THE QUANTUM WORLD AND QUANTUM COMPUTING: FUNDAMENTAL ISSUES

2011 ◽  
Vol 20 (01) ◽  
pp. 179-202
Author(s):  
WILLIAM C. PARKE ◽  
ALI ESKANDARIAN
Keyword(s):  
Quantum Computing ◽  
Quantum Theory ◽  
Quantum Information ◽  
Information Transfer ◽  
Space Time ◽  
Topological Quantum ◽  
Non Locality

Some of the fundamental issues in quantum theory related to quantum computing are reviewed and discussed. Particularly emphasized is the need to be diligent in what quantum theory predicts, and what it does not. The non-intuitive features of quantum theory, that are often associated with aspects of non-locality and that also arise in quantum computing and quantum information transfer, are described. Some discussion of topological quantum computing using space-time strings is presented, as well as general notions about quantum computing.

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.

scholarly journals Quantum Computation and Measurements from an Exotic Space-Time R4

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 736
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Klee Irwin
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Fundamental Group ◽  
Quantum Computation ◽  
Quantum Measurement ◽  
Space Time ◽  
Fano Plane ◽  
Topological Quantum ◽  
Universal Quantum ◽  
Complete Quantum

The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a ‘magic’ state ψ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite ‘contextual’ geometry. In the present work, we choose G as the fundamental group π 1 ( V ) of an exotic 4-manifold V, more precisely a ‘small exotic’ (space-time) R 4 (that is homeomorphic and isometric, but not diffeomorphic to the Euclidean R 4 ). Our selected example, due to S. Akbulut and R. E. Gompf, has two remarkable properties: (a) it shows the occurrence of standard contextual geometries such as the Fano plane (at index 7), Mermin’s pentagram (at index 10), the two-qubit commutation picture G Q ( 2 , 2 ) (at index 15), and the combinatorial Grassmannian Gr ( 2 , 8 ) (at index 28); and (b) it allows the interpretation of MICs measurements as arising from such exotic (space-time) R 4 s. Our new picture relating a topological quantum computing and exotic space-time is also intended to become an approach of ‘quantum gravity’.

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 30-32
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Theoretical Physics ◽  
View Point ◽  
Research Subjects ◽  
Interactive Proof ◽  
Open Problems ◽  
Main Research ◽  
Proof Systems ◽  
Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

“Non-locality”

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Quantum States ◽  
Action At A Distance ◽  
Insight Into ◽  
Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

Quantum Becoming?

2017 ◽  
Author(s):  
Craig Callender
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Time ◽  
Quantum Non Locality ◽  
Time Quantum ◽  
Temporal Becoming ◽  
Non Locality ◽  
Quantum Wavefunction

Two of quantum mechanics’ more famed and spooky features have been invoked in defending the idea that quantum time is congenial to manifest time. Quantum non-locality is said by some to make a preferred foliation of spacetime necessary, and the collapse of the quantum wavefunction is held to vindicate temporal becoming. Although many philosophers and physicists seek relief from relativity’s assault on time in quantum theory, assistance is not so easily found.

scholarly journals Relativity and the quantum theory

1928 ◽  
Vol 117 (778) ◽  
pp. 630-637 ◽  
Keyword(s):  
Quantum Theory ◽  
Space Time ◽  
Theory Of Gravitation ◽  
The Law

In Einstein’s theory of gravitation it is assumed that the geometry of space- time is characterised by the following equation for the measurement of displacement:— ds 2 = g mn dx m dx n { m n = 1, 2, 3, 4, the sign of summation being omitted for convenience. It is supposed that the coefficients, of which g mn is the type, are dependent upon the content of space, and the relation existing between them is the law of gravitation.

Quantum Information Transfer in Circuit QED with Landau—Zener Tunneling

2011 ◽  
Vol 28 (9) ◽  
pp. 090302 ◽  
Author(s):  
Jun-Wang Li ◽  
Chun-Wang Wu ◽  
Hong-Yi Dai
Keyword(s):  
Quantum Information ◽  
Information Transfer ◽  
Circuit Qed ◽  
Zener Tunneling

scholarly journals Topological Quantum Computing and 3-Manifolds

2021 ◽  
Vol 3 (1) ◽  
pp. 153-165
Author(s):  
Torsten Asselmeyer-Maluga
Keyword(s):  
Quantum Computing ◽  
Berry Phase ◽  
Basic Structure ◽  
Quantum States ◽  
Point Of View ◽  
Surface Topology ◽  
Usual Sense ◽  
Closed Curves ◽  
Topological Quantum ◽  
2D System

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Today, the basic structure is a 2D system to realize anyons with braiding operations. From the topological point of view, we have to deal with surface topology. However, usual materials are 3D objects. Possible topologies for these objects can be more complex than surfaces. From the topological point of view, Thurston’s geometrization theorem gives the main description of 3-dimensional manifolds. Here, complements of knots do play a prominent role and are in principle the main parts to understand 3-manifold topology. For that purpose, we will construct a quantum system on the complements of a knot in the 3-sphere. The whole system depends strongly on the topology of this complement, which is determined by non-contractible, closed curves. Every curve gives a contribution to the quantum states by a phase (Berry phase). Therefore, the quantum states can be manipulated by using the knot group (fundamental group of the knot complement). The universality of these operations was already showed by M. Planat et al.

On the classical character of control fields in quantum information processing

2002 ◽  
Vol 2 (1) ◽  
pp. 1-13
Author(s):  
S.J. van Enk ◽  
H.J. Kimble
Keyword(s):  
Quantum Computing ◽  
Information Processing ◽  
Quantum Information ◽  
Laser Beam ◽  
Quantum State ◽  
Quantum Communication ◽  
Quantum Information Processing ◽  
Laser Fields ◽  
Undesirable Property

Control fields in quantum information processing are almost by definition assumed to be classical. In reality, however, when such a field is used to manipulate the quantum state of qubits, the qubits always become slightly entangled with the field. For quantum information processing this is an undesirable property, as it precludes perfect quantum computing and quantum communication. Here we consider the interaction of atomic qubits with laser fields and quantify atom-field entanglement in various cases of interest. We find that the entanglement decreases with the average number of photons \bar{n} in a laser beam as $E\propto\log_2 \bar{n}/\bar{n}$ for $\bar{n}\rightarrow\infty$.

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