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Entropy
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Quantum Information: Fragility and the Challenges of Fault Tolerance
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Quantum Information: Fragility and the Challenges of Fault Tolerance

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (31 October 2019) | Viewed by 19537

Special Issue Editors

Prof. Dr. Göran Wendin

E-Mail Website
Guest Editor
Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, S-412 96 Göteborg, Sweden
Interests: superconducting qubits; quantum computing; quantum simulation; quantum neural networks; biological networks; quantum effects in biology
Dr. Giulia Ferrini

E-Mail Website
Guest Editor
Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, S-412 96 Göteborg, Sweden
Interests: quantum computing; quantum optics; continuous variables; quantum advantage; quantum supremacy

Special Issue Information

Dear Colleagues,

The recent advances in scaling up quantum processors into the range of 50–100 qubits make quantum error correction (QEC) and fault tolerance urgent practical issues in order to achieve quantum advantage or even quantum supremacy. Interesting developments in regular QEC include new classes of codes, either in the qubit setting (topological, non-abelian, holographic…) or with continuous variables, such as Gottesman-Kitaev-Preskill  (GKP) or cat-codes. However, universal fault-tolerant quantum computation based on QEC is not yet within reach. The near-term challenge is rather to make optimal use of available hardware and software resources. This requires developing useful characterization tools, typically involving the number, connectivity, and coherence of physical qubits, the available gate set, and the number of operations that can be run in parallel. On the software side, machine learning (ML) may be used for optimizing gate sequences, minimizing circuit depths, optimizing variational schemes. Other challenges involve new types of architectures, like dynamical complex systems based on (brain-inspired) adaptive quantum networks.

Prof. Dr. Göran Wendin
Dr. Giulia Ferrini
Guest Editors

Manuscript Submission Information

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Keywords

  • fault-tolerance
  • quantum computation
  • quantum simulation
  • quantum error correction
  • quantum advantage
  • quantum supremacy
  • machine learning
  • quantum networks

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Published Papers (4 papers)

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Research

12 pages, 607 KiB  
Article
On Unitary t-Designs from Relaxed Seeds
by Rawad Mezher, Joe Ghalbouni, Joseph Dgheim and Damian Markham
Entropy 2020, 22(1), 92; https://doi.org/10.3390/e22010092 - 12 Jan 2020
Cited by 3 | Viewed by 4771
Abstract
The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary t-design is designed to tackle this challenge in an efficient way, yet constructions to date rely on heavy constraints. [...] Read more.
The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary t-design is designed to tackle this challenge in an efficient way, yet constructions to date rely on heavy constraints. In particular, they are composed of ensembles of unitaries which, for technical reasons, must contain inverses and whose entries are algebraic. In this work, we reduce the requirements for generating an ε -approximate unitary t-design. To do so, we first construct a specific n-qubit random quantum circuit composed of a sequence of randomly chosen 2-qubit gates, chosen from a set of unitaries which is approximately universal on U ( 4 ) , yet need not contain unitaries and their inverses nor are in general composed of unitaries whose entries are algebraic; dubbed r e l a x e d seed. We then show that this relaxed seed, when used as a basis for our construction, gives rise to an ε -approximate unitary t-design efficiently, where the depth of our random circuit scales as p o l y ( n , t , l o g ( 1 / ε ) ) , thereby overcoming the two requirements which limited previous constructions. We suspect the result found here is not optimal and can be improved; particularly because the number of gates in the relaxed seeds introduced here grows with n and t. We conjecture that constant sized seeds such as those which are usually present in the literature are sufficient. Full article
(This article belongs to the Special Issue Quantum Information: Fragility and the Challenges of Fault Tolerance)
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14 pages, 5572 KiB  
Article
Continuous Variables Graph States Shaped as Complex Networks: Optimization and Manipulation
by Francesca Sansavini and Valentina Parigi
Entropy 2020, 22(1), 26; https://doi.org/10.3390/e22010026 - 24 Dec 2019
Cited by 6 | Viewed by 4379
Abstract
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently, complex network theory has been applied to quantum systems, where complex network topologies may emerge in multiparty quantum states and quantum [...] Read more.
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently, complex network theory has been applied to quantum systems, where complex network topologies may emerge in multiparty quantum states and quantum algorithms have been studied in complex graph structures. In this work, we study multimode Continuous Variables entangled states, named cluster states, where the entanglement structure is arranged in typical real-world complex networks shapes. Cluster states are a resource for measurement-based quantum information protocols, where the quality of a cluster is assessed in terms of the minimal amount of noise it introduces in the computation. We study optimal graph states that can be obtained with experimentally realistic quantum resources, when optimized via analytical procedure. We show that denser and regular graphs allow for better optimization. In the spirit of quantum routing, we also show the reshaping of entanglement connections in small networks via linear optics operations based on numerical optimization. Full article
(This article belongs to the Special Issue Quantum Information: Fragility and the Challenges of Fault Tolerance)
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31 pages, 691 KiB  
Article
Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
by Andrew Tranter, Peter J. Love, Florian Mintert, Nathan Wiebe and Peter V. Coveney
Entropy 2019, 21(12), 1218; https://doi.org/10.3390/e21121218 - 13 Dec 2019
Cited by 37 | Viewed by 6760
Abstract
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter [...] Read more.
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian. Full article
(This article belongs to the Special Issue Quantum Information: Fragility and the Challenges of Fault Tolerance)
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15 pages, 608 KiB  
Article
Robust Diabatic Grover Search by Landau–Zener–Stückelberg Oscillations
by Yosi Atia, Yonathan Oren and Nadav Katz
Entropy 2019, 21(10), 937; https://doi.org/10.3390/e21100937 - 25 Sep 2019
Cited by 5 | Viewed by 3136
Abstract
Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau–Zener–Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of [...] Read more.
Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau–Zener–Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O ( 2 n ) , which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms. Full article
(This article belongs to the Special Issue Quantum Information: Fragility and the Challenges of Fault Tolerance)
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