scholarly journals STATE TRANSFER INSTEAD OF TELEPORTATION IN MEASUREMENT-BASED QUANTUM COMPUTATION

2005 ◽  
Vol 03 (01) ◽  
pp. 219-223 ◽  
Author(s):  
SIMON PERDRIX
Keyword(s):  
Quantum Computation ◽  
Quantum Measurement ◽  
Unitary Transformation ◽  
New Model ◽  
Universal Family ◽  
State Transfer ◽  
Transfer State

Quantum measurement is universal for quantum computation. The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with this model, four auxiliary qubits are required. Moreover Leung exhibited a universal family of observables composed of one one-qubit measurement and four two-qubit measurements. We introduce a model of quantum computation via measurements only, relying on state transfer: state transfer only retains the part of teleportation which is necessary for computation. In order to simulate any n-qubit unitary transformation with this new model, only one auxiliary qubit is required. Moreover we exhibit a universal family of observables composed of three one-qubit measurements and only one two-qubit measurement. This model improves those of Nielsen and Leung in terms of both the number of auxiliary qubits and the number of two-qubit measurements required for quantum universality. In both cases, the minimal amounts of necessary resources are now reached: one auxiliary qubit (because measurement is destructive) and one two-qubit measurement (for creating entanglement).

scholarly journals Generation of elementary gates and Bell’s states using controlled adiabatic evolutions

2019 ◽  
Vol 17 (03) ◽  
pp. 1950020
Author(s):  
Abderrahim Benmachiche ◽  
Ali Sellami ◽  
Sherzod Turaev ◽  
Derradji Bahloul ◽  
Azeddine Messikh ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Open Systems ◽  
Circuit Model ◽  
Quantum Gates ◽  
Single Quantum ◽  
New Model ◽  
Adiabatic Quantum Computation ◽  
Usual Quantum

Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement [Formula: see text]-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.

scholarly journals NONUNITARY QUANTUM CIRCUIT

2005 ◽  
Vol 03 (04) ◽  
pp. 633-647 ◽  
Author(s):  
HIROAKI TERASHIMA ◽  
MASAHITO UEDA
Keyword(s):  
Quantum Computation ◽  
Quantum Measurement ◽  
Fault Tolerant ◽  
Quantum Circuit ◽  
Nand Gate ◽  
Gate Operation ◽  
Measurement Scheme

A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, and all one-qubit unitary gates constitute a universal set of gates for the nonunitary quantum circuit, without the necessity of introducing ancilla qubits. A reversing measurement scheme is used to improve the probability of successful nonunitary gate operation. A quantum NAND gate and Abrams–Lloyd's nonlinear gate are analyzed as examples. Our nonunitary circuit can be used to reduce the qubit overhead needed to ensure fault-tolerant quantum computation.

AN EXACT ENTANGLING GATE USING FIBONACCI ANYONS

2018 ◽  
Vol 99 (2) ◽  
pp. 319-326
Author(s):  
STEPHEN BIGELOW ◽  
CLAIRE LEVAILLANT
Keyword(s):  
State Space ◽  
Quantum Computation ◽  
Unitary Transformation ◽  
Topological Quantum ◽  
Topological Quantum Computation

Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However, there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known ‘leakage-free’ entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.

Transformation of Quantum States in Quantum Computation

2011 ◽  
Vol 80-81 ◽  
pp. 276-278
Author(s):  
Jun Lu
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Building Blocks ◽  
Quantum Systems ◽  
Quantum States ◽  
Quantum Bits ◽  
Universal Family ◽  
Unitary Transformations ◽  
Elementary Building ◽  
Arbitrary Selection

Quantum computation is based on transformation of quantum states. Quantum bits are two-level quantum systems, and as the simplest elementary building blocks for a quantum computer, they provide a convenient labeling for pairs of states and their physical realizations. Closed quantum systems evolve unitarily as determined by their Hamiltonians, but to perform quantum computation one must be able to control the Hamiltonian to effect an arbitrary selection from a universal family of unitary transformations.

scholarly journals Hamiltonian transformability, fast adiabatic dynamics and hidden adiabaticity

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lian-Ao Wu ◽  
Dvira Segal
Keyword(s):  
Hilbert Space ◽  
Existence Theorem ◽  
Quantum Computation ◽  
Unitary Transformation ◽  
Adiabatic Quantum Computation ◽  
Promising Application ◽  
Adiabatic Regime ◽  
Adiabatic Dynamics

AbstractWe prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to implementing or mimicking dynamics with the most controllable Hamiltonian. As a promising application, this existence theorem allows for a rapidly evolving realization of adiabatic quantum computation by transforming a Hamiltonian where dynamics is in the adiabatic regime into a rapidly evolving one. We illustrate the theorem with examples.

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’.

scholarly journals IMPROVING THE CONTROL STRATEGY IN TWO-WAY DETERMINISTIC CRYPTOGRAPHIC PROTOCOLS

2011 ◽  
Vol 09 (05) ◽  
pp. 1209-1222 ◽  
Author(s):  
ANITA EUSEBI ◽  
STEFANO MANCINI
Keyword(s):  
Quantum Measurement ◽  
Control Strategy ◽  
Unitary Transformation ◽  
Prime Power ◽  
Cryptographic Protocols ◽  
Protocol Security ◽  
Cryptographic Scheme

We introduce a new control strategy on a two-way deterministic cryptographic scheme, which relies on a suitable unitary transformation rather than a quantum measurement. The study is developed for d-ary alphabets and the particular choice of the transformation works when d is an odd prime power. It leads to an improvement of the protocol security, which we prove to increase with the alphabet order d.

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