Quantum Techniques for Accurate Parameter Estimation

An issue with Bayesian inference — used, for example, in our adaptive quantum sensing experiments (e.g. https://lnkd.in/dZUjs-4h, https://lnkd.in/di4t3aJe ) — is that numerical methods such as particle filtering typically scale poorly with the number of parameters, a problem known as the 'curse of dimensionality. Here we show how variational Bayesian inference, which approximates the posterior probability distribution with a family of simpler functions, can instead be used to characterize quantum systems with a large number of parameters. We test our framework on the identification of individual nuclear spins with an NV centre in diamond, showing we can learn 15 nuclear spins (30 hyperfine values) in timescales compatible with real-time adaptivity. Work led by Federico Belliardo, with Altmann Yoann Erik Gauger and Tim Taminiau - you can read it on arXiv here: https://lnkd.in/dt5FdemJ Next step will be to use it to develop real-time adaptive protocols to minimize the long data acquisition times to identify single nuclear spins for nanoscale magnetic resonance (Q-BIOMED - The UK Quantum Biomedical Sensing Research Hub) and to use them as long-lived qubits in quantum networks (The Integrated Quantum Networks (IQN) Hub).

In a recent paper published in Physical Review Research, we reported a scheme for tomography of quantum simulators which can be described by a Bose-Hubbard Hamiltonian while having measurement access to only some sites on the boundary of the lattice. We present an algorithm that uses the experimentally routine transmission and two-photon correlation functions, measured at the boundary, to extract the Hamiltonian parameters at the standard quantum limit. Furthermore, by building on quantum enhanced spectroscopy protocols that, we show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit.

🔍 Quantum Fourier Transform + Quantum Phase Estimation 📘 What These Topics Cover Quantum Fourier Transform (QFT) The QFT is the quantum version of the Discrete Fourier Transform. It transforms a quantum state from the computational basis into the Fourier basis, encoding amplitude & phase information efficiently. It requires fewer gates than classical FFT for certain problems, and is a key subroutine in many quantum algorithms (often paired with phase estimation). Quantum Phase Estimation (QPE) A fundamental algorithm used to estimate the phase (eigenvalue) associated with an eigenstate of a given unitary operator. If U∣ψ⟩=e2πiθ∣ψ⟩, QPE helps extract θ. Works by using two registers: one for “counting qubits” (to accumulate phase), another for the eigenstate, then applying controlled-unitary operations + inverse QFT + measurements. ⚙ Key Applications & Why They Matter Shor’s Algorithm (Factoring & Discrete Logarithms): QFT + QPE are central to Shor’s, which underlies much of the interest in quantum algorithms for cryptography. Quantum Chemistry & Hamiltonian Simulation: QPE lets you extract energy eigenvalues of Hamiltonians (molecules, physical systems), important for predicting molecular behavior. Linear Systems Solver (HHL Algorithm): Uses phase estimation to invert matrices in superposition in an efficient manner. Hidden Subgroup Problems & Period Finding: QFT and QPE are used in solving these, which generalize many important computational problems. 🛠 Challenges & Considerations Circuit Depth & Resource Demands: QPE (and QFT) typically require many qubits and gates; too deep circuits are problematic on current noisy hardware. Precision vs. Qubits Trade-off: More “counting qubits” yield better precision in the phase estimate, but also more resource cost. Error Accumulation & Noise: Errors in unitary operations, decoherence, and gate errors degrade the output—making real implementations much harder than theoretical ones. 💡 Takeaway Mastering QFT & QPE is critical—they’re not just abstract theory. Once you understand how phase is encoded, transformed, and read out, you unlock the ability to build powerful quantum algorithms. The principles here are what separate the possible from the impossible in quantum speedups. #Day15 #QuantumComputing #QFT #QuantumFourierTransform #PhaseEstimation #Shor #QuantumChemistry #QuantumAlgorithms #Qohort3 #21DaysChallenge QuCode

A More General Quantum Credit Risk Analysis Framework   "..Monte Carlo simulations are computationally expensive due to the rare-event simulation problems inherent in credit risk evaluation. Additionally, Monte Carlo simulations can only generate pseudo-random variables, and the quality of the simulation can be compromised by the appearance of patterns." "To overcome these limitations, researchers have explored new methods, such as those based on quantum computing, which can naturally generate true random samples due to the probabilistic nature of qubits. Moreover, quantum amplitude estimation (QAE) has shown promise in estimating the value at risk and offers a quadratic speedup over classical Monte Carlo methods."   By Emanuele Dri , Antonello Aita , Edoardo Giusto , Davide Ricossa , Davide Corbelletto , Bartolomeo Montrucchio  and Roberto Ugoccioni IBM Italy Intesa Sanpaolo Politecnico di Torino Link https://lnkd.in/dspnyG9v  

In finance, Monte Carlo simulations help us to measure risks like VaR or price derivatives, but they’re often painfully slow because you need to generate millions of scenarios. Matsakos and Nield suggest something different: they build everything directly into a quantum circuit. Instead of precomputing probability distributions classically, they simulate the future evolution of equity, interest rate, and credit variables inside the quantum computer, including binomial trees for stock prices, models for rates, and credit migration or default models. All that is done within the circuit, and then quantum amplitude estimation is used to extract risk metrics without any offline preprocessing. This means you keep the quadratic speedup of quantum MC while also removing the bottleneck of classical distribution generation. If you want to explore the topic further, here is the paper: https://lnkd.in/dMHeAGnS #physics #markets #physicsinfinance #derivativespricing #quant #montecarlo #simulation #finance #quantitativefinance #financialengineering #modeling #quantum