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Himanshu Thapliyal

Publications and source records attributed to Himanshu Thapliyal.

At least 55 records · Page 3Linked to original sources
arXiv2018

Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth

Quantum circuits for mathematical functions such as division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for integer division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. In this work, we propose two quantum integer division circuits. The first proposed quantum integer division circuit is based on the restoring division algorithm and the second proposed design implements the non-restoring division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring division circuit achieves average T-count savings from $79.03 \%$ to $91.69 \%$ compared to the existing works. Our proposed non-restoring division circuit achieves average T-count savings from $49.75 \%$ to $90.37 \%$ compared to the existing works. Further, both our proposed designs have linear T-depth.

quant-ph↗
arXiv2018

Quantum Computing Circuits and Devices

The development of quantum computing technologies builds on the unique features of quantum physics while borrowing familiar principles from the design of conventional devices. We introduce the fundamental concepts required for designing and operating quantum computing devices by reviewing state of the art efforts to fabricate and demonstrate quantum gates and qubits. We summarize the near-term challenges for devices based on semiconducting, superconducting, and trapped ion technologies with an emphasis on design tools as well as methods of verification and validation. We then discuss the generation and synthesis of quantum circuits for higher-order logic that can be carried out using quantum computing devices.

quant-ph↗
arXiv2017

Design of Efficient Reversible Logic Based Binary and BCD Adder Circuits

In this work, we present a class of new designs for reversible binary and BCD adder circuits. The proposed designs are primarily optimized for the number of ancilla inputs and the number of garbage outputs and are designed for possible best values for the quantum cost and delay. First, we propose two new designs for the reversible ripple carry adder: (i) one with no input carry $c_0$ and no ancilla input bits, and (ii) one with input carry $c_0$ and no ancilla input bits. The proposed reversible ripple carry adder designs with no ancilla input bits have less quantum cost and logic depth (delay) compared to their existing counterparts in the literature. In these designs, the quantum cost and delay are reduced by deriving designs based on the reversible Peres gate and the TR gate. Next, four new designs for the reversible BCD adder are presented based on the following two approaches: (i) the addition is performed in binary mode and correction is applied to convert to BCD when required through detection and correction, and (ii) the addition is performed in binary mode and the result is always converted using a binary to BCD converter. The proposed reversible binary and BCD adders can be applied in a wide variety of digital signal processing applications and constitute important design components of reversible computing.

quant-ph↗
arXiv2017

T-count Optimized Design of Quantum Integer Multiplication

Quantum circuits of many qubits are extremely difficult to realize; thus, the number of qubits is an important metric in a quantum circuit design. Further, scalable and reliable quantum circuits are based on Clifford + T gates. An efficient quantum circuit saves quantum hardware resources by reducing the number of T gates without substantially increasing the number of qubits. Recently, the design of a quantum multiplier is presented by Babu [1] which improves the existing works in terms of number of quantum gates, number of qubits, and delay. However, the recent design is not based on fault-tolerant Clifford + T gates. Also, it has large number of qubits and garbage outputs. Therefore, this work presents a T-count optimized quantum circuit for integer multiplication with only $4 \cdot n + 1$ qubits and no garbage outputs. The proposed quantum multiplier design saves the T-count by using a novel quantum conditional adder circuit. Also, where one operand to the controlled adder is zero, the conditional adder is replaced with a Toffoli gate array to further save the T gates. To have fair comparison with the recent design by Babu and get an actual estimate of the T-count, it is made garbageless by using Bennett's garbage removal scheme. The proposed design achieves an average T-count savings of $47.55\%$ compared to the recent work by Babu. Further, comparison is also performed with other recent works by Lin et. al. [2], and Jayashree et. al.[3]. Average T-count savings of $62.71\%$ and $26.30\%$ are achieved compared to the recent works by Lin et. al., and Jayashree et. al., respectively.

