arXiv:1603.08554 · Science Advances

Stabilizers as a design tool for new forms of the Lechner-Hauke-Zoller annealer

Andrea Rocchetto, Simon C. Benjamin, Ying Li

Published Oct 7, 2016• 47 citations

Abstract

systems (that is, qubits rather than qutrits); moreover, the interactions are very simple. We make a preliminary assessment of the impact of these design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.

DOI: 10.1126/sciadv.1601246

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arXiv:1603.08554 · Science Advances

Stabilizers as a design tool for new forms of the Lechner-Hauke-Zoller annealer

Andrea Rocchetto, Simon C. Benjamin, Ying Li

Published Oct 7, 2016• 47 citations

arXiv HTML PDF

Abstract

DOI: 10.1126/sciadv.1601246

Related papers

Performance enhancement of quantum annealing under the Lechner-Hauke-Zoller scheme by non-linear driving of the constraint term

友紀須佐, Yuki Susa, 秀稔西森 +1 more

Mar 1, 20200 citations

Simulations and Analysis of Adiabatic Quantum Annealing

Yani Shen, Tommy Wallin

This project aimed to investigate some properties of a quantum annealer by simulatingit on a classical computer. We chose the problem Hamiltonian on the form of theIsing model with interaction energies between all qubits.The results of our investigation showed at what part of the quantum annealing theminimum energy gap typically occurs for randomly generated Hamiltonians. We sawhow the quantum annealing process should proceed in order to achieve a higher probabilityof obtaining the correct answer. Additionally, we noted that the annealing timeincreases with qubit count. Interesting phenomenon as “self-rescue” and wave-like convergencearose during the investigation. We also presented an algorithm for solving thegame Minesweeper in this paper.The results in this project can be used to find potential properties of larger systemsand also as a base for possible future extensions.This project aimed to investigate some properties of a quantum annealer by simulatingit on a classical computer. We chose the problem Hamiltonian on the form of theIsing model with interaction energies between all qubits.The results of our investigation showed at what part of the quantum annealing theminimum energy gap typically occurs for randomly generated Hamiltonians. We sawhow the quantum annealing process should proceed in order to achieve a higher probabilityof obtaining the correct answer. Additionally, we noted that the annealing timeincreases with qubit count. Interesting phenomenon as “self-rescue” and wave-like convergencearose during the investigation. We also presented an algorithm for solving thegame Minesweeper in this paper.The results in this project can be used to find potential properties of larger systemsand also as a base for possible future extensions.

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Stabiliser sets and physical ancillas for the Lechner-Hauke-Zoller Annealer

Andrea Rocchetto, Simon C. Benjamin, Ying Li

In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin- $\frac{1}{2}$ particles with `all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. Here we provide a stabiliser-based formulation of this approach, which permits some generalisation to the parity constraints proposed by LHZ. One variant we obtain may simplify the physical realisation since the required ancillas are only spin- $\frac{1}{2}$ systems (i.e.~qubits, rather than qutrits) and moreover the interactions {are} very simple. We make a preliminary assessment of the impact of different design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of $N$ spin-$\frac{1}{2}$ particles with `all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. Here we provide a stabiliser-based formulation of this approach, which permits some generalisation to the parity constraints proposed by LHZ. One variant we obtain may simplify the physical realisation since the required ancillas are only spin-$\frac{1}{2}$ systems (i.e.~qubits, rather than qutrits) and moreover the interactions {are} very simple. We make a preliminary assessment of the impact of different design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.

Mar 28, 20163 citations

Efficient Classical Simulation of Quantum Circuits beyond the Stabilizer Formalism

Patrick Rall, James E. Troupe

Bulletin of the American Physical SocietyMar 7, 20180 citations

In a recent paper Lechner, Hauke and Zoller (LHZ) described a means to translate a Hamiltonian of

N

spin-

\frac{1}{2}

particles with `all-to-all' interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. Here we provide a stabiliser-based formulation of this approach, which permits some generalisation to the parity constraints proposed by LHZ. One variant we obtain may simplify the physical realisation since the required ancillas are only spin-

\frac{1}{2}

systems (i.e.~qubits, rather than qutrits) and moreover the interactions {are} very simple. We make a preliminary assessment of the impact of different design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process.