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

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 142 ◽  
Author(s):  
David T. Stephen ◽  
Hendrik Poulsen Nautrup ◽  
Juani Bermejo-Vega ◽  
Jens Eisert ◽  
Robert Raussendorf
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Cellular Automata ◽  
Quantum Computation ◽  
Quantum Information Theory ◽  
Quantum Cellular Automata ◽  
Quantum Phases ◽  
Quantum Matter ◽  
Tensor Network ◽  
Symmetry Protected

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 lower-dimensional 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.

scholarly journals Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 228 ◽  
Author(s):  
Austin K. Daniel ◽  
Rafael N. Alexander ◽  
Akimasa Miyake
Keyword(s):  
Cellular Automata ◽  
Error Correction ◽  
Quantum Computation ◽  
Cluster State ◽  
Quantum Cellular Automata ◽  
Fine Grained ◽  
Computational Capability ◽  
Lattice Geometry ◽  
Computational Universality ◽  
Symmetry Protected

What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by this observation, we analyze the computational capability of SPTO cluster phases on all vertex-translative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1-form symmetries, and the former three are fundamentally in one-to-one correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1-form symmetries and have a different capability related to error correction.

scholarly journals A general formulation based on algebraic spinors for the quantum computation

2020 ◽  
Vol 17 (14) ◽  
pp. 2050206
Author(s):  
Marco A. S. Trindade ◽  
Sergio Floquet ◽  
J. David M. Vianna
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Information ◽  
Quantum Computation ◽  
Quantum Teleportation ◽  
Clifford Algebras ◽  
Quantum Information Theory ◽  
Quantum Gates ◽  
Entangled States ◽  
Space Formulation

In this work, we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially, we present a general formulation through elements of minimal left ideals in tensor products of Clifford algebras. Posteriorly, we perform some applications in quantum computation: qubits, entangled states, quantum gates, representations of the braid group, quantum teleportation, Majorana operators and supersymmetry. Finally, we discuss advantages compared to standard Hilbert space formulation.

scholarly journals Towards a Fisher-Information Description of Complexity in de Sitter Universe

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 221 ◽  
Author(s):  
Chong-Bin Chen ◽  
Fu-Wen Shu
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Gravity ◽  
Fisher Information ◽  
Entanglement Entropy ◽  
Quantum Information Theory ◽  
Theoretical Interpretation ◽  
De Sitter ◽  
Tensor Network ◽  
De Sitter Universe

Recent developments on holography and quantum information physics suggest that quantum information theory has come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still unknown. Here, we show that some concepts in quantum information theory have cosmological descriptions. Particularly, we show that the complexity of a tensor network can be regarded as a Fisher information measure (FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for f ( R ) gravity, whose FIM exhibits the same features of a recent proposed L n norm complexity.

QALO-MOR: Improved antlion optimizer based on quantum information theory for model order reduction

2021 ◽  
pp. 1-11
Author(s):  
Rosy Pradhan ◽  
Mohammad Rafique Khan ◽  
Prabir Kumar Sethy ◽  
Santosh Kumar Majhi
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Real World ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Quantum Information Theory ◽  
Hunting Behavior ◽  
Model Order ◽  
Ant Lion Optimization ◽  
Real World Problems

The field of optimization science is proliferating that has made complex real-world problems easy to solve. Metaheuristics based algorithms inspired by nature or physical phenomena based methods have made its way in providing near-ideal (optimal) solutions to several complex real-world problems. Ant lion Optimization (ALO) has inspired by the hunting behavior of antlions for searching for food. Even with a unique idea, it has some limitations like a slower rate of convergence and sometimes confines itself into local solutions (optima). Therefore, to enhance its performance of classical ALO, quantum information theory is hybridized with classical ALO and named as QALO or quantum theory based ALO. It can escape from the limitations of basic ALO and also produces stability between processes of explorations followed by exploitation. CEC2017 benchmark set is adopted to estimate the performance of QALO compared with state-of-the-art algorithms. Experimental and statistical results demonstrate that the proposed method is superior to the original ALO. The proposed QALO extends further to solve the model order reduction (MOR) problem. The QALO based MOR method performs preferably better than other compared techniques. The results from the simulation study illustrate that the proposed method effectively utilized for global optimization and model order reduction.

scholarly journals Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 33 ◽  
Author(s):  
Liron Levy ◽  
Moshe Goldstein
Keyword(s):  
Phase Diagram ◽  
Information Theory ◽  
Quantum Information ◽  
Critical Point ◽  
Entanglement Entropy ◽  
Quantum Information Theory ◽  
Topological Phase ◽  
Many Body ◽  
Zero Modes ◽  
Many Body Systems

In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.

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