1,658 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
Fast Quantum Modular Exponentiation
We present a detailed analysis of the impact on modular exponentiation of
architectural features and possible concurrent gate execution. Various
arithmetic algorithms are evaluated for execution time, potential concurrency,
and space tradeoffs. We find that, to exponentiate an n-bit number, for storage
space 100n (twenty times the minimum 5n), we can execute modular exponentiation
two hundred to seven hundred times faster than optimized versions of the basic
algorithms, depending on architecture, for n=128. Addition on a neighbor-only
architecture is limited to O(n) time when non-neighbor architectures can reach
O(log n), demonstrating that physical characteristics of a computing device
have an important impact on both real-world running time and asymptotic
behavior. Our results will help guide experimental implementations of quantum
algorithms and devices.Comment: to appear in PRA 71(5); RevTeX, 12 pages, 12 figures; v2 revision is
substantial, with new algorithmic variants, much shorter and clearer text,
and revised equation formattin
Quantum Circuit Optimization of Arithmetic circuits using ZX Calculus
Quantum computing is an emerging technology in which quantum mechanical
properties are suitably utilized to perform certain compute-intensive
operations faster than classical computers. Quantum algorithms are designed as
a combination of quantum circuits that each require a large number of quantum
gates, which is a challenge considering the limited number of qubit resources
available in quantum computing systems. Our work proposes a technique to
optimize quantum arithmetic algorithms by reducing the hardware resources and
the number of qubits based on ZX calculus. We have utilised ZX calculus rewrite
rules for the optimization of fault-tolerant quantum multiplier circuits where
we are able to achieve a significant reduction in the number of ancilla bits
and T-gates as compared to the originally required numbers to achieve
fault-tolerance. Our work is the first step in the series of arithmetic circuit
optimization using graphical rewrite tools and it paves the way for advancing
the optimization of various complex quantum circuits and establishing the
potential for new applications of the same
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