Optimal universal quantum error correction via bounded reference frames

Yang, Yuxiang; Mo, Yin; Renes, Joseph M.; Chiribella, Giulio; Woods, Mischa P.

doi:10.1103/physrevresearch.4.023107

Cited by 17 publications

(5 citation statements)

References 77 publications

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“…When setting δ global = δ local = 0, our theorems recover previous results on exactly covariant codes 14,15,[17][18][19] . The results and methods here apply to general quantum codes beyond exactly covariant codes.…”

Section: Symmetry Vs Qecsupporting

confidence: 82%

“…It is worth noting that the transversality property is not only important in quantum computation since transversal gates are particularly desirable for fault tolerance, but also widely so in physics as a fundamental feature of internal symmetries in many-body scenarios. Further, there has been a series of recent works that consider approximate QEC by covariant codes, providing bounds on the accuracy as well as explicit constructions [14][15][16][17][18][19][20][21][22] . Viewing the gates as symmetry actions, these results indicate that the QEC accuracy of a code admitting transversal continuous symmetries is necessarily restricted to some extent.…”

Section: Introductionmentioning

confidence: 99%

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Approximate symmetries and quantum error correction

Liu,

Zhou

2023

npj Quantum Inf

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Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin–Knill theorem, which forbids the existence of QEC codes that admit transversal continuous symmetry actions (transformations). Here, we systematically study the competition between continuous symmetries and QEC in a quantitative manner. We first define a series of meaningful measures of approximate symmetries motivated from different perspectives, and then establish a series of trade-off bounds between them and QEC accuracy utilizing multiple different methods. Remarkably, the results allow us to derive general quantitative limitations of transversally implementable logical gates, an important topic in fault-tolerant quantum computation. As concrete examples, we showcase two explicit types of quantum codes, obtained from quantum Reed–Muller codes and thermodynamic codes, respectively, that nearly saturate our bounds. Finally, we discuss several potential applications of our results in physics.

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Section: Symmetry Vs Qecsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Approximate symmetries and quantum error correction

Liu,

Zhou

2023

npj Quantum Inf

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“…Notably, this scheme also works optimally for learning or estimation, and can also be viewed as a covariant code. [25] Namely, let…”

Section: Qvn-iiimentioning

confidence: 99%

A family of quantum von Neumann architecture

Wang 王

2024

Chinese Phys. B

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In this work, we develop universal quantum computing models that form a family of quantum von Neumann architectures, with modular units of memory, control, CPU, and internet, besides input and output. This family contains three generations characterized by dynamical quantum resource theory, and it also circumvents no-go theorems on quantum programming and control. Besides universality, such a family satisfies other desirable engineering requirements on system and algorithm design, such as modularity and programmability, hence serves as a unique approach to build universal quantum computers.

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“…[6] is the right starting point. With a generalized sine state |Φ acting on 2n qudits, the output U|d is approximated to the accuracy ∼ 1 Notably, this scheme also works optimally for learning or estimation, and can also be viewed as a covariant code [23]. Namely, let | f = U|d and | f → |d |p U be the isometric encoding, it is then clear this encoding is SU(d) covariant and the POVM realizes the decoding.…”

Section: Besides the Input And Output By Measurements One Can Also Do...mentioning

confidence: 99%

A prototype of quantum von Neumann architecture

Wang¹

2022

Commun. Theor. Phys.

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A modern computer system, based on the von Neumann architecture, is a complicated system with several interactive modular parts. 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. 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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Optimal universal quantum error correction via bounded reference frames

Cited by 17 publications

References 77 publications

Approximate symmetries and quantum error correction

Approximate symmetries and quantum error correction

A family of quantum von Neumann architecture

A prototype of quantum von Neumann architecture

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