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 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 Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 81
Author(s):  
Agniva Roychowdhury ◽  
Sebastian Deffner
Keyword(s):  
Time Dependence ◽  
Unitary Transformation ◽  
Ion Traps ◽  
Time Frame ◽  
Effective Potentials ◽  
Shortcuts To Adiabaticity ◽  
Weyl Semimetals ◽  
Adiabatic Dynamics

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame, the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

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 A factorisation algorithm in Adiabatic Quantum Computation

2019 ◽  
Vol 3 (2) ◽  
pp. 025014 ◽  
Author(s):  
Tien D Kieu
Keyword(s):  
Quantum Computation ◽  
Adiabatic Quantum Computation

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 Adiabatic Quantum Computation: Coherent Control Back Action

2006 ◽  
Author(s):  
Debabrata Goswami
Keyword(s):  
Quantum Computation ◽  
Coherent Control ◽  
Adiabatic Quantum Computation ◽  
Back Action

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.

scholarly journals Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation

SIAM Review ◽  
2008 ◽  
Vol 50 (4) ◽  
pp. 755-787 ◽  
Author(s):  
Dorit Aharonov ◽  
Wim van Dam ◽  
Julia Kempe ◽  
Zeph Landau ◽  
Seth Lloyd ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Standard Quantum ◽  
Adiabatic Quantum Computation
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