arXiv subjects

A. Yu. Kitaev

Publications and source records attributed to A. Yu. Kitaev.

5 recordsLinked to original sources

arXiv2020

Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane

We study the SYK$_4$ model with a weak SYK$_2$ term of magnitude $Γ$ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, $J/N \ll Γ\ll J/\sqrt{N}$, fluctuations of the Schwarzian mode are suppressed, and the SYK$_4$ mean-field solution remains valid beyond the timescale $t_0 \sim N/J$ up to $t_* \sim J/Γ^2$. Out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent $2πT$, but its prefactor scales as $T$ at low temperatures $T \leq Γ$.

cond-mat.str-el↗

arXiv2012

Quantum Superinductor with Tunable Non-Linearity

We report on the realization of a superinductor, a dissipationless element whose microwave impedance greatly exceeds the resistance quantum. The design of the superinductor, implemented as a ladder of nanoscale Josephson junctions, enables tuning of the inductance and its nonlinearity by a weak magnetic field. The Rabi decay time of the superinductor-based qubit exceeds 1 microsecond. The high kinetic inductance and strong nonlinearity offer new types of functionality, including the development of qubits protected from both flux and charge noises, fault tolerant quantum computing, and high-impedance isolation for electrical current standards based on Bloch oscillations.

cond-mat.supr-con↗

arXiv1998

Quantum codes on a lattice with boundary

A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of alternating pieces with two different types of boundary conditions. Logical operators are described in terms of relative homology groups.

quant-ph↗

arXiv1997

Fault-tolerant quantum computation by anyons

A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.

quant-ph↗

arXiv1995

Quantum measurements and the Abelian Stabilizer Problem

We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation.

quant-ph↗