scholarly journals Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 553
Author(s):  
Xiao Xiao ◽  
J. K. Freericks ◽  
A. F. Kemper
Keyword(s):  
Phase Diagrams ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Entanglement Entropy ◽  
Quantum Phase ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Model ◽  
Quantum Properties ◽  
Topological Quantum

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

scholarly journals A Short Introduction to Topological Quantum Computation

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Ville Lahtinen ◽  
Jiannis Pachos
Keyword(s):  
Quantum Computation ◽  
Condensed Matter ◽  
Quantum Computers ◽  
Short Introduction ◽  
Entry Level ◽  
Zero Modes ◽  
Topological Quantum ◽  
Topological Quantum Computation ◽  
Superconducting Nanowire ◽  
Energy Physics

This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We outline the general steps of topological quantum computation, as well as discuss various challenges faced by it. We also review the literature on condensed matter systems where anyons can emerge. Finally, the appearance of anyons and employing them for quantum computation is demonstrated in the context of a simple microscopic model -- the topological superconducting nanowire -- that describes the low-energy physics of several experimentally relevant settings. This model supports localised Majorana zero modes that are the simplest and the experimentally most tractable types of anyons that are needed to perform topological quantum computation.

scholarly journals GENERALIZED YANG–BAXTER EQUATIONS AND BRAIDING QUANTUM GATES

2012 ◽  
Vol 21 (09) ◽  
pp. 1250087 ◽  
Author(s):  
REBECCA S. CHEN
Keyword(s):  
Braid Group ◽  
Knot Theory ◽  
Information Science ◽  
Quantum Gates ◽  
Quantum Computers ◽  
Baxter Equation ◽  
Group Representations ◽  
Ongoing Research ◽  
Topological Quantum ◽  
Mathematics And Physics

Solutions to the Yang–Baxter equation — an important equation in mathematics and physics — and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum information science. In particular, unitary representations of the braid group are desired because they generate braiding quantum gates. These are actively studied in the ongoing research into topological quantum computing. A generalized Yang–Baxter equation was proposed a few years ago by Eric Rowell et al. By finding solutions to the generalized Yang–Baxter equation, we obtain new unitary braid group representations. Our representations give rise to braiding quantum gates and thus have the potential to aid in the construction of useful quantum computers.

scholarly journals Permutational quantum computing

2010 ◽  
Vol 10 (5&6) ◽  
pp. 470-497
Author(s):  
S.P. Jordan
Keyword(s):  
Quantum Computation ◽  
Polynomial Time ◽  
Particle Trajectory ◽  
Quantum Computers ◽  
Matrix Elements ◽  
Spin Network ◽  
Spin Foam Model ◽  
Topological Quantum ◽  
One Step ◽  
Topological Quantum Computation

In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle trajectory, and computes by permuting particles. Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not know whether permutational computation is universal. It may represent a new complexity class within BQP. Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and approximate certain transition amplitudes from the Ponzano-Regge spin foam model of quantum gravity. No polynomial time classical algorithms for these problems are known.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Classical Physics ◽  
Core Set ◽  
The World ◽  
Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

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