Number Partitioning With Grover’s Algorithm in Central Spin Systems

Anikeeva, Galit; Marković, Ognjen; Borish, Victoria; Hines, Jacob; Rajagopal, Shankari; Cooper, Eric S.; Periwal, Avikar; Davis, Emily Jane; Schleier-Smith, Monika

doi:10.1103/prxquantum.2.020319

Cited by 17 publications

(4 citation statements)

References 74 publications

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“…Yet many objectives in quantum simulation and computation demand more versatile control of the graph of interactions [4,5,10,11,35,36]. Engineering a wider range of nonlocal coupling graphs opens prospects for simulating exotic frustrated magnets supporting spinglass phases [4,5] and topologically ordered states [35], implementing combinatorial optimization algorithms [6,7,37,38], and probing toy models of quantum gravity [10,11,39]. These goals have motivated proposals for programming the distance-dependence of spin-exchange interactions in arrays of atoms or ions by tailoring the frequency spectrum of a drive field [10,35,36], which couples the spins to a single mode of light or motion.…”

mentioning

confidence: 99%

Programmable interactions and emergent geometry in an array of atom clouds

Periwal

Cooper

Wienand

et al. 2021

Nature

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121

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Interactions govern the flow of information and the formation of correlations in quantum systems, dictating the phases of matter found in nature and the forms of entanglement generated in the laboratory. Typical interactions decay with distance and thus produce a network of connectivity governed by geometry, e.g., by the crystalline structure of a material or the trapping sites of atoms in a quantum simulator [1,2]. However, many envisioned applications in quantum simulation and computation require richer coupling graphs including nonlocal interactions, which notably feature in mappings of hard optimization problems onto frustrated spin systems [3][4][5][6][7] and in models of information scrambling in black holes [8][9][10][11]. Here, we report on the realization of programmable nonlocal interactions in an array of atomic ensembles within an optical cavity, where photons carry information between distant atomic spins [12][13][14][15][16][17][18][19]. By programming the distance-dependence of interactions, we access effective geometries where the dimensionality, topology, and metric are entirely distinct from the physical arrangement of atoms. As examples, we engineer an antiferromagnetic triangular ladder, a Möbius strip with sign-changing interactions, and a treelike geometry inspired by concepts of quantum gravity [10,[20][21][22]. The tree graph constitutes a toy model of holographic duality [21,22], where the quantum system may be viewed as lying on the boundary of a higherdimensional geometry that emerges from measured spin correlations [23]. Our work opens broader prospects for simulating frustrated magnets and topological phases, investigating quantum optimization algorithms, and engineering new entangled resource states for sensing and computation.

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mentioning

confidence: 99%

Programmable interactions and emergent geometry in an array of atom clouds

Periwal

Cooper

Wienand

et al. 2021

Nature

Self Cite

121

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“…However, such methods use graphs and coloring theory which are themselves NP-hard problems, potentially increasing the time in the classical step of the simulation [7]. Fortunately, quantum computers can also aid with a significant speedup on NP-hard problems using, for example, Grover's algorithm [36].…”

Section: Discussionmentioning

confidence: 99%

Revisiting semiconductor bulk hamiltonians using quantum computers

Pimenta

Bezerra

2023

Phys. Scr.

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With the advent of near-term quantum computers, it is now possible to simulate solid-state properties using quantum algorithms. By an adequate description of the system’s Hamiltonian, variational methods enable to fetch of the band structure and other fundamental properties as transition probabilities. Here, we describe semiconductor structures of the III-V family using k$\cdot$p Hamiltonians and obtain their band structures using a state vector solver, a probabilistic simulator, and a real noisy-device simulator. The resulting band structures are in good agreement with those obtained by direct diagonalization of the Hamiltonian. The simulation times depend on the optimizer, circuit depth, and simulator used. Finally, with the optimized eigenstates, we convey the inter-band absorption probability, demonstrating the possibility of analyzing the fundamental properties of crystalline systems using quantum computers.

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“…For example, local Rydberg dressing beams could be used to mark a subset of sites in the lattice, such that interactions between atoms on these marked sites shifts the desired multi-particle state. Such interactions could also natively implement search oracles that effectively run a subroutine that checks the verifier to NP-complete problems of interest while maintaining a polynomial quantum speedup [76]. In the context of quantum simulation, this combination of tunable interactions and itinerance could also enable the study of a broad class of extended Hubbard models which are thought to capture a range of exotic behaviors including supersolidity, and unconventional superconductivity involving charge fluctuations [67,68].…”

Section: Prospects For Multi-particle Quantum Walks and Genuine Quant...mentioning

confidence: 99%

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice

Young¹,

Eckner²,

Schine³

et al. 2022

Preprint

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Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. Here, we do this by combining the fast, programmable control provided by optical tweezer arrays with the scalable, homogeneous environment of an optical lattice. Using this new combination of tools we study continuous-time quantum walks of single atoms on a 2D square lattice, and perform proofof-principle demonstrations of spatial search using these walks. When scaled to more particles, the capabilities demonstrated here can be extended to study a variety of problems in quantum information science and quantum simulation, including the deterministic assembly of ground and excited states in Hubbard models with tunable interactions, and performing versions of spatial search in a larger graph with increased connectivity, where search by quantum walk can be more effective.

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Number Partitioning With Grover’s Algorithm in Central Spin Systems

Cited by 17 publications

References 74 publications

Programmable interactions and emergent geometry in an array of atom clouds

Programmable interactions and emergent geometry in an array of atom clouds

Revisiting semiconductor bulk hamiltonians using quantum computers

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice

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