Related papers: Prime Factorization of Arbitrary Integers with a L…

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…

The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the…

Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…

General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…

We report the first experimental realization of the prime number quantum potential $V_N(x)$, defined as the potential entering the single-particle Schr\"{o}dinger Hamiltonian with eigenvalues given by the first $N$ prime numbers. We use…

We present a quantum algorithm that provides a general approach for obtaining the energy spectrum of a physical system without making a guess on its eigenstates. In this algorithm, a probe qubit is coupled to a quantum register $R$ which…

The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…

There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of…

Bayesian methods which utilize Bayes' theorem to update the knowledge of desired parameters after each measurement, are used in a wide range of quantum science. For various applications in quantum science, efficiently and accurately…

We consider energy absorption in an externally driven complex system of noninteracting fermions with the chaotic underlying dynamics described by the unitary random matrices. In the absence of quantum interference the energy absorption rate…

We introduce a randomized algorithm based on qDrift to compute Hamiltonian dynamics on digital quantum computers. We frame it as physDrift because conservation laws in physics are obeyed during evolution of arbitrary quantum states.…

A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…

We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…

We present superconducting quantum circuits which exhibit atomic energy spectrum and selection rules as ladder and lambda three-level configurations designed by means of genetic algorithms. These heuristic optimization techniques are…

A new strategy for trapping quantum particles is presented, which behaves like an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed…

Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation and communication. Here we propose a method for the generation of very good approximations to highly squeezed vacuum states…

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr\"obner bases. We present a novel scalable algorithm which combines the two approaches and leads to the…

We consider a non-interacting Fermi gas in a combined harmonic and periodic potential. We calculate the energy spectrum and simulate the motion of the gas after sudden replacement of the trap center. For different parameter regimes, the…

We propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there…

Rabi oscillations of a two-level atom appear as a quantum interference effect between the amplitudes associated to atomic superpositions, in analogy with the classic double-slit experiment which manifests a sinusoidal interference pattern.…