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arXiv:2009.05310 · PRX Quantum

Quantum Ising Hamiltonian Programming in Trio, Quartet, and Sextet Qubit Systems

Minhyuk Kim, Yunheung Song, Jaewan Kim, Jaewook Ahn

Published Dec 18, 2020• 37 citations
arXivHTMLPDF

Abstract

Rydberg-atom quantum simulators are of keen interest because of their possibilities towards highdimensional qubit architectures.Here we report continuous tuning of quantum Ising Hamiltonians of Rydberg atoms in three-dimensional arrangements.Various connected graphs of Rydberg atoms constructed with vertices and edges respectively representing atoms and Rydberg-blockaded atom pairs, and their eigenenergies are probed along with their geometric intermediates during structural transformations.Conformation spectra of star, complete, cyclic, and diamond graphs are probed for four interacting atoms and antiprism structures for six atoms.The energy level shifts and merges of the tested structural transformations are clearly observed with Fourier-transform spectroscopy, in good agreement with the model few-body quantum Ising Hamiltonian.This result demonstrates the possibility of continuous geometry tuning and thus programming of many-body spin-Hamiltonian systems.

DOI
10.1103/prxquantum.1.020323

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Rydberg-atom quantum simulators are of keen interest because of their possibilities towards highdimensional qubit architectures.Here we report continuous tuning of quantum Ising Hamiltonians of Rydberg atoms in three-dimensional arrangements.Various connected graphs of Rydberg atoms constructed with vertices and edges respectively representing atoms and Rydberg-blockaded atom pairs, and their eigenenergies are probed along with their geometric intermediates during structural transformations.Conformation spectra of star, complete, cyclic, and diamond graphs are probed for four interacting atoms and antiprism structures for six atoms.The energy level shifts and merges of the tested structural transformations are clearly observed with Fourier-transform spectroscopy, in good agreement with the model few-body quantum Ising Hamiltonian.This result demonstrates the possibility of continuous geometry tuning and thus programming of many-body spin-Hamiltonian systems.
Significant efforts are being directed towards developing a quantum annealer capable of solving combinatorial optimization problems. The challenges are Hamiltonian programming and large-scale implementations. Here we report quantum annealing demonstration of Ising Hamiltonians programmed with up to N=22N=22N=22 spins mapped on various Cayley tree graphs. Experiments are performed with a Rydberg-atom quantum simulator, in which rubidium single atoms are arranged in three dimensional space in such a way that their Rydberg atoms and blockaded strong couplings respectively represent the nodes and edges of each graph. Three different Cayley-tree graphs of Z=3Z=3Z=3 neighbors and of up to S=4S=4S=4 shells are constructed, and their ground-state phases and N\'{e}el's order formations are probed. In good agreement with model calculations, the anti-ferromagnetic phase in regular Cayley trees and frustrated competing ground-states in a dual-center Cayley tree are directly observed. This demonstrates the possibilities of high-dimensional qubit connection programming in quantum simulators.
A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.
Quantum annealing aims at solving optimization problems efficiently by preparing the ground state of an Ising spin-Hamiltonian quantum mechanically.A prerequisite of building a quantum annealer is the implementation of programmable long-range two-, three-, or multispin Ising interactions.We discuss an architecture, where the required spin interactions are implemented via two-port or in general multiport quantum Ising wires connecting the spins of interest.This quantum annealing architecture of spins connected by Ising quantum wires can be realized by exploiting the three-dimensional (3D) character of atomic platforms, including atoms in optical lattices and Rydberg tweezer arrays.The realization only requires engineering on-site terms and two-body interactions between nearest neighboring qubits.The locally coupled spin model on a 3D cubic lattice is sufficient to effectively produce arbitrary all-to-all coupled Ising Hamiltonians.We illustrate the approach for few-spin devices solving Max-Cut and prime factorization problems, and discuss the potential scaling to large atom-based systems.
We present quantum simulation experiments of Ising-like spins on Platonic graphs, which are performed with two-dimensional arrays of Rydberg atoms and quantum-wire couplings. The quantum wires are used to couple otherwise uncoupled long-distance atoms, enabling topology-preserving transformtions of the three-dimensional graphs to the two-dimensional plane. We implement three Platonic graphs, tetrahedron, cube, and octahedron of Platonic solids, and successfully probe their ground many-body spin configurations before and after the quasi-adiabatic control of the system Hamiltonians from the paramagnetic phase to anti-ferromagnetic-like phases. Our small-scale quantum simulations of using less than 22 atoms are limited by experimental imperfections, which can be easily improved by the state-of-the-art Rydberg-atom technologies for more than 1000-atom scales. Our quantum-wire approach is expected to pave a new route towards large-scale quantum simulations.
Programmable quantum systems provide insights into many-body quantum phenomena and enable new methods for computation and metrology. The frontier challenge for these systems is scaling up in the number of quantum particles while retaining a high degree of quantum control. In recent years arrays of neutral atoms have emerged as a scalable and powerful platform for tackling these challenges, thanks to their large number of qubits, flexible geometry, and a well-established toolbox for preparation, detection, coherent control. At the forefront of quantum science and engineering, these systems have been used for quantum simulation of various spin models and have also demonstrated building blocks of quantum computation. In this thesis I will present advances in development of large two-dimensional atom arrays, where hundreds of individual atoms are trapped, rearranged, and initialized in various defect-free arrangements in one or two dimensions. Afterwards, interactions between atoms is controlled via coherent excitation to highly excited Rydberg states, resulting in strong long-range van der Waals forces. We utilize these interaction for quantum simulation of many-body spin Hamiltonians by demonstrating preparation of several exotic phases of matter, study phase transitions, and probe non-equilibrium dynamics. Further, we study the quantum speedup in solving a hard combinatorial optimization problem via efficiently mapping the problem onto the Rydberg atom array. We also utilize Rydberg interactions to demonstrate high-fidelity two-qubit gate operations in a reconfigurable atom array architecture. Lastly I will demonstrate recent technical improvements that have enabled larger system sizes, higher fidelity rydberg excitations, and local control of individual atoms, paving the way for novel approaches for studying quantum many-body phenomena.