Related papers: Calculating response functions of coupled oscillat…
In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the…
We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both…
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…
Quantum harmonic oscillators are central to many modern quantum technologies. We introduce a method to determine the frequency noise spectrum of oscillator modes through coupling them to a qubit with continuously driven…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase…
We show that the Schr\"{o}dinger equation for the quantum harmonic oscillator can be derived as an approximation to the Newtonian mechanics of a classical harmonic oscillator subject to a random force for time intervals $O( m / \hbar)$,…
Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…