Adiabatic Quantum Simulators

Abstract

In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.

9 pages, 1 figure

References in corpus (9)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Simulated Quantum Computation of Molecular Energies
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Towards Fault Tolerant Adiabatic Quantum Computation
• Non-perturbative k-body to two-body commuting conversion Hamiltonians and embedding problem instances into Ising spins
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
• Making Classical Ground State Spin Computing Fault-Tolerant

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• Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
• Work statistics across a quantum phase transition
• Ground State Spin Logic
• Hamiltonian gadgets with reduced resource requirements
• Breaking the quantum adiabatic speed limit by jumping along geodesics
• On The Power Of Coherently Controlled Quantum Adiabatic Evolutions
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• Accelerated quantum control in a three-level system by jumping along the geodesics
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• Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: application to the $XXZ$ model on the square lattice
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