quant-ph↗
arXiv2017

Design of Quantum Circuits for Galois Field Squaring and Exponentiation

This work presents an algorithm to generate depth, quantum gate and qubit optimized circuits for $GF(2^m)$ squaring in the polynomial basis. Further, to the best of our knowledge the proposed quantum squaring circuit algorithm is the only work that considers depth as a metric to be optimized. We compared circuits generated by our proposed algorithm against the state of the art and determine that they require $50 \%$ fewer qubits and offer gates savings that range from $37 \%$ to $68 \%$. Further, existing quantum exponentiation are based on either modular or integer arithmetic. However, Galois arithmetic is a useful tool to design resource efficient quantum exponentiation circuit applicable in quantum cryptanalysis. Therefore, we present the quantum circuit implementation of Galois field exponentiation based on the proposed quantum Galois field squaring circuit. We calculated a qubit savings ranging between $44\%$ to $50\%$ and quantum gate savings ranging between $37 \%$ to $68 \%$ compared to identical quantum exponentiation circuit based on existing squaring circuits.

quant-ph↗
arXiv2016

Quantum Circuit Design of Integer Division Optimizing Ancillary Qubits and T-Count

In this paper, we present Clifford+T gates based quantum circuit design of integer division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring division algorithm. The proposed quantum circuit of integer division consists of (i) quantum circuitry of conditional addition operation, (ii) quantum circuitry of integer subtraction. To design ancillary and T-count optimized design of quantum integer division, the optimized quantum circuit design of integer conditional addition operation and integer subtraction are presented. The proposed quantum integer division circuitry has 50\% improvement in terms of ancillary qubits, and 90\% improvement in terms of T-count compared to the existing design of integer quantum division based on quantum fourier transform.

quant-ph↗
arXiv2016

Ancilla-Input and Garbage-Output Optimized Design of a Reversible Quantum Integer Multiplier

A reversible logic has application in quantum computing. A reversible logic design needs resources such as ancilla and garbage qubits to reconfigure circuit functions or gate functions. The removal of garbage qubits and ancilla qubits are essential in designing an efficient quantum circuit. In the literature, there are multiple designs that have been proposed for a reversible multiplication operation. A multiplication hardware is essential for the circuit design of quantum algorithms, quantum cryptanalysis, and digital signal processing (DSP) applications. The existing designs of reversible quantum integer multipliers suffer from redundant garbage qubits. In this work, we propose a reversible logic based, garbage-free and ancilla qubit optimized design of a quantum integer multiplier. The proposed quantum integer multiplier utilizes a novel add and rotate methodology that is specially suitable for a reversible computing paradigm. The proposed design methodology is the modified version of a conventional shift and add method. The proposed design of the quantum integer multiplier incorporates add or no operation based on multiplier qubits and followed by a rotate right operation. The proposed design of the quantum integer multiplier produces zero garbage qubits and shows an improvement ranging from 60% to 90% in ancilla qubits count over the existing work on reversible quantum integer multipliers.

quant-ph↗
arXiv2011

Reversible Logic Based Concurrent Error Detection Methodology For Emerging Nanocircuits

Reversible logic has promising applications in emerging nanotechnologies, such as quantum computing, quantum dot cellular automata and optical computing, etc. Faults in reversible logic circuits that result in multi-bit error at the outputs are very tough to detect, and thus in literature, researchers have only addressed the problem of online testing of faults that result single-bit error at the outputs based on parity preserving logic. In this work, we propose a methodology for the concurrent error detection in reversible logic circuits to detect faults that can result in multi-bit error at the outputs. The methodology is based on the inverse property of reversible logic and is termed as 'inverse and compare' method. By using the inverse property of reversible logic, all the inputs can be regenerated at the outputs. Thus, by comparing the original inputs with the regenerated inputs, the faults in reversible circuits can be detected. Minimizing the garbage outputs is one of the main goals in reversible logic design and synthesis. We show that the proposed methodology results in 'garbageless' reversible circuits. A design of reversible full adder that can be concurrently tested for multi-bit error at the outputs is illustrated as the application of the proposed scheme. Finally, we showed the application of the proposed scheme of concurrent error detection towards fault detection in quantum dot cellular automata (QCA) emerging nanotechnology.

cs.AR↗
arXiv2007

Combined Integer and Variable Precision (CIVP) Floating Point Multiplication Architecture for FPGAs

