Related papers: Constant-Optimized Quantum Circuits for Modular Mu…
We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting -- a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the…
We optimize the area and latency of Shor's factoring while simultaneously improving fault tolerance through: (1) balancing the use of ancilla generators, (2) aggressive optimization of error correction, and (3) tuning the core adder…
We present optimized quantum circuits for GF$(2^m)$ multiplication and division operations, which are essential computing primitives in various quantum algorithms. Our ancilla-free GF multiplication circuit has the gate count complexity of…
In this paper, we study the generalized problem that minimizes or maximizes a multi-order complex quadratic form with constant-modulus constraints on all elements of its optimization variable. Such a mathematical problem is commonly…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…
Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $\pi/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing…
The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to…
A central aspect for operating future quantum computers is quantum circuit optimization, i.e., the search for efficient realizations of quantum algorithms given the device capabilities. In recent years, powerful approaches have been…
We provide two improvements to Regev's recent quantum factoring algorithm (Journal of the ACM 2025), addressing its space efficiency and its noise-tolerance. Our first contribution is to improve the quantum space efficiency of Regev's…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Recently, various quantum computing and communication tasks have been implemented using IBM's superconductivity-based quantum computers which are available on the cloud. Here, we show that the circuits used in most of those works were not…
Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
Optimising quantum circuits to minimise resource usage is crucial, especially with near-term hardware limited by quantum volume. This paper introduces an optimisation algorithm aiming to minimise non-Clifford gate count and two-qubit gate…
As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the…