Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

Abstract

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that aren't universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner et. al. [Phys. Rev. A, 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

References in corpus (28)

• Time Optimal Control in Spin Systems
• Optimal Quantum Circuits for General Two-Qubit Gates
• Simulating Physical Phenomena by Quantum Networks
• Minimal Universal Two-qubit Quantum Circuits
• A practical scheme for quantum computation with any two-qubit entangling gate
• A universal quantum circuit for two-qubit transformations with three CNOT gates
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Entanglement capabilities of non-local Hamiltonians
• Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
• Universal simulation of Hamiltonian dynamics for qudits
• Optimal simulation of two-qubit Hamiltonians using general local operations
• Characterization of non-local gates
• Interaction cost of non-local gates
• Exact two-qubit universal quantum circuit
• Effective three-body interactions in triangular optical lattices
• Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates
• An Arbitrary Two-qubit Computation In 23 Elementary Gates
• Simulating Hamiltonians in Quantum Networks: Efficient Schemes and Complexity Bounds
• Canonical Decompositions of n-qubit Quantum Computations and Concurrence
• Three and Four-Body Interactions in Spin-Based Quantum Computers
• Lower bounds on the complexity of simulating quantum gates
• Catalysis in non--local quantum operations
• Fungible dynamics: there are only two types of entangling multiple-qubit interactions
• Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer
• Gate simulation and lower bounds on the simulation time
• Optimal simulation of nonlocal Hamiltonians using local operations and classical communication
• On the practicality of time-optimal two-qubit Hamiltonian simulation

Cited by in corpus (13)

• Quantum Simulation
• A fault-tolerant one-way quantum computer
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Symmetry criteria for quantum simulability of effective interactions
• Quantum simulation of interacting high-dimensional systems: the influence of noise
• Equivalence of Decoupling Schemes and Orthogonal Arrays
• Quantum simulations under translational symmetry
• Towards Large-Scale Quantum Computation
• Toward a more economical cluster state quantum computation
• Globally controlled universal quantum computation with arbitrary subsystem dimension
• The Synthetic Hilbert Space of Laser-Driven Free-Electrons
• An upper bound on the time required to implement unitary operations
• Stroboscopically Robust Gates For Capacitively Coupled Singlet-Triplet Qubits