Related papers: A Modular, Adaptive, and Scalable Quantum Factorin…

We implement the first open-source quantum computing emulator that includes arithmetic operations, the quantum Fourier transform, and quantum phase estimation. The emulator provides significant savings in both temporal and spatial resources…

Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum…

Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…

Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient…

The Quantum Fourier Transform (QFT) is required by hidden subgroup problem (HSP) algorithms, including Shor's algorithm for factoring. The circuit depth of the QFT remains challenging for near-term hardware. To find shallower alternatives…

The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…

In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with…

Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We…

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…

Given n=p*q with p and q prim and y in Z_{p*q}^*. Shor's Algorithm computes the order r of y, i.e. y^r=1 (mod n). If r=2k is even and y^k \ne -1 (mod n) we can easily compute a non trivial factor of n: gcd(y^k-1,n). In the original paper it…

We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…

The multiplication of superpositions of numbers is a core operation in many quantum algorithms. The standard method for multiplication (both classical and quantum) has a runtime quadratic in the size of the inputs. Quantum circuits with…

Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…

Order finding is the core subroutine of Shor's algorithm. On NISQ hardware, phase estimation output distributions are often distorted by noise, making correct order recovery difficult. We study recoverability in noisy order finding: given a…

In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…

Shor's algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm, showing that the coherence in each step relies on the…

We isolate and generalize a technique implicit in many quantum algorithms, including Shor's algorithms for factoring and discrete log. In particular, we show that the distribution sampled after a Fourier transform over ${\mathbb Z}_p$ can…

The phase estimation algorithm, which is at the heart of a variety of quantum algorithms, including Shor's factoring algorithm, allows a quantum computer to accurately determine an eigenvalue of an unitary operator. Quantum nondemolition…

Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is…