934"]}, url={https://doi.org/10.1103/PhysRevA.105.032420}, DOI={10.1103/PhysRevA.105.032420}, abstractNote={Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits whose depth scales with the number of steps. When the circuit elements are limited to a subset of SU(4) -- or equivalently, when the Hamiltonian may be mapped onto free fermionic models -- several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.}, number={3}, journal={PHYSICAL REVIEW A}, author={Kokcu, Efekan and Camps, Daan and Bassman, Lindsay and Freericks, J. K. and Jong, Wibe A. and Van Beeumen, Roel and Kemper, Alexander F.}, year={2022}, month={Mar} }