Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems

We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal O~(dκlog⁡(1/ϵ)) query complexity for a d-sparse matrix, where κ is the condition number, and ϵ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.

Low-Power Adiabatic Computing with Modified Quasi Static Energy Recovery Logic of MQSERL 4x4 multiplier

This work depends on another methodology for limiting vitality utilization in semi static vitality recuperation rationale of Modified Quasi Static Energy Recovery Logic (MQSERL) circuit which includes enhancement by expelling the non-adiabatic misfortunes totally. Vitality recouping hardware dependent on adiabatic standards is a promising system driving towards low power superior circuit plan. The productivity of such circuits might be expanded by lessening the adiabatic and non-adiabatic misfortunes drawn by them amid the charging and recuperation tasks. In this paper, execution of the proposed rationale style is broke down and contrasted and CMOS in their agent inverters, entryways, flip- flop and snake circuits. Every one of the circuit was reproduced by test system of TANNER TOOL in 0.18μm innovation. In our proposed inverter the vitality proficiency has been enhanced to practically 30% and 20% up to 20MHz and 20fF outside load capacitance in contrast with CMOS and MQSERL circuits individually. Our proposed circuit gives vitality proficient execution up to 100 MHz and in this way it has ended up being utilized in superior VLSI hardware.