scholarly journals Simple Proof of Equivalence between Adiabatic Quantum Computation and the Circuit Model

2007 ◽  
Vol 99 (7) ◽  
Author(s):  
Ari Mizel ◽  
Daniel A. Lidar ◽  
Morgan Mitchell
Keyword(s):  
Quantum Computation ◽  
Simple Proof ◽  
Circuit Model ◽  
Adiabatic Quantum Computation

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.

Classical simulation of quantum computation, the gottesman-Knill theorem, and slightly beyond

2010 ◽  
Vol 10 (3&4) ◽  
pp. 258-271 ◽  
Author(s):  
M. Van den Nest
Keyword(s):  
Normal Form ◽  
Quantum Computation ◽  
Simple Proof ◽  
Quantum Circuit ◽  
Circuit Model ◽  
Computational Power ◽  
Classical Simulation ◽  
Starting Point

We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a simple proof of the Gottesman-Knill theorem without resorting to stabilizer techniques. The normal form highlights why Clifford circuits have such limited computational power in spite of their high entangling power. At the same time, the normal form shows how the classical simulation of Clifford circuits fits into the standard way of embedding classical computation into the quantum circuit model. This leads to simple extensions of Clifford circuits which are classically simulatable. These circuits can be efficiently simulated by classical sampling (``weak simulation'') even though the problem of exactly computing the outcomes of measurements for these circuits (``strong simulation'') is proved to be $\#\mathbf{P}$-complete---thus showing that there is a separation between weak and strong classical simulation of quantum computation.

scholarly journals Realization of a classical counterpart of a scalable design for adiabatic quantum computation

2007 ◽  
Vol 90 (2) ◽  
pp. 022501 ◽  
Author(s):  
V. Zakosarenko ◽  
N. Bondarenko ◽  
S. H. W. van der Ploeg ◽  
A. Izmalkov ◽  
S. Linzen ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Classical Counterpart ◽  
Adiabatic Quantum Computation ◽  
Scalable Design

scholarly journals Assessing the quantumness of the annealing dynamics via Leggett Garg’s inequalities: a weak measurement approach

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
V. Vitale ◽  
G. De Filippis ◽  
A. de Candia ◽  
A. Tagliacozzo ◽  
V. Cataudella ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computers ◽  
Quantum Annealing ◽  
Adiabatic Quantum Computation ◽  
Universal Quantum ◽  
Full Quantum ◽  
Measurement Approach ◽  
Coherent Behavior ◽  
Sizable Number

Abstract Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact that the detrimental role of decoherence and dephasing seems to have poor impact on the annealing towards the ground state. While many papers show interesting optimization results with a sizable number of qubits, a clear evidence of a full quantum coherent behavior during the whole annealing procedure is still lacking. In this paper we show that quantum non-demolition (weak) measurements of Leggett Garg inequalities can be used to efficiently assess the quantumness of the QA procedure. Numerical simulations based on a weak coupling Lindblad approach are compared with classical Langevin simulations to support our statements.

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