Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays

Ebadi, Sepehr; Keesling, Alexander; Cain, Madelyn; Wang, Tout T.; Levine, Harry; Bluvstein, Dolev; Semeghini, Giulia; Omran, Ahmed; Liu, Jinguo; Samajdar, Rhine; Luo, Xiu-Zhe; Nash, Beatrice; Gao, Xun; Barak, Boaz; Farhi, Edward; Sachdev, Subir; Gemelke, Nathan; Zhou, Leo; Choi, Soonwon; Pichler, Hannes; Wang, Shengtao; Greiner, Markus; Vuletic, Vladan; Lukin, Mikhail D.

doi:10.48550/arxiv.2202.09372

Cited by 10 publications

(13 citation statements)

References 68 publications

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“…The second significant task for future is to accumulate benchmark results by both classical and quantum simulation, including higher-dimensional cases, shortranged interacting cases, and long-ranged interacting cases. Several programmable quantum simulators, such as superconducting qubits [57] and Rydberg atoms [58], have recently achieved a few hundred qubits with highcontrollability and two-dimensionality, and they will be available for both the local compilation and the quantum execution of the compressed time evolution. For instance, as an immediate task to be tackled, it may be possible to observe long-time dynamics beyond the current coher-ence time on such compiled quantum simulators by the classical local compilation for tens of qubits.…”

Section: Discussionmentioning

confidence: 99%

Local variational quantum compilation of a large-scale Hamiltonian dynamics

Mizuta¹,

Nakagawa²,

Mitarai³

et al. 2022

Preprint

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Implementing time evolution operators on quantum circuits is important for quantum simulation. However, the standard way, Trotterization, requires a huge numbers of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows to accurately and efficiently compile a time evolution operators on a large-scale quantum system by the optimization with smaller-size quantum systems. LVQC utilizes a subsystem cost function, which approximates the fidelity of the whole circuit, defined for each subsystem as large as approximate causal cones brought by the Lieb-Robinson (LR) bound. We rigorously derive its scaling property with respect to the subsystem size, and show that the optimization conducted on the subsystem size leads to the compilation of whole-system time evolution operators. As a result, LVQC runs with limited-size quantum computers or classical simulators that can handle such smaller quantum systems. For instance, finite-ranged and short-ranged interacting L-size systems can be compiled with O(L 0 )-or O(log L)-size quantum systems depending on observables of interest. Furthermore, since this formalism relies only on the LR bound, it can efficiently construct time evolution operators of various systems in generic dimension involving finite-, short-, and long-ranged interactions. We also numerically demonstrate the LVQC algorithm for one-dimensional systems. Employing classical simulation by time-evolving block decimation, we succeed in compressing the depth of a time evolution operators up to 40 qubits by the compilation for 20 qubits. LVQC not only provides classical protocols for designing large-scale quantum circuits, but also will shed light on applications of intermediate-scale quantum devices in implementing algorithms in larger-scale quantum devices.

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Section: Discussionmentioning

confidence: 99%

Local variational quantum compilation of a large-scale Hamiltonian dynamics

Mizuta¹,

Nakagawa²,

Mitarai³

et al. 2022

Preprint

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“…σx,z and n = (σ z + 1)/2 are the operators for Pauli x, z and Rydberg excitation number. This Hamiltonian for quantum Ising spins [20,21] has been considered for maximum independent set problems (MIS) of G [31][32][33][34].…”

Section: Quantum Wires For Platonic Graphsmentioning

confidence: 99%

“…In reported experiments [29,30], the number of Rydberg atoms starts to exceed a few hundred, boosting the expectation towards computational advantages of Rydberg-atom systems in solving combinatorial optimization problems [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of Ising spins on Platonic graphs

Byun¹,

Kim²,

Ahn³

2022

Preprint

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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.

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“…Concrete examples include modifying the objective functions [35], applying the iterative training strategy [36,37] using adaptive mixing operators [34,[38][39][40]. Despite the remarkable achievements, little progress has been made in overcoming the scalability issue of QAOAs, whereas the ultimate goal of the most advanced QAOA is solving a problem with hundreds of vertices [41]. The main challenges come from the fact that manipulating a graph with n-nodes requires O(n) qubits but the most advanced quantum machines nowadays can only provide a very limited number of qubits with n ≈ 100.…”

Section: Introductionmentioning

confidence: 99%