In this paper, we propose an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication. The proposed work will of great importance in applications which requires variable precision floating point multiplication such as multi-media processing applications. In the proposed architecture/methodology, we propose the replacement of existing 18x18 bit and 25x18 bit dedicated multipliers in FPGAs with dedicated 24x24 bit and 24x9 bit multipliers, respectively. We have proved that our approach of providing the dedicated 24x24 bit and 24x9 bit multipliers in FPGAs will make them efficient for performing integer as well as single precision, double precision, and Quadruple precision floating point multiplications.

cs.AR↗
arXiv2007

Partial Reversible Gates(PRG) for Reversible BCD Arithmetic

IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. Furthermore, in the recent years reversible logic has emerged as a promising computing paradigm having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. The major goal in reversible logic is to minimize the number of reversible gates and garbage outputs. Thus, this paper proposes the novel concept of partial reversible gates that will satisfy the reversibility criteria for specific cases in BCD arithmetic. The partial reversible gate is proposed to minimize the number of reversible gates and garbage outputs, while designing the reversible BCD arithmetic circuits.

cs.AR↗
arXiv2006

Reversible Logic to Cryptographic Hardware: A New Paradigm

Differential Power Analysis (DPA) presents a major challenge to mathematically-secure cryptographic protocols. Attackers can break the encryption by measuring the energy consumed in the working digital circuit. To prevent this type of attack, this paper proposes the use of reversible logic for designing the ALU of a cryptosystem. Ideally, reversible circuits dissipate zero energy. Thus, it would be of great significance to apply reversible logic to designing secure cryptosystems. As far as is known, this is the first attempt to apply reversible logic to developing secure cryptosystems. In a prototype of a reversible ALU for a crypto-processor, reversible designs of adders and Montgomery multipliers are presented. The reversible designs of a carry propagate adder, four-to-two and five-to-two carry save adders are presented using a reversible TSG gate. One of the important properties of the TSG gate is that it can work singly as a reversible full adder. In order to design the reversible Montgomery multiplier, novel reversible sequential circuits are also proposed which are integrated with the proposed adders to design a reversible modulo multiplier. It is intended that this paper will provide a starting point for developing cryptosystems secure against DPA attacks.

cs.CR↗
arXiv2006

Combined Integer and Floating Point Multiplication Architecture(CIFM) for FPGAs and Its Reversible Logic Implementation

In this paper, the authors propose the idea of a combined integer and floating point multiplier(CIFM) for FPGAs. The authors propose the replacement of existing 18x18 dedicated multipliers in FPGAs with dedicated 24x24 multipliers designed with small 4x4 bit multipliers. It is also proposed that for every dedicated 24x24 bit multiplier block designed with 4x4 bit multipliers, four redundant 4x4 multiplier should be provided to enforce the feature of self repairability (to recover from the faults). In the proposed CIFM reconfigurability at run time is also provided resulting in low power. The major source of motivation for providing the dedicated 24x24 bit multiplier stems from the fact that single precision floating point multiplier requires 24x24 bit integer multiplier for mantissa multiplication. A reconfigurable, self-repairable 24x24 bit multiplier (implemented with 4x4 bit multiply modules) will ideally suit this purpose, making FPGAs more suitable for integer as well floating point operations. A dedicated 4x4 bit multiplier is also proposed in this paper. Moreover, in the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. It is not possible to realize quantum computing without reversible logic. Thus, this paper also paper provides the reversible logic implementation of the proposed CIFM. The reversible CIFM designed and proposed here will form the basis of the completely reversible FPGAs.

cs.AR↗
arXiv2006

Reduced Area Low Power High Throughput BCD Adders for IEEE 754r Format

IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. Firstly, this paper proposes novel two transistor AND and OR gates. The proposed AND gate has no power supply, thus it can be referred as the Powerless AND gate. Similarly, the proposed two transistor OR gate has no ground and can be referred as Groundless OR. Secondly for IEEE 754r format, two novel BCD adders called carry skip and carry look-ahead BCD adders are also proposed in this paper. In order to design the carry look-ahead BCD adder, a novel 4 bit carry look-ahead adder called NCLA is proposed which forms the basic building block of the proposed carry look-ahead BCD adder. Finally, the proposed two transistors AND and OR gates are used to provide the optimized small area low power high throughput circuitries of the proposed BCD adders.

cs.AR↗
arXiv2006

VLSI Implementation of RSA Encryption System Using Ancient Indian Vedic Mathematics

