paper / aramharrow / Feb 9
This paper demonstrates that a broad class of representation-theoretic multiplicities, including plethysm coefficients, belong to the #BQP complexity class. This finding unifies and extends previous results on the quantum complexity of various coefficients, leveraging multiple applications of the Schur transform. The research also indicates that these multiplicities are naturally in GapP, allowing for polynomial-time classical algorithms under fixed parameters.
quantum-complexityrepresentation-theoryplethysm-coefficientscomputational-complexityschur-transformquantum-information
“A broad class of representation-theoretic multiplicities, including plethysm coefficients, are in #BQP.”
paper / aramharrow / Feb 3
This paper details advancements in quantum algorithms for pricing exotic derivatives, extending proven quadratic speedups beyond the simplified Black-Scholes model to more complex models like Cox-Ingersoll-Ross (CIR) and a variant of Heston's stochastic volatility model. It also introduces a quantum Milstein sampler for general models lacking "fast-forwardability," enabling quadratic speedups for multi-dimensional stochastic processes. The research critiques quantum PDE solvers, identifying theoretical barriers to achieving quantum speedups in that domain.
quantum-algorithmsderivative-pricingquantitative-financemonte-carlostochastic-modelsfinancial-modeling
“Quantum algorithms can achieve quadratic speedups in derivative pricing for models beyond Black-Scholes.”
paper / aramharrow / Oct 9
This paper introduces efficient algorithms for approximating quantum states using randomized mixtures of sparse states. These methods improve upon deterministic approximations by achieving quadratically better trace distances and enhanced robustness. The practical application of this research lies in improving the accuracy of matrix product state algorithms without increasing memory requirements.
quantum-informationquantum-statessparse-statesmatrix-product-statesquantum-algorithmsconvex-optimization
“Randomized mixtures of sparse states can achieve quadratically improved trace distances compared to deterministic methods.”
paper / aramharrow / Sep 30
This paper articulates a co-design methodology for hybrid quantum-classical algorithms, aiming for empirical quantum advantage (EQA) in biomarker discovery. The authors contend that a persistent EQA is achievable despite continuous classical algorithmic improvements by integrating quantum subroutines for tasks like feature selection. Resource analysis indicates a plausible EQA region on near/intermediate-term quantum hardware, highlighting potential clinical impact beyond oncology.
quantum-computingbiomarker-discoveryhybrid-algorithmsprecision-oncologyfeature-selectionquantum-advantage
“Empirical quantum advantage (EQA) is defined as a measurable performance gain of quantum hardware over state-of-the-art classical methods for the same task.”
paper / aramharrow / Jun 25
This paper introduces FreeQuantum, a computational pipeline that combines quantum-mechanical calculations with machine learning to accurately determine biomolecular free energies. The method addresses the challenge of scaling accurate quantum calculations to large biomolecules by employing a two-fold quantum embedding strategy. It demonstrates viability for drug-protein interactions, outlining how quantum computers can enhance these simulations with exponential speedups for electronic interactions.
quantum-computingbiomolecular-free-energiesdrug-discoverymachine-learningquantum-mechanicscomputational-chemistrybiophysics
“Accurate free energy calculations for biomolecular processes require computational models that capture both electronic interactions and entropic contributions.”