scholarly journals Exactly solvable Hamiltonians in quantum computing

2021 ◽  
Author(s):  
Grigori Giorgadze
Keyword(s):  
Quantum Computing ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

scholarly journals SUSUSY Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 171-176 ◽  
Author(s):  
David J. Fernández C.
Keyword(s):  
Quantum Mechanics ◽  
Shift Operator ◽  
Second Order ◽  
Parametric Family ◽  
First Order ◽  
Shift Operators ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

scholarly journals New quasi-exactly solvable Hamiltonians in two dimensions

1994 ◽  
Vol 159 (3) ◽  
pp. 503-537 ◽  
Author(s):  
Artemio González-López ◽  
Niky Kamran ◽  
Peter J. Olver
Keyword(s):  
Two Dimensions ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

scholarly journals EVALUATION OF DECOHERENCE FOR QUANTUM COMPUTING ARCHITECTURES: QUBIT SYSTEM SUBJECT TO TIME-DEPENDENT CONTROL

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1476-1495 ◽  
Author(s):  
DMITRY SOLENOV ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Quantum Computing ◽  
Heat Bath ◽  
Time Dependent ◽  
Approximation Schemes ◽  
Qubit System ◽  
Exactly Solvable ◽  
Rotating Wave ◽  
Reduced Density ◽  
Short Time ◽  
External Time

We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.

scholarly journals New exactly solvable Hamiltonians: Shape invariance and self-similarity

1993 ◽  
Vol 48 (4) ◽  
pp. 2786-2797 ◽  
Author(s):  
D. T. Barclay ◽  
R. Dutt ◽  
A. Gangopadhyaya ◽  
Avinash Khare ◽  
A. Pagnamenta ◽  
...  
Keyword(s):  
Self Similarity ◽  
Shape Invariance ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

scholarly journals DARBOUX TRANSFORMATIONS FOR QUASI-EXACTLY SOLVABLE HAMILTONIANS

2002 ◽  
Vol 17 (11) ◽  
pp. 1577-1587 ◽  
Author(s):  
N. DEBERGH ◽  
B. VAN DEN BOSSCHE ◽  
BORIS F. SAMSONOV
Keyword(s):  
Second Order ◽  
Darboux Transformations ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Complex Valued ◽  
Exactly Solvable Hamiltonians

We construct new quasi-exactly solvable one-dimensional potentials through Darboux transformations. Three directions are investigated: Reducible and two types of irreducible second-order transformations. The irreducible transformations of the first type give singular intermediate potentials and the ones of the second type give complex-valued intermediate potentials while final potentials are meaningful in all cases. These developments are illustrated on the so-called radial sextic oscillator.

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