Universal gates with wires in a row

We give some optimal size generating sets for the group generated by shifts and local permutations on the binary full shift. We show that a single generator, namely the fully asynchronous application of the elementary cellular automaton 57 (or, by symmetry, ECA 99), suffices in addition to the shift. In the terminology of logical gates, we have a single reversible gate whose shifts generate all (finitary) reversible gates on infinitely many binary-valued wires that lie in a row and cannot (a priori) be rearranged. We classify pairs of words u, v such that the gate swapping these two words, together with the shift and the bit flip, generates all local permutations. As a corollary, we obtain analogous results in the case where the wires are arranged on a cycle, confirming a conjecture of Macauley-McCammond-Mortveit and Vielhaber.

FinFET based Design and Performance Analysis of Nano-processor for Low Area, Low Power and Minimum Delay using 32nm

The recent technologies in VLSI chips has grown in terms of scaling of transistor and device parameters but still there is a challenging task for controlling of current between source and drain terminals. For effective control of device current, the FinFET transistors have come into VLSI chip manufacturing, through which current can be effectively controlled. This section addresses the issues present in CMOS technology and majorly concentrated on proposed 4-bit Nano processor using FinFET 32nm technology by using Cadence Virtuoso software tool. In the proposed Nanoprocessor design, the first portion of the design is done using 4bit ALU which includes all basic and universal gates, high speed adder, multiplier and multiplexer. The Carry Save Adder (CSA) and multiplier are the major sub component which can optimize the power consumption and area reduction. The second portion of the proposed Nano processor design is 4-bit 6T SRAM and encoder and decoder and also using Artificial Neural Network (ANN). All these sub components are designed at analog transistors (Schematic level) through which the Graphic Data System (GDS-II) is generated through mask layout design. Finally, the verification and validation are done using DRC and LVS and at the last chip level circuit is generated for chip fabrication. The ALU is designed by using CMOS inverters and the designed ALU schematic is simulated through 32nm FinFET using technological library and compared with CMOS technology which is simulated through 32nm CMOS library (without FinFET). The power consumption of AND, OR, XOR, NOT, NAND gates, SRAM, Encoder, Decoder and ANN are 36.09nW, 64.970nW, 61.13nW, 33.31nW, 37.45nW, 32.5% with optimization in power dissipation of 47% along with optimization in leakage current, with 2.68uW, 1.98uW and 7.5% improvement in power consumption and 0.5% information loses are compressed subsequently respectively. The basic gates, universal gates, CSA, subtraction and MUX are integrated for 4-bit ALU design and its delay, power consumption and area are found to be 0.104nsec, 314.4uW and 56.8μsqm respectively.

Design and Performance Analysis of 4-bit Nano-processor Design for Low Area, Low Power and Minimum Delay Using 32nm FinFET Technology

The recent technologies in VLSI Chips have grown in terms of scaling of transistor and device parameters but still, there is challenging task for controlling current between the source and drain terminals. For effective control of device current, the FinFET transistors have come into VLSI chip, through which current can be controlled effectively. This paper is to address the issues present in CMOS technology and majorly concentrated on the proposed 4-bit Nano processor using FinFET 32nm technology by using the Cadence Virtuoso software tool. In the proposed Nano processor, the first part is to design using 4bit ALU which includes all basic and universal gates, efficient and high-speed adder, multiplier, and multiplexer. The Carry Save Adder (CSA) and multiplier are the major subcomponents which can optimize the power consumption and area reduction. The second part of the proposed Nano processor is 4-bit 6T SRAM and Encoder and decoder and also Artificial Neural Network (ANN). All these subcomponents are designed at analog transistors (Schematic level) through which the Graphic Data System (GDS-II) is generated through mask layout design. Finally, the verification and validation are done using DRC and LVS, at the last chip-level circuit is generated for chip fabrication. The ALU is designed by using CMOS inverters and the designed ALU schematic is simulated through 32nm FinFET technological library and compared with CMOS technology which is simulated through 32nm CMOS library (without FinFET). The power consumption of AND, OR, XOR, NOT, NAND gates, SRAM, Encoder, Decoder and ANN are 36.09nW, 64.970nW, 61.13nW, 33.31nW, 37.45nW, 32.5% optimization in power dissipation and 47% optimization in leakage current, 2.68uW, 1.98uW and 7.5% improvement in power consumption and 0.5% information loses compressed subsequently respectively. The basic gates and universal gates, CSA, subtraction, and MUX are integrated for 4-bit ALU design, and its delay, power consumption, and area are 0.104nsec, 314.4uW, and 56.8usqm respectively

Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics

Clifford circuits are insufficient for universal quantum computation or creating tt-designs with t\ge 4t≥4. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8)(π/8) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.