Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code

Abstract

We estimate the resource requirements for the quantum simulation of the ground state energy of the one dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault tolerant quantum computer. The surface code approach has one of the highest known tolerable error rates (1%) which makes it currently one of the most practical quantum computing schemes. Compared to results of the same model using the concatenated Steane code, the current results indicate that the simulation time is comparable but the number of physical qubits for the surface code is 2-3 orders of magnitude larger than that of the concatenation code. Considering that the error threshold requirements of the surface code is four orders of magnitude higher than the concatenation code, building a quantum computer with a surface code implementation appears more promising given current physical hardware capabilities.

11 pages,14 figures and 2 tables

References in corpus (46)

• Surface codes: Towards practical large-scale quantum computation
• Good Quantum Error-Correcting Codes Exist
• Topological quantum memory
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Simulated Quantum Computation of Molecular Energies
• Multiple Particle Interference and Quantum Error Correction
• Quantum Computing with Very Noisy Devices
• Fault-tolerant quantum computation with high threshold in two dimensions
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• High threshold universal quantum computation on the surface code
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Efficient Simulation of Quantum Systems by Quantum Computers
• Simulating chemistry using quantum computers
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Resilient Quantum Computation: Error Models and Thresholds
• Experimental demonstration of topological error correction
• Layered architecture for quantum computing
• Towards practical classical processing for the surface code
• Topological Computation without Braiding
• Fast simulation of stabilizer circuits using a graph state representation
• Strong Resilience of Topological Codes to Depolarization
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Improved magic states distillation for quantum universality
• Using Quantum Computers for Quantum Simulation
• Quantum computation with Turaev-Viro codes
• Distributed Quantum Computation Architecture Using Semiconductor Nanophotonics
• Architectural design for a topological cluster state quantum computer
• Fault tolerant architectures for superconducting qubits
• Two-dimensional cavity grid for scalable quantum computation with superconducting circuits
• Clifford Gates by Code Deformation
• The Photonic Module: an on-demand resource for photonic entanglement
• A scalable, high-speed measurement-based quantum computer using trapped ions
• 2-D color code quantum computation
• A bridge to lower overhead quantum computation
• Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
• Introduction to Quantum Algorithms for Physics and Chemistry
• Towards practical classical processing for the surface code: timing analysis
• Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices
• Quantum Circuits for Measuring Levin-Wen Operators
• Time-optimal quantum computation
• Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

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