Related papers: Efficient realization of quantum primitives for Sh…
The practical application of quantum technologies to chemical problems faces significant challenges, particularly in the treatment of realistic basis sets and the accurate inclusion of electron correlation effects. A direct approach to…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
Simulation is essential for developing quantum hardware and algorithms. However, simulating quantum circuits on classical hardware is challenging due to the exponential scaling of quantum state space. While factorized tensors can greatly…
This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization,…
Commercially impactful quantum algorithms such as quantum chemistry and Shor's algorithm require a number of qubits and gates far beyond the capacity of any existing quantum processor. Distributed architectures, which scale horizontally by…
While significant progress has been made on the hardware side of quantum computing, support for high-level quantum programming abstractions remains underdeveloped compared to classical programming languages. In this article, we introduce…
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…
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to…
We introduce PennyLane's Lightning suite, a collection of high-performance state-vector simulators targeting CPU, GPU, and HPC-native architectures and workloads. Quantum applications such as QAOA, VQE, and synthetic workloads are…
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…
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…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
With the increasing rise of publicly available high level quantum computing languages, the field of Quantum Computing has reached an important milestone of separation of software from hardware. Consequently, the study of Quantum Algorithms…
The security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994,…
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,…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…
With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum…