267 research outputs found
Quantum Circuits for Toom-Cook Multiplication
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 are further improved by employing reversible pebble
games through uncomputing the intermediate results. The asymptotic bounds for
different performance metrics of the proposed quantum circuit are superior to
the prior implementations of multiplier circuits using schoolbook and Karatsuba
algorithms
Improved reversible and quantum circuits for Karatsuba-based integer multiplication
Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor\u27s algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to implement arithmetic as low as possible. This applies in particular to the number of qubits required in the implementation as for the foreseeable future this number is expected to be small. We present a reversible circuit for integer multiplication that is inspired by Karatsuba\u27s recursive method. The main improvement over circuits that have been previously reported in the literature is an asymptotic reduction of the amount of space required from O(n^1.585) to O(n^1.427). This improvement is obtained in exchange for a small constant increase in the number of operations by a factor less than 2 and a small asymptotic increase in depth for the parallel version. The asymptotic improvement are obtained from analyzing pebble games on complete ternary trees
A technology based complexity model for reversible Cuccaro ripple-carry adder
Reversible logic provides an alternative to classical computing, that may overcome many of the power dissipation problems. The paper presents a simple complexity model, from the study of a cascade of Cuccaro adders processed in standard 0.35 micrometer CMOS technology
Scalable Design and Synthesis of Reversible Circuits
The expectations on circuits are rising with their number of applications, and technologies alternative to CMOS are becoming more important day by day. A promising alternative is reversible computation, a computing paradigm with applications in quantum computation, adiabatic circuits, program inversion, etc. An elaborated design flow is not available to reversible circuit design yet. In this work, two directions are considered: Exploiting the conventional design flow and developing a new flow according to the properties of reversible circuits. Which direction should be taken is not obvious, so we discuss the possible assets and drawbacks of taking either direction. We present ideas which can be exploited and outline open challenges which still have to be addressed. Preliminary results obtained by initial implementations illustrate the way to go. By this we present and discuss two promising and complementary directions for the scalable design and synthesis of reversible circuits
How to Efficiently Handle Complex Values? Implementing Decision Diagrams for Quantum Computing
Quantum computing promises substantial speedups by exploiting quantum
mechanical phenomena such as superposition and entanglement. Corresponding
design methods require efficient means of representation and manipulation of
quantum functionality. In the classical domain, decision diagrams have been
successfully employed as a powerful alternative to straightforward means such
as truth tables. This motivated extensive research on whether decision diagrams
provide similar potential in the quantum domain -- resulting in new types of
decision diagrams capable of substantially reducing the complexity of
representing quantum states and functionality. From an implementation
perspective, many concepts and techniques from the classical domain can be
re-used in order to implement decision diagrams packages for the quantum realm.
However, new problems -- namely how to efficiently handle complex numbers --
arise. In this work, we propose a solution to overcome these problems.
Experimental evaluations confirm that this yields improvements of orders of
magnitude in the runtime needed to create and to utilize these decision
diagrams. The resulting implementation is publicly available as a quantum DD
package at http://iic.jku.at/eda/research/quantum_dd
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