Compressed Simulation of evolutions of the XY-model

Abstract

We extend the notion of compressed quantum simulation to the XY-model. We derive a quantum circuit processing log(n) qubits which simulates the 1D XY-model describing n qubits. In particular, we demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which witnesses a quantum phase transition can be observed. Furthermore, we analyze several dynamical processes, like quantum quenching and finite time evolution and derive the corresponding compressed quantum circuit.

20 pages, 11 figures, corrected minor typos

References in corpus (5)

• Universal digital quantum simulation with trapped ions
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Matchgates and classical simulation of quantum circuits
• Compressed quantum simulation of the Ising model

Cited by in corpus (11)

• Efficient classical simulation of matchgate circuits with generalized inputs and measurements
• Compressed quantum computation using the IBM Quantum Experience
• Compressed quantum metrology for the Ising Hamiltonian
• Compression for quantum population coding
• Compressed simulation of thermal and excited states of the 1-D XY-model
• Quantum Compression of Tensor Network States
• Kibble-Zurek mechanism from different angles: The transverse XY model and subleading scalings
• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Compressed variational quantum eigensolver for the Fermi-Hubbard model
• The computational power of matchgates and the XY interaction on arbitrary graphs
• The Computational Power of Non-interacting Particles