Quantum supremacy and quantum phase transitions

Thanasilp, Supanut; Tangpanitanon, Jirawat; Lemonde, Marc-Antoine; Dangniam, Ninnat; Angelakis, Dimitris G.

doi:10.1103/physrevb.103.165132

Cited by 4 publications

(10 citation statements)

References 66 publications

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“…(i) multiplicative approximation of the output distribution is #P hard on average and (ii) anti-concentration of the output distribution. Ref [8] shows that indeed COE satisfies both conditions. The #P hardness is proven in the worst case scenario.…”

Section: Computational Complexity Of Sampling From Coe Dynamicsmentioning

confidence: 93%

“…Based on the sampling results, we further analyse the multipoint correlation functions [11,23,[36][37][38][39] of the manybody system. In a Floquet system, multi-particle interactions emerge, which marks the breakdown of the Magnus expansion [7,8,40] and leads to enhanced highorder correlations. We exploit the multi-point density correlations to probe the many-body nature of the system.…”

Section: Entanglement Entropymentioning

confidence: 99%

“…Periodically driven systems can exhibit exotic quantum phases of matter, such as discrete time crystals [1,2] and many-body scars [3,4]. In the driven ergotic phases, emergent long-range interactions lead to an infinite temperature thermalization [5][6][7][8] and a chaotic spreading throughout the entire Hilbert space. Rapid increasing entanglement during the evolution hinders efficient classical simulations of these dynamics with the currently known algorithms [9,10], and in turn impedes extracting multi-point correlations to characterize the quantum many-body system [11].…”

mentioning

confidence: 99%

“…Notably, the computational task of sampling from a periodically driven thermalized many-body system has been proposed to demonstrate practical quantum computational advantage backed by complexity-theoretic foundations [8,18], which also provides identifications of dynamical phases in the driven system through multi-point density correlations simultaneously. For low-frequency driving and low disorders, the system will thermalize and the associated temperature becomes infinite.…”

mentioning

confidence: 99%

“…For low-frequency driving and low disorders, the system will thermalize and the associated temperature becomes infinite. In this limit, the Floquet operator U F is intimately related to a random matrix drawn from the circular orthogonal ensemble (COE), where sampling the probability distribution of the final state is classically intractable [8,18]. In contrast, classical simulation is feasible in the manybody-localized (MBL) phase due to an area-law scaling of entanglement.…”

mentioning

confidence: 99%

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Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System

Zheng¹,

Zhang²,

Shen³

et al. 2022

Preprint

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Nonequilibrium dynamics of many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. It is proposed to be classically intractable to sample driven thermalized many-body states of Bose-Hubbard systems, and further extract multi-point correlations for characterizing quantum phases. Here, leveraging dedicated precise manipulations and number-resolved detection through a quantum gas microscope, we implement and sample a 32-site driven Hubbard chain in the thermalized phase. Multi-point correlations of up to 14th-order extracted from experimental samples offer clear distinctions between the thermalized and many-body-localized phases. In terms of estimated computational powers, the quantum simulator is comparable to the fastest supercomputer with currently known best algorithms. Our work paves the way towards practical quantum advantage in simulating Floquet dynamics of many-body systems.

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Section: Computational Complexity Of Sampling From Coe Dynamicsmentioning

confidence: 93%

Section: Entanglement Entropymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System

Zheng¹,

Zhang²,

Shen³

et al. 2022

Preprint

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Signatures of a sampling quantum advantage in driven quantum many-body systems

Tangpanitanon

Thanasilp

Lemonde

et al. 2023

Quantum Sci. Technol.

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A crucial milestone in the ﬁeld of quantum simulation and computation is to demonstrate that a quantum device can perform a computation task that is classically intractable. A key question is to identify setups that can achieve such goal within current technologies. In this work, we provide formal evidence that sampling bit-strings from a periodic evolution of a unitary drawn from the Circular Orthogonal Ensemble (COE) cannot be eﬃciently simulated with classical computers. As the statistical properties of COE coincide with a large class of driven analog quantum systems thanks to the Floquet eigenstate thermalization hypothesis, our results indicate the possibility that those driven systems could constitute practical candidates for a sampling quantum advantage. To further support this, we give numerical examples of driven disordered Ising chains and 1D driven Bose-Hubbard model.

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Detecting quantum phase transition via magic resource in the XY spin model

Luo

2022

Phys. Rev. A

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Quantum supremacy and quantum phase transitions

Cited by 4 publications

References 66 publications

Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System

Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System

Signatures of a sampling quantum advantage in driven quantum many-body systems

Detecting quantum phase transition via magic resource in the XY spin model

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