Related papers: Unconditional correctness of recent quantum algori…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It…
We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a…
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
Solitude verification is arguably one of the simplest fundamental problems in distributed computing, where the goal is to verify that there is a unique contender in a network. This paper devises a quantum algorithm that exactly solves the…
Shor's algorithm is examined critically from the standpoint of it's eventual use to obtain the factors of large integers.
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
We present improved quantum circuit for modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. While previous work mostly focuses on minimizing the number of qubits or the…
We introduce a novel deterministic quantum search algorithm that provides a practical alternative to conventional probabilistic search approaches. Our scheme eliminates the inherent uncertainty of quantum search without relying on arbitrary…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21.…
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…
Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…