Quantum Research
Curated publications, open problems in quantum computing, and current research explorations pushing the boundaries of what's possible.
Selected Publications
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
The landmark paper that introduced polynomial-time quantum algorithms for integer factorization and discrete logarithm — the foundation of what is now known as Shor's algorithm. This work demonstrated that quantum computers could break widely-used public-key cryptosystems like RSA and Diffie-Hellman.
Quantum Mechanics Helps in Searching for a Needle in a Haystack
Introduced Grover's algorithm — a quantum search algorithm that provides a quadratic speedup for unstructured database search problems. With O(sqrt(N)) queries instead of O(N), this work showed quantum computing advantages even without the algebraic structure exploited by Shor's algorithm.
Quantum Computing in the NISQ Era and Beyond
Defines the NISQ (Noisy Intermediate-Scale Quantum) era — the current stage of quantum computing with 50-1000 noisy qubits. Explores near-term applications, the path to fault tolerance, and the scientific opportunities that bridge today's imperfect devices and tomorrow's error-corrected quantum computers.
Quantum Supremacy Using a Programmable Superconducting Processor
Reports the first experimental demonstration of quantum supremacy using Google's 53-qubit Sycamore processor. The device performed a specific sampling task in 200 seconds that would take the world's most powerful supercomputer approximately 10,000 years — a watershed moment in quantum computing history.
Quantum Error Correction Beyond Qubits
A comprehensive review of quantum error correction schemes extending beyond discrete qubit systems. Covers bosonic codes (cat states, GKP states), topological codes, and surface codes, with detailed analysis of their thresholds, overheads, and suitability for near-term fault-tolerant implementations.
Open Problems in Quantum Computing
These are some of the most fascinating unsolved questions in quantum computing today. Solving any of them would represent a major breakthrough.
Quantum PCP Conjecture
Does quantum PCP (Probabilistically Checkable Proofs) exist? Classical PCP theorem shows NP problems have proofs checkable with O(1) queries. The quantum analogue — whether QMA-hard problems have efficiently verifiable local Hamiltonians — remains one of the deepest open questions in quantum complexity theory.
BQP vs NP Relationship
Can quantum computers efficiently solve NP-complete problems? While BQP (bounded-error quantum polynomial time) captures quantum advantage, its relationship to NP remains unknown. Proving BQP != NP would separate quantum from brute-force classical search; proving BQP subset NP would revolutionize computing.
Fault-Tolerant Threshold
What is the true maximum error rate allowing scalable fault-tolerant quantum computing? Current estimates place thresholds around 1% for surface codes, but tight bounds and optimal codes remain elusive. Pushing this threshold higher would dramatically reduce the qubit overhead for practical quantum computers.
Ideas I'm Exploring
Informal research notes and ongoing explorations — the messy, curious work that happens between formal publications.
Quantum-inspired Classical Algorithms for Recommendation Systems
Ewin Tang's breakthrough showed that certain quantum speedups for recommendation systems can be matched classically using sampling techniques. I'm exploring whether similar "dequantization" applies to other QML algorithms — specifically quantum kernel methods and variational classifiers.
Preliminary finding: many apparent quantum advantages in QML may be artifacts of comparing against suboptimal classical baselines. Need tighter lower bounds.
Hardware-Efficient Ansatz Design for VQE
Investigating whether entangler gate placement in hardware-efficient variational ansatze follows learnable patterns. Hypothesis: gradient-based optimization of circuit topology itself (meta-learning the ansatz) could outperform hand-designed circuits on NISQ devices.
Running experiments on IBM and IonQ backends — early results suggest topology matters more than depth for chemical accuracy.
Pedagogical Visualization of Quantum Error Correction
Building interactive web-based visualizations for surface codes that let students see stabilizer measurements, error chains, and minimum-weight perfect matching in real time. Goal: make QEC intuitive without requiring a physics PhD.
Prototype live in the Virtual Lab — feedback welcome from educators.