Related papers: Further Applications of the Generalised Phase Kick…
The Gottesman-Kitaev-Preskill (GKP) code encodes a qubit into a bosonic mode using periodic wavefunctions. This periodicity makes the GKP code a natural setting for the Zak transform, which is tailor-made to provide a simple description for…
A general algebraic method of quantum corrections evaluations is presented. Quantum corrections to a few classical solutions of Landau-Ginzburg model (phi-in-quadro) are calculated in arbitrary dimensions. The Green function for heat…
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…
We show the power of Bruno Buchberger's seminal Groebner Basis algorithm, interfaced, seamlessly, with what we call symbolic dynamical programming, to automatically generate algebraic equations satisfied by the generating functions…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
Quantum information processing has been one of the pillars of the new information age. In this sense, the control and processing of quantum information plays a fundamental role, and computers capable of manipulating such information have…
We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…
That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
It has previously been established that adiabatic quantum computation, operating based on a continuous Zeno effect due to dynamical phases between eigenstates, is able to realise an optimal Grover-like quantum speedup. In other words, is…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
The Deustch-Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0,1}^n to {0,1} and suppose we have a black-box to compute f. The Deutsch-Jozsa problem is to…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
We provide algorithmic versions of the Polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Ann. of Math., 2025). In particular, we give a polynomial-time algorithm that, given a set $A \subseteq \mathbb{F}_2^n$ with…
This paper examines inverse Cauchy problems that are governed by a kind of elliptic partial differential equation. The inverse problems involve recovering the missing data on an inaccessible boundary from the measured data on an accessible…
We implemented the refined Deutsch-Jozsa algorithm on a 3-bit nuclear magnetic resonance quantum computer, which is the meaningful test of quantum parallelism because qubits are entangled. All of the balanced and constant functions were…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any…
We give quantum speedups of several general-purpose numerical optimisation methods for minimising a function $f:\mathbb{R}^n \to \mathbb{R}$. First, we show that many techniques for global optimisation under a Lipschitz constraint can be…
A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum…