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A logarithmic-depth quantum carry-lookahead adder
TLDR
The quantum carry-lookahead (QCLA) adder proposed in this paper can be used within current modular multiplication circuits to reduce substantially the run-time of Shor's algorithm.Abstract:
We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead (QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both in-place and out-of-place versions, as well as versions that add modulo 2^n and modulo 2^n - 1.
Previously, the linear-depth ripple-carry addition circuit has been the method of choice. Our work reduces the cost of addition dramatically with only a slight increase in the number of required qubits. The QCLA adder can be used within current modular multiplication circuits to reduce substantially the run-time of Shor's algorithm.read more
Citations
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Journal ArticleDOI
Halving the cost of quantum addition
TL;DR: In this article, the number of T gates needed to perform an n-bit adder was reduced from 8n + O(1) to 4n+O(1).
Journal ArticleDOI
A linear-size quantum circuit for addition with no ancillary qubits
TL;DR: An affirmative answer to the question of Kutin as to whether a linear-depth quantum circuit for addition can be constructed without ancillary qubits using the ripple-carry approach is given.
Journal ArticleDOI
Halving the cost of quantum addition
TL;DR: An n-bit controlled adder circuit with T-count of 8n+O(1), a temporary adder that can be computed for the same cost as the normal adder but whose result can be kept until it is later uncomputed without using T gates, and some other constructions whose T- Count is improved by the temporary logical-AND.
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Improved quantum circuits for elliptic curve discrete logarithms
TL;DR: A full implementation of point addition in the Q# quantum programming language that allows unit tests and automatic quantum resource estimation for all components and presents various trade-offs between different cost metrics including the number of qubits, circuit depth and $T$-gate count.
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A note on quantum related-key attacks
TL;DR: A quantum version of the Winternitz-Hellman related-key attack model, where if the secret key is uniquely determined by a small number of plaintext-ciphertext pairs, the block cipher can be evaluated efficiently, and a superposition of related keys can be queried, then the key can be extracted efficiently.
References
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Journal ArticleDOI
Quantum networks for elementary arithmetic operations.
TL;DR: This work provides an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation, and shows that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorized.
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Addition on a Quantum Computer
TL;DR: A new method for computing sums on a quantum computer is introduced that uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits.
Journal ArticleDOI
A One-Microsecond Adder Using One-Megacycle Circuitry
A. Weinberger,J. L. Smith +1 more
TL;DR: An analysis of the functional representation of the carry digits in the addition process shows that the one-megacycle circuitry of SEAC and DYSEAC can be organized logically to permit the formation of many successive carries simultaneously.