Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

Ermilov, A. S.; Zobov, V. E.

doi:10.1134/s0030400x07120211

Cited by 9 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Matrix ( 13) can be diagonalized by means of a sequence of selective rotations. Such sequences were explicitly found for N = 3, 5, and 7 in [21] and N = 4 and 8 in [22]. For the gate (…”

Section: Quantum Fourier Transform On a Qutritmentioning

confidence: 76%

Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei

Shauro

Zobov

2013

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

We demonstrate the relation between a global phase of the quantum gate and the layout of energy levels of its effective Hamiltonian required for implementing the gate for minimum time.By an example of the quantum Fourier transform gate for a qudit represented by a quadrupole nucleus with the spin I = 1, the effective Hamiltonians and minimum implementation times for different global phases are found. Using numerical optimal control methods, the problem of the global phase in searching for the optimal pulse shape is considered in detail for the quantum

show abstract

“…Matrix ( 13) can be diagonalized by means of a sequence of selective rotations. Such sequences were explicitly found for N = 3, 5, and 7 in [21] and N = 4 and 8 in [22]. For the gate (…”

Section: Quantum Fourier Transform On a Qutritmentioning

confidence: 76%

Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei

Shauro

Zobov

2013

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…According to (6), we should multiply this product by the opera tors exp(-itH c ). It turned out that, when deriving H c (4), we could apply a simpler transformation, omitting phase shifts and a part of operators of y rotations in the decompositions for the operators of QFT [26,36]: (29) Substituting the products obtained into (5), we find an evolution operator that implements the factorization algorithm. In the computations, we will use the fol lowing property of neighboring factors in (5):…”

Section: Implementation Of Algorithm On the System Of Two Quadrupole mentioning

confidence: 99%

Implementation of a quantum adiabatic algorithm for factorization on two qudits

Zobov

Ermilov

2012

J. Exp. Theor. Phys.

Self Cite

View full text Add to dashboard Cite

Implementation of an adiabatic quantum algorithm for factorization on two qudits with the number of levels d 1 and d 2 is considered. A method is proposed for obtaining a time dependent effective Hamiltonian by means of a sequence of rotation operators that are selective with respect to the transitions between neighboring levels of a qudit. A sequence of RF magnetic field pulses is obtained, and a factoriza tion of the numbers 35, 21, and 15 is numerically simulated on two quadrupole nuclei with spins 3/2 (d 1 = 4) and 1 (d 2 = 3).

show abstract

“…The Hadamard gate for qudits essentially performs the order-d Fourier transform, likewise the Hadamard gate for qubits performs the order-2 Fourier transform. Methods for implementation of the H (d) gate are proposed in [2,49].…”

Section: Hadamard Gatementioning

confidence: 99%

“…Using q qudits of d levels [2], [49], and setting N = d q , the q qudits basis consists of |j = |j 1 . .…”

Section: Quantum Fourier Transformmentioning

confidence: 99%

See 1 more Smart Citation

Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform

Pavlidis,

Floratos

2017

Preprint

View full text Add to dashboard Cite

We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an alternative basis after they have been Fourier transformed. Several arithmetic circuits operating on Fourier transformed integers have appeared in the literature for two level qubits. Here we extend these techniques on multilevel qudits, as they may offer some advantages relative to qubits implementations. The arithmetic circuits presented can be used as basic building blocks for higher level algorithms such as quantum phase estimation, quantum simulation, quantum optimization etc., but they can also be used in the implementation of a quantum fractional Fourier transform as it is shown in a companion work presented separately.

show abstract

Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

Cited by 9 publications

References 21 publications

Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei

Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei

Implementation of a quantum adiabatic algorithm for factorization on two qudits

Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform

Contact Info

Product

Resources

About