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Andrei Galiautdinov

Publications and source records attributed to Andrei Galiautdinov.

45 records · Page 3Linked to original sources
arXiv2007

Single-step controlled-NOT logic from any exchange interaction

A self-contained approach to studying the unitary evolution of coupled qubits is introduced, capable of addressing a variety of physical systems described by exchange Hamiltonians containing Rabi terms. The method automatically determines both the Weyl chamber steering trajectory and the accompanying local rotations. Particular attention is paid to the case of anisotropic exchange with tracking controls, which is solved analytically. It is shown that, if computational subspace is well isolated, any exchange interaction can always generate high-fidelity, single-step controlled-NOT (CNOT) logic, provided that both qubits can be individually manipulated. The results are then applied to superconducting qubit architectures, for which several CNOT gate implementations are identified. The paper concludes with consideration of two CNOT gate designs having high efficiency and operating with no significant leakage to higher-lying non-computational states.

quant-ph↗
arXiv2007

Controlled-NOT gate design for Josephson phase qubits with tunable inductive coupling: Weyl chamber steering and area theorem

Superconducting qubits with tunable coupling are ideally suited for fast and accurate implementation of quantum logic. Here we present a simple approach, based on Weyl chamber steering, to CNOT gate design for inductively coupled phase qubits with tunable coupling strength g. In the presence of simultaneous rf pulses on the individual qubits that appropriately track the coupling strength as it is varied, we show that an infinite family of switching sequences preserving the time integral or "area" of g can be used to generate CNOT logic. We demonstrate our approach by considering time-dependencies most likely to be used in actual implementations: trapezoidal, sine, and soft quartic (also known as Landau's hat).

quant-ph↗
arXiv2007

Generation of high-fidelity controlled-not logic gates by coupled superconducting qubits

Building on the previous results of the Weyl chamber steering method, we demonstrate how to generate high-fidelity controlled-not by direct application of certain, physically relevant Hamiltonians with fixed coupling constants containing Rabi terms. Such Hamiltonians are often used to describe two superconducting qubits driven by local rf-pulses. It is found that in order to achieve 100% fidelity in a system with capacitive coupling of strength g one Rabi term suffices. We give the exact values of the physical parameters needed to implement such CNOT. The gate time and all possible Rabi frequencies are found to be t=pi/(2g) and Omega_1/g = sqrt(64n^2-1), n=1,2,3,... . Generation of a perfect CNOT in a system with inductive coupling, characterized by additional constant k, requires the presence of both Rabi terms. The gate time is again t = pi/(2g), but now there is an infinite number of solutions, each of which is valid in a certain range of k and is characterized by a pair of positive integers (n,m). We distinguish two cases, depending on the sign of the coupling constant: (1) the antiferromagnetic case (k>=0); (2) the ferromagnetic case (k<=0). The paper concludes with consideration of fidelity degradation by switching to resonance. Simulation of time-evolution based on the 4th order Magnus expansion reveals characteristics of the gate similar to those found in the exact case, with slightly shorter gate time and shifted values of Rabi frequencies.

cond-mat.supr-con↗
arXiv2004

Elementary Operations

A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is substantially richer than Boolean algebra. We use it as a bridge to a Clifford algebraic quantum logic that is richer than the usual Hilbert space quantum logic and admits iteration. This leads to a higher-order Clifford-algebraic logic. We formulate a toy Dirac equation with this logic. It isexactly Lorentz-invariant, yet it approximates the usual Dirac equation as closely as desired and all its variables have finite spectra. It is worth considering as a Lorentz-invariant improvement on lattice space-times.

quant-ph↗
arXiv2004

Modified Einstein equations

Standard general relativity fails to take into account the changes in coordinates induced by the variation of metric in the Hilbert action principle. We propose to include such changes by introducing a fundamental compensating tensor field and modifying the usual variational procedure.

gr-qc↗
arXiv2003

Ultraquantum Dynamics

Segal proposed ultraquantum commutation relations with two ultraquantum constants hbar' and hbar'' besides Planck's quantum constant hbar with a variable i. The Heisenberg quantum algebra is a contraction - in a more general sense than that of Inonu and Wigner - of the Segal ultraquantum algebra. The usual constant i arises as a vacuum order-parameter in the quantum limit where hbar' and hbar'' approach zero. One physical consequence is a discrete spectrum for canonical variable and space-time coordinates. Another is an interconvention of time and energy accompnying space-time meltdown (disorder), with a fundamental conversion factor of some kilograms of energy per second.

hep-th↗
arXiv2002

The Qubits of Qunivac

We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a reversible quantum logic for the Quantum Universe As Computer, or Qunivac. Qunivac has an orthogonal group of cosmic dimensionality. It has a Clifford algebra of ``cosmonions,'' extending the quaternions to a cosmological number of anticommuting units. Its qubits obey Clifford-Wilczek statistics and are associated with unit cosmonions. This makes it relatively easy to program the Dirac equation on Qunivac in a Lorentz-invariant way. Qunivac accommodates a field theory and a gauge theory. Its gauge group is necessarily a quantum group.

hep-th↗
arXiv2000

Clifford algebra as quantum language

We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors and spinors respectively. Physical spinors may actually be plexors describing quantum ensembles, not simple individuals. We use Clifford statistics to define quantum fields on a quantum space-time, and to formulate a quantum dynamics-field-space-time unity that evades the compactification problem. The quantum bits of history regarded as a quantum computation seem to obey a Clifford statistics.

hep-th↗