Related papers: Quantum simulation of the integer factorization pr…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
We demonstrate that a single-photon field modulated with n different pseudorandom phase sequences (PPSs) can constitute a 2^n-dimensional Hilbert space that contains tensor product structure. By using the single photon field modulated with…
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…
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of…
The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This…
Designing and implementing algorithms for medium and large scale quantum computers is not easy. In previous work we have suggested, and developed, the idea of using machine learning techniques to train a quantum system such that the desired…
We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beamsplitters, phase shifters, single photon…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum…
We demonstrate that locally connected networks of machines that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of quantum computation. We present simulation results for basic quantum…
Feynman's circuit-to-Hamiltonian construction enables the mapping of a quantum circuit to a time-independent Hamiltonian. This model introduces a Hilbert space made from an ancillary clock register tracking the progress of the computation.…
We present a quantum algorithm for simulating quantum chemistry with gate complexity $\tilde{O}(N^{1/3} \eta^{8/3})$ where $\eta$ is the number of electrons and $N$ is the number of plane wave orbitals. In comparison, the most efficient…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
In this work a method based on a topological invariance of rational tangles commonly used in knot theory determines filling factors in the fractional quantum Hall effect. The main sustain for this hypothesis are the Schubert's theorems…
The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of…
Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…