Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

Abstract

We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the Quantum Logic Array (QLA) architecture. Our results show that due to the exponential scaling of the computational time with the desired precision of the energy, significant amount of error correciton is required to implement the TIM problem. Comparison of our results to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.

19 pages, 8 figures

References in corpus (20)

• Simulated Quantum Computation of Molecular Energies
• Quantum Algorithms Revisited
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Quantum repeaters based on entanglement purification
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• A microfabricated surface-electrode ion trap for scalable quantum information processing
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Ising models of quantum frustration
• Efficient Simulation of Quantum Systems by Quantum Computers
• Overhead and noise threshold of fault-tolerant quantum error correction
• Fast Quantum Modular Exponentiation
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Quantum information processing with trapped ions
• Efficient factorization with a single pure qubit and $logN$ mixed qubits
• Fault-Tolerant Quantum Computation with Local Gates
• Hyperfine Coherence in the Presence of Spontaneous Photon Scattering
• Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
• Space, time, parallelism and noise requirements for reliable quantum computing
• On Ising and dimer models in two and three dimensions
• Quantum Ising model in a transverse random field: A density-matrix renormalization group analysis

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