Related papers: Simplified Factoring Algorithms for Validating Sma…
Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package…
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…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
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…
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
We consider a probabilistic quantum implementation of a variable of the Pocklington-Lehmer $N-1$ primality test using Shor's algorithm. O($\log^3 N \log\log N \log\log\log N$) elementary q-bit operations are required to determine the…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
With the race to build large-scale quantum computers and efforts to exploit quantum algorithms for efficient problem solving in science and engineering disciplines, the requirement to have efficient and scalable verification methods are of…
Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities.…
When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam.…
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally…
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size…
Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…