Liquid state NMR simulations of quantum many-body problems

Abstract

Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid state Nuclear Magnetic Resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results allow us to assess the limits of the degree of quantum control attained in these kinds of experiments. The simulation of other physical systems, with different particle statistics, is also discussed.

34 pages, 16 figures

References in corpus (1)

• Introduction to NMR Quantum Information Processing

Cited by in corpus (37)

• Quantum Simulation
• Simulating chemistry using quantum computers
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Computational advantage of quantum random sampling
• Using Quantum Computers for Quantum Simulation
• Simulation of a Heisenberg XY- chain and realization of a perfect state transfer algorithm using liquid nuclear magnetic resonance
• Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
• Simulation of chemical reaction dynamics on an NMR quantum computer
• Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• Adiabatic Quantum Simulators
• A Two-Dimensional Lattice Ion Trap for Quantum Simulation
• Characterization of complex quantum dynamics with a scalable NMR information processor
• Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
• Experimental simulation of quantum tunneling in small systems
• Computing partition functions in the one clean qubit model
• Quantum Simulation of Tunneling in Small Systems
• Quantum information processing using nuclear and electron magnetic resonance: review and prospects
• Experimental Demonstration of Quantum Tunneling in IBM Quantum Computer
• Energy protection arguments fail in the interaction picture
• Low-temperature environments for quantum computation and quantum simulation
• Quantum simulations of a particle in one-dimensional potentials using NMR
• Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Writing electronic ferromagnetic states in a high-temperature paramagnetic nuclear spin system
• Mitigating the information degradation in a massive Unruh-DeWitt theory
• Quantum Simulation of Simple Many-Body Dynamics
• Discrimination of unitary transformations in the Deutsch-Jozsa algorithm
• Experimental Virtual Quantum Broadcasting
• Quantum Phase Estimation Algorithm for Finding Polynomial Roots
• Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
• Spin-Boson Model to Demonstrate Quantum Tunneling in Biomolecules using IBM Quantum Computer
• Sampling and the complexity of nature
• Linear-optical generation of eigenstates of the two-site XY model
• Quantum Simulation of Molecular Collisions in the Time-Dependent Formulation
• Hamiltonian Engineering in Quantum Spin Networks
• Velocity effects slightly mitigating the quantumness degradation of an Unruh-DeWitt detector