Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer

Alderete, C. Huerta; Singh, Shivani; Nguyen, Nhung H.; Zhu, Daiwei; Balu, Radhakrishnan; Monroe, Christopher; Chandrashekar, C. M.; Linke, Norbert

doi:10.1038/s41467-020-17519-4

Cited by 46 publications

(26 citation statements)

References 66 publications

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“…These were first considered by Feynman in studying possible discretisations for the Dirac path integral [1,2]. They were later introduced in a systematic manner by Aharonov et al [3] and Meyers [4], and they have been realized experimentally in a number of ways [5], which include cold atoms [6], photonic systems [7,8] and trapped ions [9,10]. With the recent development of Noisy Intermediate Scale Quantum (NISQ) devices, it is now possible to implement short-depth quantum circuits with several qubits such as QWs [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Dirac Spatial Search with Electric Fields

Zylberman

2021

Entropy

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Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of N points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as N for small values of N and tends asymptotically to a constant for larger Ns, thus offering a speed-up over conventional methods.

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Section: Introductionmentioning

confidence: 99%

Dirac Spatial Search with Electric Fields

Zylberman

2021

Entropy

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“…Among several quantum algorithms implemented on noisy intermediate-scale quantum (NISQ) devices [1][2][3][4][5][6][7][8][9][10][11][12], the quantum approximate optimization algorithm (QAOA) offers an opportunity to approximately solve combinatorial optimization problems such as MaxCut, Max Independent Set, and Max k-cover [13][14][15][16][17][18][19][20][21][22]. QAOA tunes a set of classical parameters to optimize the cost function expectation value for a quantum state prepared by well-defined sequence of operators acting on a known initial state.…”

Section: Introductionmentioning

confidence: 99%

Multi-angle Quantum Approximate Optimization Algorithm

Herrman¹,

Lotshaw²,

Ostrowski³

et al. 2021

Preprint

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The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we introduce a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.

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“…8,9 They are also important for quantum simulation, 10 and they have been realized experimentally in a number of ways, 7 which include cold atoms, 11 photonic systems, 12,13 and trapped ions. 14 There is now growing literature on the geometrical aspects of QWs. QWs can indeed be used to simulate Dirac fermions interacting with arbitrary Yang-Mills gauge fields 15,16 and arbitrary relativistic gravitational fields.…”

Section: Introductionmentioning

confidence: 99%

Quantum walks simulating non-commutative geometry in the Landau problem

Debbasch

2021

Journal of Mathematical Physics

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Non-Commutative Geometry (NCG) is considered in the context of a charged particle moving in a uniform magnetic field. The classical and quantum mechanical treatments are revisited, and a new marker of NCG is introduced. This marker is then used to investigate NCG in magnetic Quantum Walks (QWs). It is proven that these walks exhibit NCG at and near the continuum limit. For the purely discrete regime, two illustrative walks of different complexities are studied in full detail. The most complex walk does exhibit NCG, but the simplest, most degenerate one does not. Thus, NCG can be simulated by QWs, not only in the continuum limit but also in the purely discrete regime.

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Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer

Cited by 46 publications

References 66 publications

Dirac Spatial Search with Electric Fields

Dirac Spatial Search with Electric Fields

Multi-angle Quantum Approximate Optimization Algorithm

Quantum walks simulating non-commutative geometry in the Landau problem

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