Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of Quantum State Transfer

Abstract

We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The algorithm product-decomposes $U$ in a chosen operator basis by identifying a certain symmetry of $U$ that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the $n$-qubit Quantum State Transfer unitary by Di Franco et. al. (Phys. Rev. Lett. 101, 230502 (2008)) that transports quantum information from one end of a spin chain to the other; and then implement it in Nuclear Magnetic Resonance to demonstrate that the decomposition is experimentally viable and well-scaled. We furthur experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Published version

References in corpus (8)

• Spin Chains as Perfect Quantum State Mirrors
• Perfect state transfer on a spin-chain without state initialization
• Liquid State NMR as a Test-bed for Developing Quantum Control Methods
• Simulations of Information Transport in Spin Chains
• Robustness of spin-coupling distributions for perfect quantum state transfer
• Experimental Test of Quantum No-Hiding Theorem
• Theoretical analysis of perfect quantum state transfer with superconducting qubits
• Iterative quantum state transfer along a chain of nuclear spin qubits

Cited by in corpus (14)

• Optimized dynamical control of state transfer through noisy spin chains
• Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks
• Quantum Interpolation for High Resolution Sensing
• Singlet state creation and Universal quantum computation in NMR using Genetic Algorithm
• Simulation of mirror inversion of quantum states in an XY spin chain using NMR
• Perfect quantum transport in arbitrary spin networks
• Ballistic quantum state transfer in spin chains: general theory for quasi-free models and arbitrary initial states
• Mixed-state quantum transport in correlated spin networks
• Robustness of spin-chain state-transfer schemes
• Electron-to-nuclear spectral mapping via "Galton board" dynamic nuclear polarization
• Emulating quantum state transfer through a spin-1 chain on a 1D lattice of superconducting qutrits
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Continuously tracked, stable, large excursion trajectories of dipolar coupled nuclear spins
• "Galton board" nuclear hyperpolarization