Statistical properties of eigenvalues for an operating quantum computer with static imperfections
نویسندگان
چکیده
We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we discuss the quantum chaos border induced by static imperfections by analyzing the statistical properties of the quantum computer eigenvalues. For small imperfection strengths the level spacing statistics is close to the case of quasi-integrable systems while above the border it is described by the random matrix theory. We have found that the border drops exponentially with the number of qubits, both in the ergodic and quasi-integrable dynamical regimes of the map characterized by a complex phase space structure. On the contrary, the regime with integrable map dynamics remains more stable against static imperfections since in this case the border drops only algebraically with the number
منابع مشابه
Eigenstates of an operating quantum computer: hypersensitivity to static imperfections
We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits nq, it is shown that the ideal eigenstates become mixed and strongly modified by static imperfections above a certain threshold which drops exponentially with nq . Above this threshold the ...
متن کاملModulation Response and Relative Intensity Noise Spectra in Quantum Cascade Lasers
Static properties, relatively intensity noise and intensity modulation response in quantum cascade lasers (QCLs) studied theoretically in this paper. The present rate equations model consists of three equations for the electrons density in the conduction band and one equation for photons density in cavity length. Two equations were derived to calculate the noise and modulation response. Calcula...
متن کاملQuantum chaos and random matrix theory for fidelity decay in quantum computations with static imperfections
We determine the universal law for fidelity decay in quantum computations of complex dynamics in presence of internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied to quantum computations in presence of imperfections. The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chao...
متن کاملRandom numbers and random matrices: Quantum chaos meets number theory
The statistical analysis of the eigenvalues of quantum systems has become an important tool in understanding the connections between classical and quantum physics. The statistical properties of the eigenvalues of a quantum system whose classical counterpart is integrable match those of random numbers. The eigenvalues of a chaotic classical system have statistical properties like those of the ei...
متن کاملQuantum pathology of static internal imperfections in flawed quantum computers
Even in the absence of external influences the operability of a quantum computer (QC) is not guaranteed because of the effects of residual one– and two–body imperfections. Here we investigate how these internal flaws affect the performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC. First we find that the performance of the CNOT gate is considerably better when the two–bod...
متن کامل