Hamiltonian quantum simulation with bounded-strength controls

Abstract

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a suitable modification of an "Eulerian decoupling cycle," that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system, while suppressing unwanted decoherence to the leading order. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

24 pages, 5 color figures

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Cited by in corpus (11)

• Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems
• A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
• Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
• Qudit Dynamical Decoupling on a Superconducting Quantum Processor
• Quantum and classical resources for unitary design of open-system evolutions
• Dynamical enhancement of symmetries in many-body systems
• Realization and detection of Kitaev quantum spin liquid with Rydberg atoms
• Robust symmetry-protected metrology with the Haldane phase
• Improved bounded-strength decoupling schemes for local Hamiltonians
• Engineering Precise and Robust Effective Hamiltonians
• Error suppression in Hamiltonian based quantum computation using energy penalties