Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

Muraleedharan, Gopikrishnan; Miyake, Akimasa; Deutsch, Ivan

doi:10.1088/1367-2630/ab0610

Cited by 35 publications

(23 citation statements)

References 92 publications

(152 reference statements)

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“…(54) and integrating over time, we obtain Eq. (53). ▪ We now analyze the cost of estimating hAðtÞi using quantum algorithms, although we note that Proposition 6 applies equally well to classical simulation algorithms.…”

Section: Simulation Of Local Observablesmentioning

confidence: 99%

“…The boson sampling problem was proposed by Aaronson and Arkhipov [25] as a potential candidate for the demonstration of quantum supremacy. While simulating the dynamics of bosons hopping on a lattice is generally a difficult task for classical computers, early-time evolutions where the bosons do not have enough time to hop too far from their initial positions can be simulated efficiently [10,26,53]. In particular, Ref.…”

Section: E Efficient Early-time Classical Boson Samplingmentioning

confidence: 99%

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Hierarchy of Linear Light Cones with Long-Range Interactions

et al. 2020

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In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute-given a many-body state jψi, O x ðtÞO y jψi ≈ O y O x ðtÞjψi with arbitrarily small errors-so long as jx − yj ≳ vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy VðrÞ ∝ 1=r α. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state jψi when α > 3 (Lieb-Robinson light cone); for a typical state jψi chosen uniformly at random from the Hilbert space when α > 5 2 (Frobenius light cone); and for every state of a noninteracting system when α > 2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones-and their tightness-also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as manybody quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

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Section: Simulation Of Local Observablesmentioning

confidence: 99%

Section: E Efficient Early-time Classical Boson Samplingmentioning

confidence: 99%

Hierarchy of Linear Light Cones with Long-Range Interactions

et al. 2020

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“…Sub-wavelength optical tweezers will allow state-preserving transfer into an optical lattice potential, which provides a highly coherent Hubbard-type system typically accessed through evaporative cooling. This new approach would prove advantageous for studies of many-body phenomena at low energy scalessuch as magnetism -for which tailored state preparation can be useful [55,56], for scaling of protocols to measure and quantify entanglement [9,17,57], as well as for novel directions like atom-based studies of sampling problems [58,59].…”

mentioning

confidence: 99%

Microscopic Control and Detection of Ultracold Strontium in Optical-Tweezer Arrays

2018

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We demonstrate a set of tools for microscopic control of neutral strontium atoms. We report single-atom loading into an array of sub-wavelength scale optical tweezers, light-shift free control of a narrow-linewidth optical transition, three-dimensional ground-state cooling, and high-fidelity nondestructive imaging of single atoms on sub-wavelength spatial scales. Extending the microscopic control currently achievable in single-valence-electron atoms to species with more complex internal structure, like strontium, unlocks a wealth of opportunities in quantum information science, including tweezer-based metrology, new quantum computing architectures, and new paths to low-entropy many-body physics.

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“…These efforts have largely focused on finding approximate sampling problems that are robust against certain experimental errors [20,21]; tailoring quantum sampling problems to existing implementations [22,24,27]; verifying such devices with efficient quantum resources [23,24,28] or exponential classical ones [22,[29][30][31]. Some works have also brought a many-body physics perspective to previously existing quantum advantage proposals, through the study of the connections between transitions in sampling complexity and dynamical phase transitions [32][33][34]. All these works, however, mostly rely on "unphysical" sampling problems that were discovered for the sole purpose of demonstrating a quantum advantage, and further connections with questions of central interest in many-body physics are yet to be explored.…”

Section: Introductionmentioning

confidence: 99%

Quantum advantage from energy measurements of many-body quantum systems

Novo

Bermejo-Vega

García−Patrón

2021

Quantum

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The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage demonstrations can be achieved for more physically-motivated sampling problems, related to measurements of physical observables. We focus on the problem of sampling the outcomes of an energy measurement, performed on a simple-to-prepare product quantum state – a problem we refer to as energy sampling. For different regimes of measurement resolution and measurement errors, we provide complexity theoretic arguments showing that the existence of efficient classical algorithms for energy sampling is unlikely. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions on a 2D lattice that can be efficiently measured with high resolution using a quantum circuit of commuting gates (IQP circuit), whereas an efficient classical simulation of this process should be impossible. In this high resolution regime, which can only be achieved for Hamiltonians that can be exponentially fast-forwarded, it is possible to use current theoretical tools tying quantum advantage statements to a polynomial-hierarchy collapse whereas for lower resolution measurements such arguments fail. Nevertheless, we show that efficient classical algorithms for low-resolution energy sampling can still be ruled out if we assume that quantum computers are strictly more powerful than classical ones. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity.

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Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

Cited by 35 publications

References 92 publications

Hierarchy of Linear Light Cones with Long-Range Interactions

Hierarchy of Linear Light Cones with Long-Range Interactions

Microscopic Control and Detection of Ultracold Strontium in Optical-Tweezer Arrays

Quantum advantage from energy measurements of many-body quantum systems

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