Quantum Sampling Techniques for Maximum Accuracy

I'm excited to share our latest work, Demonstration of robust and efficient quantum property learning with shallow shadows, published in Nature Communications! 🎉 📝 Authors: Hong-Ye Hu, Andi Gu, Swarnadeep Majumder, Hang Ren, Yipei Zhang, Derek S. Wang, Yi-Zhuang You, Zlatko Minev, Susanne F. Yelin, Alireza Seif 🔍 Context: Extracting information efficiently from quantum systems is crucial for advancing quantum information processing. Classical shadow tomography offers a powerful technique, but it struggles with noisy, high-dimensional quantum states and complex observables. 🤔 Key Question: Can we overcome noise limitations and improve sample efficiency in quantum state learning, especially for high-weight and non-local observables, using shallow quantum circuits? 💡 Our Findings: We introduce robust shallow shadows—a protocol designed to mitigate noise using Bayesian inference, enabling highly efficient learning of quantum state properties, even in the presence of noise. Our experiments on a 127-qubit superconducting quantum processor confirm the protocol’s practical use, showing up to 5x reduction in sample complexity compared to traditional methods. ✨ Key Takeaways: 1. Noise-resilience: Accurate predictions across diverse quantum state properties. 2. Sample Efficiency: Substantial reduction in sample complexity for high-weight and non-local observables. 3. Scalability: The protocol is well-suited for near-term quantum devices, even with noise. Paper: https://lnkd.in/dW4NJ23Q

Markov-chain Monte Carlo method enhanced by a quantum alternating operator ansatz https://lnkd.in/eygdQBCx Quantum computation is expected to accelerate certain computational tasks over classical counterparts. Its most primitive advantage is its ability to sample from classically intractable probability distributions. A promising approach to make use of this fact is the so-called quantum-enhanced Markov-chain Monte Carlo (qe-MCMC) method [D. Layden et al., Nature (London) 619, 282 (2023)], which uses outputs from quantum circuits as the proposal distributions. In this paper, we propose the use of a quantum alternating operator ansatz (QAOA) for qe-MCMC and provide a strategy to optimize its parameters to improve convergence speed while keeping its depth shallow. The proposed QAOA-type circuit is designed to satisfy the specific constraint which qe-MCMC requires with arbitrary parameters. Through our extensive numerical analysis, we find a correlation in a certain parameter range between an experimentally measurable value, acceptance rate of MCMC, and the spectral gap of the MCMC transition matrix, which determines the convergence speed. This allows us to optimize the parameter in the QAOA circuit and achieve quadratic speedup in convergence. Since MCMC is used in various areas such as statistical physics and machine learning, this paper represents an important step toward realizing practical quantum advantage with currently available quantum computers through qe-MCMC.

Quantum Algorithm Demonstrates Provable Advantage Over Classical Methods Introduction Researchers have achieved a new milestone in quantum computing by demonstrating a quantum algorithm that outperforms classical methods on a specific problem known as complement sampling. The work, developed by scientists at Quantinuum and QuSoft, provides a provable and experimentally verifiable form of quantum advantage based not on speed, but on dramatically reduced sampling requirements. Key Breakthrough Understanding the complement sampling problem The task begins with a universe of elements and an unknown subset S. Samples are drawn from S, and the objective is to identify an element that does not belong to S (the complement set). Classical algorithms must collect many samples to determine which elements are missing. Classical limitations When the subset contains half of the total elements, classical algorithms require roughly as many samples as there are elements in the entire universe. Without structural information, classical systems must gather nearly complete knowledge of the subset before identifying a valid complement element. Quantum advantage through sample complexity The quantum algorithm receives a single quantum sample: a superposition representing all elements of the subset simultaneously. Using a simple quantum transformation, the system converts this state into the superposition of the complement set. A measurement then produces a valid element outside the subset with certainty. A different form of quantum superiority The advantage does not come from faster computation. Instead, it arises from how quantum information stores and manipulates data efficiently. One quantum sample replaces the large number of classical samples normally required. Experimental validation Thousands of complement sampling tests were run on Quantinuum’s trapped-ion quantum computers. Results closely matched theoretical predictions, demonstrating that current quantum hardware can already implement the algorithm effectively. Potential implications Complement sampling could strengthen certain cryptographic constructions because the task is difficult for classical systems under standard assumptions. The work also highlights a new path for demonstrating practical quantum advantage using near-term quantum devices. Conclusion: Why This Matters Quantum advantage is often framed in terms of computational speed, but this research reveals another powerful dimension: information efficiency. By dramatically reducing the number of samples required to solve a problem, quantum algorithms can outperform classical systems in entirely new ways. This result strengthens the case that quantum computers may soon deliver measurable advantages in specialized tasks using existing hardware. Keith King https://lnkd.in/gHPvUttw