Related papers: Quantum simulation with sum-of-squares spectral am…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
We introduce matrix quantum phase-space distributions. These extend the idea of a quantum phase-space representation via projections onto a density matrix of global symmetry variables. The method is applied to verification of low-loss…
Following the first paper on quantum algorithms for SDP-solving by Brand\~ao and Svore in 2016, rapid developments has been made on quantum optimization algorithms. Recently Brand\~ao et al. improved the quantum SDP-solver in the so-called…
Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrodinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
The scalar auxiliary variable (SAV) approach is a very popular and efficient method to simulate various phase field models. To save the computational cost, a new SAV approach is given by introducing a new variable $\theta$. The new SAV…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial…
We demonstrate the ability of a phase-sensitive amplifier (PSA) to pre-amplify a selected quadrature of one mode of a two-mode squeezed state in order to improve the measurement of two-mode quantum correlations that exist before degradation…
Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both…
Quantum simulation is a promising pathway toward practical quantum advantage by simulating large-scale quantum systems. In this work, we propose communication-efficient distributed quantum simulation protocols by exploring three quantum…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…
In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…
We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let $p = \sum_i q^2_i$ be an…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
Quantum circuit simulations are critical for evaluating quantum algorithms and machines. However, the number of state amplitudes required for full simulation increases exponentially with the number of qubits. In this study, we leverage data…
We present SPARC: Simulation Package for Ab-initio Real-space Calculations. SPARC can perform Kohn-Sham density functional theory calculations for isolated systems such as molecules as well as extended systems such as crystals and surfaces,…
Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condition for nonnegativity is the Sum of Squares (SOS) property,…
Particle swam optimization (PSO) is a popular stochastic optimization method that has found wide applications in diverse fields. However, PSO suffers from high computational complexity and slow convergence speed. High computational…
We study sum of squares (SOS) relaxations to optimize polynomial functions over a set $V\cap R^n$, where $V$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description, represents…