A quantum computer with fixed interaction is universal

We propose a method for implementation of an universal set of one-and two-quantum-bit gates for quantum computation in the system of two coupled electrons with constant non-diagonal exchange interaction. Suppression of the exchange interaction is offered to implement by all-the-time repetition of single spin rotations. Small g-factor difference of electrons allows to address qubits and to avoid strong magnetic field pulses. It is shown by means of numerical experiments that for implementation of one-and two-qubit operations it is sufficient to change the amplitude of the magnetic field within a few Gauss, introducing in a resonance one and then the other electron. To find the evolution of the two-qubit system, we use the algorithms of the optimal control theory.

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“…Parameters A, ω, ϕ, C were chosen to minimize the deviation of the fidelity from 1, using the optimization methods described in Ref. 12. Fig.…”

Section: Resultsmentioning

confidence: 99%

Quantum logic gates from time-dependent global magnetic field in a system with constant exchange

Nenashev

Zinovieva

Двуреченский

et al. 2015

Journal of Applied Physics

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Section: Partial Measurements Mixed Statesmentioning

confidence: 99%

“…The formula (25) sets the general form of the mixed state, which we will identify with the density matrix ρ 1 . However, for a given density matrix ρ 1 , the decomposition of (25) is not uniquely defined. The fact is that a system that is in a pure state |Ψ can also be in another pure state |Φ with a probability of | Ψ|Φ | 2 .…”

Section: Partial Measurements Mixed Statesmentioning

confidence: 99%

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Quantum computations (course of lectures)

Ozhigov¹

2021

Preprint

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This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The course is devoted to a new type of computations based on quantum mechanics. Quantum computations are fundamentally different from classical ones in that they occur in the space of so-called quantum states, and not in ordinary binary strings. The physical implementation of quantum computing -a device called a quantum computer has already been partially created, and its technology continues to develop intensively. Quantum computing is a real process in which the mathematical description is inextricably linked with quantum physics. In particular, the quantum mechanics of complex systems, the model of which is a quantum computer, is currently only being created, so quantum computing is a fundamental direction to a greater extent than an applied one. Therefore, in the course -in general, mathematical, much attention is paid to the physical implementation of this new type of computations. Various forms of quantum computing are considered: the Feynman gate model, fermionic and adiabatic computations. A class of problems is described in which quantum computing is not only more efficient than classical ones, but also cannot be replaced by them. These are the most important tasks of describing complex processes at the predictive level. In particular, using the phenomenon of quantum nonlocality, discovered at the end of the 20th century. Estimates of the ultimate possibility of quantum computing are also given -lower estimates of quantum complexity. The course is designed for students of physics and mathematics and natural science specialties as well as all those interested in this subject. It requires familiarity with the basics of linear algebra and mathematical analysis in the first two courses of the university.

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“…(2) The reversal transformation for QFT can be performed by the following gate array. (1) multiplied by P0 equals it and a unit of the length so that r = j -k then U will be exactly the transformation of a state vector induced by the considered Hamiltonian in the unit time frame.…”

Section: Implementation Of Qft Within Phase Shiftsmentioning

confidence: 99%

<title>Realistic models of a quantum computer</title>

Ozhigov¹

2003

SPIE Proceedings

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We study a realistic quantum computational model with the permanent interaction of diagonal type between qubits. Its universality was proved in quant-ph/0202030. We propose two types of control over computations: random and periodical NOTs. The slowdown of computations in comparison with the abstract model is estimated. It is shown how fermionic computations can be implemented in the framework of this model.

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A quantum computer with fixed interaction is universal

Abstract: It is proved that a quantum computer with fixed and permanent interaction of diagonal type between qubits proposed in the work quant-ph/0201132 is universal. Such computer is controlled only by one-qubit quick transformations, and this makes it fea-

Cited by 10 publications

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Quantum logic gates from time-dependent global magnetic field in a system with constant exchange

Quantum logic gates from time-dependent global magnetic field in a system with constant exchange

Quantum computations (course of lectures)

<title>Realistic models of a quantum computer</title>

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