Related papers: Prime Factorization Using Quantum Variational Imag…
We introduce a family of variational quantum algorithms called quantum iterative power algorithms (QIPA) that outperform existing hybrid near-term quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as applied to…
In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
The aim of this work is to show a brand-new way of making deterministic Quantum Computing (short QC), in the sense of Theory of Calculability, by meaning of unitary evolution. We start from the original Shor's Algorithm to explain how 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…
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…
With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic…
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an…
We propose an iterative scheme to factor numbers based on the quantum dynamics of an ensemble of interacting bosonic atoms stored in a trap where the single-particle energy spectrum depends logarithmically on the quantum number. When…
We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…
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…
Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common…
The execution cost of quantum algorithms is typically quantified through asymptotic gate counts and qubit register sizes, yet these metrics do not directly capture which genuinely quantum resources, and in what amount, must be created and…
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…
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…
Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications,…
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…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…