دسته بندی:

محاسبات کوانتومی - Quantum-Computing

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سال انتشار:

2022

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عنوان انگلیسی مقاله:

Efficient Floating Point Arithmetic for Quantum Computers

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ترجمه فارسی عنوان مقاله:

محاسبات ممیز شناور کارآمد برای کامپیوترهای کوانتومی

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منبع:

ieee - ieee Access;2022;10; ;10:1109/ACCESS:2022:3188251

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نویسنده:

RAPHAEL SEIDEL 1, NIKOLAY TCHOLTCHEV1, SEBASTIAN BOCK 1, COLIN KAI-UWE BECKER 1, AND MANFRED HAUSWIRTH1,2, (Senior Member, IEEE)

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چکیده انگلیسی:

One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of qubits, we can easily reach situations where we pay less than a single quantum gate per data point for data-processing instructions, which would be rather expensive in classical computing. Formulating such instructions in terms of quantum gates, however, still remains a challenging task. Laying out the foundational functions for more advanced data-processing is therefore a subject of paramount importance for advancing the realm of quantum computing. In this paper, we introduce the formalism of encoding so called-semi-boolean polynomials. As it turns out, arithmetic Z=2nZ ring operations can be formulated as semi-boolean polynomial evaluations, which allows convenient generation of unsigned integer arithmetic quantum circuits. For arithmetic evaluations, the resulting algorithm has been known as Fourier-arithmetic. We extend this type of algorithm with additional features, such as ancillafree in-place multiplication and integer coefficient polynomial evaluation. Furthermore, we introduce a tailor-made method for encoding signed integers succeeded by an encoding for arbitrary floating-point numbers. This representation of floating-point numbers and their processing can be applied to any quantum algorithm that performs unsigned modular integer arithmetic. We discuss some further performance enhancements of the semi boolean polynomial encoder and finally supply a complexity estimation. The application of our methods to a 32-bit unsigned integer multiplication demonstrated a 90% circuit depth reduction compared to carry-ripple approaches.
INDEX TERMS: Quantum arithmetic | quantum computing | floating point arithmetic.

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قیمت: رایگان

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توضیحات اضافی:

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