A comparative study of universal quantum computing models: Toward a physical unification

Wang, Dongsheng

doi:10.1002/que2.85

“…A mathematical milestone is the development of quantum superchannel (and comb) theory [22][23][24] based on channel-state duality [3,25]. It has been used in quantum metrology [26], computing schemes beyond circuit model [27], and recently used in resource theory of channels [28], non-Markovian dynamics with quantum memory effects [29], and quantum algorithms [30]. Therefore, it is worthy to explore more applications of superchannels in quantum computing.…”

Section: Introductionmentioning

confidence: 99%

Quantum circuit simulation of superchannels

Wang

¹

,

Wang

²

2023

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Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum channels. In this work, we study the quantum circuit simulation task of superchannels.We develop a quantum superchannel simulation algorithm based on the convex decomposition into sum of extreme superchannels.We demonstrate the algorithm by numerical simulation of qubit superchannels with high accuracy, making it applicable to current experimental platforms.Our study stands as an expansion of the superchannel theory to the field of quantum simulation and algorithm, as well as an extension of quantum simulation from channels and open-system dynamics to superchannels and processes with manifest quantum memory effects.

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“…There are a few universal quantum computing models [41] and here we employ the quantum circuit model (QCM) in our study. In the setting of QCM, universality means that any unitary operator U ∈ SU (2 n ) can be efficiently approximated by Ũ to an arbitrary accuracy .…”

Section: B Quantum Circuit Modelmentioning

confidence: 99%

“…The study above also extends to more general quantum algorithms. Just as quantum combs are able to describe general quantum operations, it is natural to see that they also describe more general types of quantum algorithms [41]. A quantum comb takes a set of quantum objects {Q n } as input, but uses quantum operations to change them into a desired output, with a quantum adversary as resource.…”

Section: Algorithmic Universalitymentioning

confidence: 99%

“…The QPU in our model is described by the quantum circuit model, which can be replaced by other universal models, such as quantum Turing machine and quantum cellular automata, which are the quantum versions of their classical analogs [41]. Meanwhile, if we view the composition as a whole, it prepares matrix-product states or tensor-network states, which are universal forms of quantum states [66][67][68].…”

Section: Featuresmentioning

confidence: 99%

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A prototypical model of universal quantum computer system

Wang

2021

Preprint

0

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A modern computer system, based on the von Neumann architecture, is a complicated system with several interactive modular parts. It requires a thorough understanding of the physics of information storage, processing, protection, readout, etc. Quantum computing, as the most generic usage of quantum information, follows a hybrid architecture so far, namely, quantum algorithms are stored and controlled classically, and mainly the executions of them are quantum, leading to the so-called quantum processing units. Such a quantum-classical hybrid is constrained by its classical ingredients, and cannot reveal the computational power of a fully quantum computer system as conceived from the beginning of the field. Recently, the nature of quantum information has been further recognized, such as the no-programming and no-control theorems, and the unifying understandings of quantum algorithms and computing models. As a result, in this work we propose a model of universal quantum computer system, the quantum version of the von Neumann architecture. It uses ebits (i.e., Bell states) as elements of the quantum memory unit, and qubits as elements of the quantum control unit and processing unit. As a digital quantum system, its global configurations can be viewed as tensor-network states. Its universality is proved by the capability to execute quantum algorithms based on a program composition scheme via a universal quantum gate teleportation. It is also protected by the uncertainty principle, the fundamental law of quantum information, making it quantum-secure distinct from the classical case. In particular, we introduce a few variants of quantum circuits, including the tailed, nested, and topological ones, to characterize the roles of quantum memory and control, which could also be of independent interest in other contexts. In all, our primary study demonstrates the manifold power of quantum information and paves the way for the creation of quantum computer systems in the near future.

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“…The neural network decoder is fast enough to decode in topological quantum error correction codes 20 . It achieves an exponential improvement, and solves the hardware overhead 21 problem by using the algorithmic improvement. In order to improve the decoding effect of the surface-GKP code, we introduce the currently popular neural network decoder, which uses the convolution operation of the neural network to decode the surface-GKP code under the continuous variable system, with a threshold of σ ≈ 0.78 ( p % 15:12%).…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Bose quantum error correction based on neural network decoder

Wang

¹

,

Xue

²

,

Qu

³

et al. 2022

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Boson quantum error correction is an important means to realize quantum error correction information processing. In this paper, we consider the connection of a single-mode Gottesman-Kitaev-Preskill (GKP) code with a two-dimensional (2D) surface (surface-GKP code) on a triangular quadrilateral lattice. On the one hand, we use a Steane-type scheme with maximum likelihood estimation for surface-GKP code error correction. On the other hand, the minimum-weight perfect matching (MWPM) algorithm is used to decode surface-GKP codes. In the case where only the data GKP qubits are noisy, the threshold reaches σ ≈ 0.5 ($$\bar{p}\approx 12.3 \%$$ p ¯ ≈ 12.3 % ). If the measurement is also noisy, the threshold is reached σ ≈ 0.25 ($$\bar{p}\approx 10.02 \%$$ p ¯ ≈ 10.02 % ). More importantly, we introduce a neural network decoder. When the measurements in GKP error correction are noise-free, the threshold reaches σ ≈ 0.78 ($$\bar{p}\approx 15.12 \%$$ p ¯ ≈ 15.12 % ). The threshold reaches σ ≈ 0.34 ($$\bar{p}\approx 11.37 \%$$ p ¯ ≈ 11.37 % ) when all measurements are noisy. Through the above optimization method, multi-party quantum error correction will achieve a better guarantee effect in fault-tolerant quantum computing.

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A comparative study of universal quantum computing models: Toward a physical unification

Cited by 15 publications

References 139 publications

Quantum circuit simulation of superchannels

Quantum circuit simulation of superchannels

A prototypical model of universal quantum computer system

Multidimensional Bose quantum error correction based on neural network decoder

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