Architectures for Quantum Simulation Showing a Quantum Speedup

Bermejo-Vega, Juan; Hangleiter, Dominik; Schwarz, Martin; Raussendorf, Robert; Eisert, Jens

doi:10.1103/physrevx.8.021010

Cited by 108 publications

(263 citation statements)

References 91 publications

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“…This CQCA is the QCA of the 2D cluster state [31], and it has appeared several times already in the context of quantum computation [72,75,83]. The subscript g refers to the term glider which we shall introduce shortly.…”

Section: Quantum Cellular Automatamentioning

confidence: 99%

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter

Stephen

Nautrup

Bermejo-Vega

et al. 2019

Quantum

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104

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Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lowerdimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.The fields of study of quantum phases of matter and of quantum computation have been evolving alongside each other for over a decade, such that they are now deeply intertwined. This is on the one hand because many instances of non-trivial quantum order are key to storing or processing quantum informa-Figure 1: Interrelation between symmetry-protected topological (SPT) order, measurement-based quantum computation (MBQC), and quantum cellular automata (QCA). By framing both subsystem SPT order and MBQC in terms of QCA, we develop a new framework for characterizing subsystem SPT order and constructing computationally universal phases of matter.tion, an idea that has stimulated a plethora of theoretical and experimental research in both fields. Perhaps the most familiar example is the idea of topological quantum computation which leverages the anyonic excitations of topologically ordered systems to perform error-resilient quantum computation [1][2][3]. A complementing approach to topological quantum computation uses Majorana fermions located at the edges of one-dimensional (1D) chains with symmetryprotected topological (SPT) order [4][5][6]. On the other hand, quantum states exhibiting SPT order can be used as resources for instances of measurement-based quantum computation [7-22] -an insight most relevant to the present work. Various further examples can be found [23][24][25]; indeed, every time a new type of quantum order is discovered, it is not long before its uses in notions of quantum computation are being investigated.The m...

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Section: Quantum Cellular Automatamentioning

confidence: 99%

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter

Stephen

Nautrup

Bermejo-Vega

et al. 2019

Quantum

Self Cite

104

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“…Compared to a universal digital quantum computer, the resources required for experimental boson sampling appear much less demanding. This approach of designing quantum algorithms to demonstrate computational supremacy with nearterm experimental capabilities has inspired a raft of proposals suited to different hardware platforms [18][19][20] .Based on a simple architecture, the boson sampling problem is similarly straightforward to state. A number n of indistinguishable noninteracting bosons (for example, photons) should be injected into n input ports of a circuit comprised of a number m of linearly coupled bosonic modes.…”

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confidence: 99%

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confidence: 99%

Classical boson sampling algorithms with superior performance to near-term experiments

et al. 2017

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It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, largescale universal quantum computers are yet to be built. Boson sampling 1 is a rudimentary quantum algorithm tailored to the platform of linear optics, which has sparked interest as a rapid way to demonstrate such quantum supremacy 2-6 . Photon statistics are governed by intractable matrix functions, which suggests that sampling from the distribution obtained by injecting photons into a linear optical network could be solved more quickly by a photonic experiment than by a classical computer. The apparently low resource requirements for large boson sampling experiments have raised expectations of a near-term demonstration of quantum supremacy by boson sampling 7,8 . Here we present classical boson sampling algorithms and theoretical analyses of prospects for scaling boson sampling experiments, showing that near-term quantum supremacy via boson sampling is unlikely. Our classical algorithm, based on Metropolised independence sampling, allowed the boson sampling problem to be solved for 30 photons with standard computing hardware. Compared to current experiments, a demonstration of quantum supremacy over a successful implementation of these classical methods on a supercomputer would require the number of photons and experimental components to increase by orders of magnitude, while tackling exponentially scaling photon loss.It is believed that new types of computing machines will be constructed to exploit quantum mechanics for an exponential speed advantage in solving certain problems compared with classical computers 9 . Recent large state and private investments in developing quantum technologies have increased interest in this challenge. However, it is not yet experimentally proven that a large computationally useful quantum system can be assembled, and such a task is highly non-trivial given the challenge of overcoming the effects of errors in these systems.Boson sampling is a simple task which is native to linear optics and has captured the imagination of quantum scientists because it seems possible that the anticipated supremacy of quantum machines could be demonstrated by a near-term experiment. The advent of integrated quantum photonics 10 has enabled large, complex, stable and programmable optical circuitry 11,12 , while recent advances in photon generation [13][14][15] and detection 16,17 have also been impressive. The possibility to generate many photons, evolve them under a large linear optical unitary transformation, then detect them, seems feasible, so the role of a boson sampling machine as a rudimentary but legitimate computing device is particularly appealing. Compared to a universal digital quantum computer, the resources required for experimental boson sampling appear much less demanding. This approach of designing quantum algorithms to demonstrate computational supremacy with nearterm experimental capabilities has inspired a raft of proposals suited to different hardware platforms [18]...

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“…However, there may also be the possibility of going further by exploiting the structure of the entangled resource being used to reduce the overall complexity and put a given simulation within reach of current technology. Recently, the first steps in this direction have been taken theoretically [57]. Despite this potential, the realisation and simulation of realistic quantum systems using the measurement-based model has not yet been explored.…”

Section: Introductionmentioning

confidence: 99%

Experimental demonstration of a measurement-based realisation of a quantum channel

et al. 2018

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We introduce and experimentally demonstrate a method for realising a quantum channel using the measurement-based model. Using a photonic setup and modifying the bases of single-qubit measurements on a four-qubit entangled cluster state, representative channels are realised for the case of a single qubit in the form of amplitude and phase damping channels. The experimental results match the theoretical model well, demonstrating the successful performance of the channels. We also show how other types of quantum channels can be realised using our approach. This work highlights the potential of the measurement-based model for realising quantum channels which may serve as building blocks for simulations of realistic open quantum systems.

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Architectures for Quantum Simulation Showing a Quantum Speedup

Cited by 108 publications

References 91 publications

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter

Classical boson sampling algorithms with superior performance to near-term experiments

Experimental demonstration of a measurement-based realisation of a quantum channel

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