This paper proposes the hardware implementation of RSA encryption/decryption algorithm using the algorithms of Ancient Indian Vedic Mathematics that have been modified to improve performance. The recently proposed hierarchical overlay multiplier architecture is used in the RSA circuitry for multiplication operation. The most significant aspect of the paper is the development of a division architecture based on Straight Division algorithm of Ancient Indian Vedic Mathematics and embedding it in RSA encryption/decryption circuitry for improved efficiency. The coding is done in Verilog HDL and the FPGA synthesis is done using Xilinx Spartan library. The results show that RSA circuitry implemented using Vedic division and multiplication is efficient in terms of area/speed compared to its implementation using conventional multiplication and division architectures

cs.AR↗
arXiv2006

Reversible Programmable Logic Array (RPLA) using Fredkin & Feynman Gates for Industrial Electronics and Applications

In recent years, reversible logic has emerged as a promising computing paradigm having application in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not reversible. In this paper, the authors have proposed reversible programmable logic array (RPLA) architecture using reversible Fredkin and Feynman gates. The proposed RPLA has n inputs and m outputs and can realize m functions of n variables. In order to demonstrate the design of RPLA, a 3 input RPLA is designed which can perform any 28 functions using the combination of 8 min terms (23). Furthermore, the application of the designed 3 input RPLA is shown by implementing the full adder and full subtractor functions through it.

cs.AR↗
arXiv2006

Novel Reversible TSG Gate and Its Application for Designing Components of Primitive Reversible/Quantum ALU

In recent years, reversible logic has emerged as a promising computing paradigm having application in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not reversible. This paper utilizes a new 4 * 4 reversible gate called TSG gate to build the components of a primitive reversible/quantum ALU. The most significant aspect of the TSG gate is that it can work singly as a reversible full adder, that is reversible full adder can now be implemented with a single gate only. A Novel reversible 4:2 compressor is also designed from the TSG gate which is later used to design a novel 8x8 reversible Wallace tree multiplier. It is proved that the adder, 4:2 compressor and multiplier architectures designed using the TSG gate are better than their counterparts available in literature, in terms of number of reversible gates and garbage outputs. This is perhaps, the first attempt to design a reversible 4:2 compressor and a reversible Wallace tree multiplier as far as existing literature and our knowledge is concerned. Thus, this paper provides an initial threshold to build more complex systems which can execute complicated operations using reversible logic.

cs.AR↗
arXiv2006

Novel Reversible Multiplier Architecture Using Reversible TSG Gate

In the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not reversible. Recently a 4 * 4 reversible gate called TSG is proposed. The most significant aspect of the proposed gate is that it can work singly as a reversible full adder, that is reversible full adder can now be implemented with a single gate only. This paper proposes a NXN reversible multiplier using TSG gate. It is based on two concepts. The partial products can be generated in parallel with a delay of d using Fredkin gates and thereafter the addition can be reduced to log2N steps by using reversible parallel adder designed from TSG gates. Similar multiplier architecture in conventional arithmetic (using conventional logic) has been reported in existing literature, but the proposed one in this paper is totally based on reversible logic and reversible cells as its building block. A 4x4 architecture of the proposed reversible multiplier is also designed. It is demonstrated that the proposed multiplier architecture using the TSG gate is much better and optimized, compared to its existing counterparts in literature; in terms of number of reversible gates and garbage outputs. Thus, this paper provides the initial threshold to building of more complex system which can execute more complicated operations using reversible logic.

cs.AR↗
arXiv2006

A New Reversible TSG Gate and Its Application For Designing Efficient Adder Circuits

In the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not reversible. This paper proposes a new 4 * 4 reversible gate called TSG gate. The proposed gate is used to design efficient adder units. The most significant aspect of the proposed gate is that it can work singly as a reversible full adder i.e reversible full adder can now be implemented with a single gate only. The proposed gate is then used to design reversible ripple carry and carry skip adders. It is demonstrated that the adder architectures designed using the proposed gate are much better and optimized, compared to their existing counterparts in literature; in terms of number of reversible gates and garbage outputs. Thus, this paper provides the initial threshold to building of more complex system which can execute more complicated operations using reversible logic.

cs.AR↗