The Computational Complexity of Linear Optics

Aaronson, Scott; Архипов, A. A.

doi:10.48550/arxiv.1011.3245

Cited by 75 publications

(219 citation statements)

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“…Verification of quantum processors become particularly challenging and relevant in the regimes of quantum advantage, where quantum devices outperform their classical counterparts [99,100]. As solving a "useful" computational task (such as factoring a large number) would neither be feasible with noisy intermediate-scale quantum computers nor necessary to demonstrate quantum superiority, one focuses on sampling problems [101][102][103], in this context. However, these approaches entail difficulties in demonstrating quantum superiority.…”

Section: Discussionmentioning

confidence: 99%

Theoretical and Experimental Perspectives of Quantum Verification

Carrasco,

Elben,

Kokail

et al. 2021

Preprint

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In this perspective we discuss verification of quantum devices in the context of specific examples, formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input Hamiltonian as design goal is compared with the parent Hamiltonian for the quantum states prepared on the device. The second example discusses crossdevice verification on the quantum level, i.e. by comparing quantum states prepared on different quantum devices. We focus in particular on protocols using randomized measurements, and we propose establishing a central data repository, where existing experimental devices and platforms can be compared. In our final example, we address verification of the output of a quantum device from a computer science perspective, addressing the question of how a user of a quantum processor can be certain about the correctness of its output, and propose minimal demonstrations on present day devices.

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Section: Discussionmentioning

confidence: 99%

Theoretical and Experimental Perspectives of Quantum Verification

Carrasco,

Elben,

Kokail

et al. 2021

Preprint

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“…with eigenvalue e iθ . Since, by assumption, |φ is a product state |φ (1) ⊗ |φ (2) |) , then |φ (l) must be an eigenvector of both W (l) 0,x and W (l) 1,x . This means that qubit i does not act (non-trivially) as a control qubit on qubit l, contradicting our assumption above.…”

Section: Main Proofsmentioning

confidence: 99%

“…The action of the circuit on this state is One method for disproving this conjecture (or rather, showing it to be very unlikely to be true) is to find a class of separable computations for which a 'quantum supremacy' result can be proved. Such a result would state that no classical simulation (to multiplicative [3] or additive [2,4]) error can exist unless certain complexity theoretic conjectures are false. Multiplicative error results of this type usually rely on showing that post selection boosts the class to PostBQP 3 .…”

Section: Main Proofsmentioning

confidence: 99%

The one clean qubit model without entanglement is classically simulable

Yoganathan¹,

Cade²

2019

Preprint

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Entanglement has been shown to be necessary for pure state quantum computation to have an advantage over classical computation. However, it remains open whether entanglement is necessary for quantum computers that use mixed states to also have an advantage. The one clean qubit model is a form of quantum computer in which the input is the maximally mixed state plus one pure qubit. Previous work has shown that there is a limited amount of entanglement present in these computations, despite the fact that they can efficiently solve some problems that are seemingly hard to solve classically. This casts doubt on the notion that entanglement is necessary for quantum speedups. In this work we show that entanglement is indeed crucial for efficient computation in this model, because without it the one clean qubit model is efficiently classically simulable.

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“…Quantum computing is deemed a disruptive paradigm for solving many classically intractable problems such as factoring big numbers [1], data fitting [2], combinatorial optimization [3], and boson sampling [4]. The development of quantum-computing platforms has significantly progressed over the last decade [5][6][7][8][9], but outstanding challenges associated with the system scalability, fidelity of quantum gates, and controllability of qubits remain.…”

Section: Introductionmentioning

confidence: 99%

Quantum-Computing Architecture based on Large-Scale Multi-Dimensional Continuous-Variable Cluster States in a Scalable Photonic Platform

Wu,

Alexander,

Liu

et al. 2019

Preprint

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Quantum computing is a disruptive paradigm widely believed to be capable of solving classically intractable problems. However, the route toward full-scale quantum computers is obstructed by immense challenges associated with the scalability of the platform, the connectivity of qubits, and the required fidelity of various components. One-way quantum computing is an appealing approach that shifts the burden from high-fidelity quantum gates and quantum memories to the generation of high-quality entangled resource states and high fidelity measurements. Cluster states are an important ingredient for one-way quantum computing, and a compact, portable, and mass producible platform for large-scale cluster states will be essential for the widespread deployment of one-way quantum computing. Here, we bridge two distinct fields-Kerr microcombs and continuous-variable (CV) quantum information-to formulate a one-way quantum computing architecture based on programmable large-scale CV cluster states. The architecture can accommodate hundreds of simultaneously addressable entangled optical modes multiplexed in the frequency domain and an unlimited number of sequentially addressable entangled optical modes in time domain. One-dimensional, two-dimensional, and three-dimensional CV cluster states can be deterministically produced. We note cluster states of at least three dimensions are required for fault-tolerant one-way quantum computing with known error-correction strategies. This architecture can be readily implemented with silicon photonics, opening a promising avenue for quantum computing at a large scale.

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The Computational Complexity of Linear Optics

Cited by 75 publications

References 0 publications

Theoretical and Experimental Perspectives of Quantum Verification

Theoretical and Experimental Perspectives of Quantum Verification

The one clean qubit model without entanglement is classically simulable

Quantum-Computing Architecture based on Large-Scale Multi-Dimensional Continuous-Variable Cluster States in a Scalable Photonic Platform

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