Related papers: Reversible addition circuit using one ancillary bi…

We present a new linear-depth ripple-carry quantum addition circuit. Previous addition circuits required linearly many ancillary qubits; our new adder uses only a single ancillary qubit. Also, our circuit has lower depth and fewer gates…

To build a general-purpose quantum computer, it is crucial for the quantum devices to implement classical boolean logic. A straightforward realization of quantum boolean logic is to use auxiliary qubits as intermediate storage. This…

This paper is motivated by two key observations. First, Toffoli ladders can be implemented in three distinct ways: with linear or polylogarithmic depth using no ancilla, or with logarithmic depth using ancilla qubits. Second, two…

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…

Reversible logic has become one of the promising research directions in low power dissipating circuit design in the past few years and has found its applications in low power CMOS design, cryptography, optical information processing and…

We improve the number of T gates needed to perform an n-bit adder from 8n + O(1) to 4n + O(1). We do so via a "temporary logical-AND" construction which uses four T gates to store the logical-AND of two qubits into an ancilla and zero T…

Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using…

Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…

Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the…

Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource…

Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum…

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…

The Toffoli gate is an important universal quantum gate, and will alongside the Clifford gates be available in future fault-tolerant quantum computing hardware. Many quantum algorithms rely on performing arbitrarily small single-qubit…

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…

The Toffoli gate is the essential ingredient for reversible computing, an energy efficient classical computational paradigm that evades the energy dissipation resulting from Landauer's principle. In this paper we analyze different setups to…

The family of $n$-bit Toffoli gates, with the two-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. We present a…

We design a circuit structure with linear depth to implement an $n$-qubit Toffoli gate. The proposed construction uses a quadratic-size circuit consists of elementary 2-qubit controlled-rotation gates around the x axis and uses no ancilla…

In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds…

The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…

We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements…