arXiv subjects

Sophia Simon

Publications and source records attributed to Sophia Simon.

8 recordsLinked to original sources

arXiv2026

Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems

We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes an entry of the solution matrix with query complexity $\widetilde{\mathcal{O}}(\nu \mathcal{L} t/\epsilon)$, where the constant $\nu$ depends on the problem parameters, $\mathcal{L}$ involves a time integral of upper bounds on the norms of evolution operators, and $\epsilon$ is the error. In particular, $\nu \mathcal{L}$ is linear in $t$ for unitary dynamics and can be a constant for dissipative dynamics. Our result contrasts prior quantum approaches for differential equations that typically require exponential time for this problem due to the encoding in a quantum state, which can lead to exponentially small amplitudes. We demonstrate the utility of the algorithm through an end-to-end application, namely the simulation of dissipative dynamics for non-interacting fermions, which can be extended to other quantum and classical systems. We compare with classical algorithms and give evidence of polynomial quantum speedups for systems in a lattice, which become more pronounced for systems with long-range interactions and can be shown to be exponential in general. We also provide a lower bound of $\Omega(\nu \mathcal{L} t/\epsilon)$ for unitary or dissipative dynamics that proves our algorithm is optimal up to logarithmic factors.

quant-ph↗

arXiv2025

Fullqubit alchemist: Quantum algorithm for alchemical free energy calculations

Accurately computing the free energies of biological processes is a cornerstone of computer-aided drug design, but it is a daunting task. The need to sample vast conformational spaces and account for entropic contributions makes the estimation of binding free energies very expensive. While classical methods, such as thermodynamic integration and alchemical free energy calculations, have significantly contributed to reducing computational costs, they still face limitations in terms of efficiency and scalability. We tackle this through a quantum algorithm for the estimation of free energy differences by adapting the existing Liouvillian approach and introducing several key algorithmic improvements. We directly implement the Liouvillian operator and provide an efficient description of electronic forces acting on both nuclear and electronic particles on the quantum ground state potential energy surface. This leads to super-polynomial runtime scaling improvements in the precision of our Liouvillian simulation approach and quadratic improvements in the scaling with the number of particles relative to prior quantum algorithms. Second, our algorithm calculates free energy differences via a fully quantum implementation of thermodynamic integration and alchemy, thereby foregoing expensive entropy estimation subroutines used in prior works. Our results open new avenues towards the application of quantum computers in drug discovery.

quant-ph↗

arXiv2025

Dividing and Conquering the Van Vleck Catastrophe

The quantum-computational cost of determining ground state energies through quantum phase estimation depends on the overlap between an easily preparable initial state and the targeted ground state. The Van Vleck orthogonality catastrophe has frequently been invoked to suggest that quantum computers may not be able to efficiently prepare ground states of large systems because the overlap with the initial state tends to decrease exponentially with the system size, even for non-interacting systems. We show that this intuition is not necessarily true. Specifically, we introduce a divide-and-conquer strategy that repeatedly uses phase estimation to merge ground states of increasingly larger subsystems. We provide rigorous bounds for this approach and show that if the minimum success probability of each merge is lower bounded by a constant, then the query complexity of preparing the ground state of $N$ interacting systems is in $O(N^{\log\log(N)} {\rm poly}(N))$, which is quasi-polynomial in $N$, in contrast to the exponential scaling anticipated by the Van Vleck catastrophe. We also discuss sufficient conditions on the Hamiltonian that ensure a quasi-polynomial running time.

quant-ph↗

arXiv2025

Efficient Quantum Optimization via Dynamical Simulation

We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We focus on the setting where the objective function can \emph{only} be accessed via a phase oracle. Our first two algorithms can find local optima of a differentiable function $f: \mathbb{R}^N \rightarrow \mathbb{R}$ by simulating either classical or quantum dynamics with friction via a time-dependent Hamiltonian. We show that for the benchmark problem of optimizing a locally quadratic objective function, these methods require a total of $O(N^2\kappa^2/h_x^2\epsilon)$ queries to a phase oracle to find an $\epsilon$-approximate local optimum, where $\kappa$ is the condition number of the Hessian matrix and $h_x$ is the discretization spacing. In contrast, we show that methods based on gradient descent require $O(N^{3/2}(1/\epsilon)^{\kappa \log(3)/4})$ queries. This corresponds to an exponential separation between the query upper bounds for the benchmark problem. Our third algorithm can find the global optimum of $f$ by preparing a classical low-temperature thermal state via simulation of the classical Liouvillian operator associated with the Nos\'e Hamiltonian. We use results from the quantum thermodynamics literature to bound the thermalization time for the discrete system. Additionally, we analyze barren plateau effects that commonly plague quantum optimization algorithms and observe that our approach is vastly less sensitive to this problem than standard gradient-based optimization. Our results suggests that these dynamical optimization approaches may be far more scalable for future quantum machine learning, optimization and variational experiments than was widely believed.

quant-ph↗

arXiv2024

Amplified Amplitude Estimation: Exploiting Prior Knowledge to Improve Estimates of Expectation Values

We provide a method for estimating the expectation value of an operator that can utilize prior knowledge to accelerate the learning process on a quantum computer. Specifically, suppose we have an operator that can be expressed as a concise sum of projectors whose expectation values we know a priori to be $O(ε)$. In that case, we can estimate the expectation value of the entire operator within error $ε$ using a number of quantum operations that scales as $O(1/\sqrtε)$. We then show how this can be used to reduce the cost of learning a potential energy surface in quantum chemistry applications by exploiting information gained from the energy at nearby points. Furthermore, we show, using Newton-Cotes methods, how these ideas can be exploited to learn the energy via integration of derivatives that we can estimate using a priori knowledge. This allows us to reduce the cost of energy estimation if the block-encodings of directional derivative operators have a smaller normalization constant than the Hamiltonian of the system.

quant-ph↗

arXiv2023

Improved precision scaling for simulating coupled quantum-classical dynamics

We present a super-polynomial improvement in the precision scaling of quantum simulations for coupled classical-quantum systems in this paper. Such systems are found, for example, in molecular dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman-von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a super-polynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density.

quant-ph↗

arXiv2022

Ultrasound detection of emergent photons in generic quantum spin ice

Experimental identification of quantum spin ice (QSI), a U(1) quantum spin liquid on the pyrochlore lattice hosting emergent photons, is a major challenge in frustrated magnets. In this work, we propose ultrasound measurements as a novel tool for probing the emergent photons of various QSI phases. Our analysis includes QSI phases in non-Kramers doublet compounds such as $\rm{Pr}_2 \rm{Zr}_2 \rm{O}_7$ as well as dipolar-octupolar Kramers doublet compounds such as $\rm{Ce}_2 \rm{Zr}_2 \rm{O}_7$. The latter may host emergent photons associated with an octupolar component which renders them difficult to detect with inelastic neutron scattering. We demonstrate theoretically how the speed of the emergent photons can be obtained from the renormalization of the phonon spectrum and show that ultrasound measurements provide a means of distinguishing the dipolar from the octupolar QSI phase in dipolar-octupolar materials.

cond-mat.str-el↗

arXiv2022

Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry

Using a systematic relation between topological gapless phases in three dimensions and topological gapped phases in two dimensions, we identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy "Fermi arcs" at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hinge modes, or (iv) flat zero-energy hinge arcs connecting nodes only at finite momentum. Bulk-boundary correspondence relates the hinge states to the bulk topology protecting the nodal point or loop. We classify all HOTS for all tenfold-way classes with an order-two crystalline (anti-)symmetry, such as mirror, twofold rotation, or inversion.

cond-mat.mes-hall↗