Simulation of many-qubit quantum computation with matrix product states

Abstract

Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete problem. Errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. The property of finding the right solution for an instance and the expected value of the energy are found to be remarkably robust against these errors. As a symbolic example, we simulate the algorithm solving a 100-qubit hard instance, that is, finding the correct product state out of ~ 10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow growth of the average minimum time to solve hard instances with highly-truncated simulations of adiabatic quantum evolution.

5 pages, 4 figures, final version

References in corpus (10)

• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Efficient simulation of one-dimensional quantum many-body systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• DMRG and periodic boundary conditions: a quantum information perspective
• Renormalization group transformations on quantum states
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Adiabatic Quantum Computing for Random Satisfiability Problems
• Universality of Entanglement and Quantum Computation Complexity
• Adiabatic quantum computation and quantum phase transitions

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