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arXiv:1306.3760

A Space-Efficient Design for Reversible Floating Point Adder in Quantum Computing

Nguyen, Trung Duc, Rodney Van Meter

Published Jun 17, 2013• 7 citations
arXivHTMLPDF

Abstract

Reversible logic has applications in low-power computing and quantum computing. However, there are few existing designs for reversible floating-point adders and none suitable for quantum computation. In this paper we propose a space-efficient reversible floating-point adder, suitable for binary quantum computation, improving the design of Nachtigal et al. Our work focuses on improving the reversible designs of the alignment unit and the normalization unit, which are the most expensive parts. By changing a few elements of the existing algorithm, including the circuit designs of the RLZC (reversible leading zero counter) and converter, we have reduced the cost about 68%. We also propose fault-tolerant designs for the circuits. The KQ for our fault-tolerant design is almost sixty times as expensive as for a 32-bit fixed-point addition. We note that the floating-point representation makes in-place, truly reversible arithmetic impossible, requiring us to retain both inputs, which limits the sustainability of its use for quantum computation.

DOI
10.48550/arxiv.1306.3760

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Reversible logic has applications in low-power computing and quantum computing. However, there are few existing designs for reversible floating-point adders and none suitable for quantum computation. In this paper we propose a space-efficient reversible floating-point adder, suitable for binary quantum computation, improving the design of Nachtigal et al. Our work focuses on improving the reversible designs of the alignment unit and the normalization unit, which are the most expensive parts. By changing a few elements of the existing algorithm, including the circuit designs of the RLZC (reversible leading zero counter) and converter, we have reduced the cost about 68%. We also propose fault-tolerant designs for the circuits. The KQ for our fault-tolerant design is almost sixty times as expensive as for a 32-bit fixed-point addition. We note that the floating-point representation makes in-place, truly reversible arithmetic impossible, requiring us to retain both inputs, which limits the sustainability of its use for quantum computation.
Reversible logic has applications in low-power computing and quantum computing. However, there are few existing designs for reversible floating-point adders and none suitable for quantum computation. In this article, we propose a resource-efficient reversible floating-point adder, suitable for binary quantum computation, improving the design of Nachtigal et al. [2011]. Our work focuses on improving the reversible designs of the alignment unit and the normalization unit, which are the most expensive parts. By changing a few elements of the existing algorithm, including the circuit designs of the RLZC (reversible leading zero counter) and converter, we have reduced the cost by about 68%. We also propose quantum designs adapted to use gates from fault-tolerant libraries. The KQ for our fault-tolerant design is almost 60 times as expensive as for a 32-bit fixed-point addition. We note that the floating-point representation makes in-place, truly reversible arithmetic impossible, requiring us to retain both inputs, which limits the sustainability of its use for quantum computation.
Reversible logic is characterized by its feature of being a prominent application in low-power conventional computers and the most compatible logic in quantum computers. Quantum circuits executes quantum algorithms and are important in a new generation of advanced computing. However, they are highly error-prone and also subject to the use of limited and sensitive physical resources like qubits and quantum gates. This paper introduces a comprehensive fault tolerant quantum-based reversible circuit which can calculate a high variety number of arithmetic and logic operations. It uses both: parity preserving method for detecting one or an odd number of bit errors, and Clifford + T implementation for protecting circuits against decoherence faults. First, we propose a new fault-tolerant (parity preserving and Clifford + T) adder/subtractor and derive a quantum reversible Arithmetic and Logic Unit (ALU). These modules reach the most optimized extent of circuit line, ancilla inputs, and garbage outputs according to the logical analysis done in this work. This article focuses on reducing T-cost metrics in conjunction with enhancing the number of operations and quantum costs in proposed circuits compared to other counterparts. We propose 4-bit fault tolerant ALU derived from our proposed single-bit module to show the proposed circuit can be extended to any larger size. The proposed circuit is implemented in the Qiskit simulation tool, and output results confirm the accuracy of our design functionality. The proposed full adder/ subtractor achieves an average of 64% and 43%, and the proposed ALU circuit achieves an average of 38% and 27% improvement in T-count and T-depth, respectively compared to their counterparts. The proposed reversible quantum-optimized fault tolerant adder/subtractor and ALU units can be applied as the basic part of DSP systems and quantum processor units in quantum computing devices.
Reversible logic is gaining significance in the context of emerging technologies such as quantum computing since reversible circuits do not lose information during computation and there is one-to-one mapping between the inputs and outputs. 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. In reversible circuits, in addition to the primary inputs, some constant input bits are used to realize different logic functions which are referred to as ancilla inputs and are overheads that need to be reduced. Further, the garbage outputs which do not contribute to any useful computations but are needed to maintain reversibility are also overheads that need to be reduced in reversible designs. 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.
Reversible logic is becoming increasingly important with the rise of technologies like quantum computing, as it retains information during computation and maintains a one-to-one mapping between input and output patterns. Quantum circuits are inherently reversible and the best computational model in quantum computing systems. Some quantum signal processing applications like filters and image processing applications require the results of arithmetic operations to be saturated. Saturation occurs when adding two numbers with the same sign and this can be done through a quantum saturating adder. This paper proposed a reversible quantum saturating adder with efficient quantum criteria like quantum cost, number of ancilla, and number of garbage outputs. We firstly propose a reversible n-bit quantum saturation generator block which is applied to a quantum adder and construct a quantum saturating adder circuit. The proposed circuit is simulated using the Quirk online tool and the result confirms the accuracy of the design. This design achieves 18% and 33% improvement in quantum cost and garbage outputs, compared to its counterpart, respectively.
This paper presents the design, optimization, and simulation of arithmetic circuits using reversible logic for quantum computing applications. The motivation behind this work is to achieve resource-efficient computation through reduced quantum cost, minimized garbage outputs, and lower ancilla requirements. The methodology involves implementing Half Adders, Full Adders, Multiplexers, and Ripple Carry Adders (RCAs) using Toffoli and Peres gates. The proposed 8-bit RCA achieves a quantum cost of 58 using 24 qubits, 8 garbage outputs, and 6 ancilla inputs—showing a significant improvement over conventional Toffoli-based designs that require higher quantum cost and resources. Simulations were conducted on IBM Qiskit and Google Colab using the Qiskit SDK to validate circuit correctness and scalability. The obtained results demonstrate superior resource efficiency and confirm the feasibility of reversible-logic-based quantum arithmetic as a foundation for scalable quantum arithmetic logic units (ALUs) and processors.
Reversible logic is becoming increasingly important with the rise of technologies like quantum computing, as it retains information during computation and maintains a direct match between each input and its corresponding output. Quantum circuits are inherently reversible and the best computational model in quantum computing systems. Quantum computers require quantum processors. A critical component of any computer's processor is the arithmetic component, that handles binary operations like addition, subtraction, multiplication, and division. Notably, multiplication can be accomplished by repeatedly adding, while division can be carried out by repeatedly subtracting. This paper proposes a new design of quantum-controlled adder/subtractor (QCAS) with efficient quantum criteria like delay, quantum cost, number of ancilla and of garbage outputs. We propose a quantum reversible controlled full adder/subtractor block which is applied to construct an n-bit quantum adder/subtractor circuit. The proposed circuit is simulated using the Quirk online tool and the result confirms the accuracy of the design. This design achieves 28.5% and 61.3% improvement in delay and garbage outputs, and 14% and 41.2% increase in quantum cost and constant input, compared to its counterpart, respectively.