Space-Curved Quantum Control Beyond the Rotating Wave Approximation for Driven Two-Level Systems

Chase, Adarsh, Shivam, Aarya

EXTERNAL MENTOR: Hunter Nelson, Virginia Tech Center for Quantum Information Science and Engineering

A common tool for simplifying driven two-level systems is the rotating wave approximation (RWA). It applies when the driving pulse is weak compared to the transition energy difference and has a frequency near it.

However, in some instances, it would be interesting to go beyond this assumption and account for more general driving regimes.

Can we use the SCQC framework to account for noise that is induced under the violation of the RWA assumption?

Secure computation in the Quantum Era

Ethan

External Mentor: Atul Mantri, Virginia Tech Center for Quantum Information Science and Engineering

Efficient Device Independent Quantum Number Generator Design and Analysis

Max

Introduction

Monte Carlo simulations [Metropolis, 1949] are a powerful class of computational algorithms used to model and analyze complex systems or processes involving uncertainty. These simulations are widely used across various scientific and engineering domains, including physics, finance, and machine learning. A typical Monte Carlo simulation involves four main steps:

Model definition: Develop a mathematical or computational model of the system under investigation.

Randomization: Introduce random variables into the model to represent uncertain or variable inputs.

Sampling and simulation: Conduct a large number of simulation runs (often in the millions) by sampling from the input distributions and evaluating the model for each instance.

Statistical analysis: Aggregate the simulation outputs and compute statistical measures such as means, variances, percentiles, and probabilities.

Among these steps, Step 2 — randomization — is particularly critical. The quality of the random number generator (RNG) directly affects both the accuracy and reliability of the simulation. Poor-quality RNGs can introduce subtle biases, increase estimator variance, or compromise convergence, ultimately affecting the validity of the results.

Conventional pseudorandom number generators (PRNGs) rely on deterministic algorithms initialized with a finite seed, producing sequences that mimic randomness but are inherently predictable if the internal state is known. In contrast, quantum random number generators (QRNGs) exploit fundamental quantum mechanical phenomena — such as photon path selection or quantum phase noise — to generate intrinsically unpredictable sequences. Device-independent QRNGs (DI-QRNGs) further strengthen this unpredictability by avoiding reliance on assumptions about the internal workings of the device, instead using principles like Bell inequality violations to certify randomness.

The motivation for this work lies in understanding how the source of randomness influences the behavior and reliability of Monte Carlo simulations. While PRNGs are widely used and efficient, they may be inadequate in high-assurance applications such as cryptography, security-sensitive simulations, and quantum computing. QRNGs, particularly DI-QRNGs, offer a potential alternative with provable guarantees of randomness rooted in quantum physics.

Despite the theoretical advantages of QRNGs, there is limited practical analysis comparing their performance with PRNGs in computational settings. This work aims to bridge that gap by quantitatively evaluating how different RNG types impact key metrics in Monte Carlo simulations.

Intellectual Merit

We propose a new measure to compare two sampling algorithms, focusing on how each algorithm’s estimate of an extreme quantile (e.g., the 99.9th percentile) is affected by the use of imperfect random numbers in the simulation. More specifically, we propose a finite-sample, distribution-free quantile-error bound that explicitly trades RNG imperfection against sample size. If time permits, we also aim to propose a novel and efficient DI-QRNG design that works on IBM quantum computers.

Broader Impact

Monte Carlo simulations play a critical role in physics and mathematics, serving as essential tools for optimization, numerical integration, and generating draws from probability distributions. Examples include simulating fluid and cellular systems, engineering designs, and the stock market. Beyond Monte Carlo simulations, strong random number generation is crucial for any intentionally unpredictable process, including computer simulations, randomized design procedures, gambling, and cryptography.

Lightweight NV Diamond CW-ODMR Magnetometer and Application

Eric, Harry, Isaac

The proposed research will aim to utilize Nitrogen Vacancy (NV)-Diamond based Continuous Wave- Optically Detected Magnetic Resonance (CW-ODMR) Magnetometers to measure magnetic fields with targeted sensitivity. The proposed NV-Diamonds to be used in the contraption will be grown in the lab. Ideally, the research will utilize two different NV diamonds: one grown from a seed diamond in the lab and one obtained from an industrial source to compare their performance in the magnetometer. Once a magnetometer has been constructed, we will apply it in a small scale GPS scenario within TJHSST, where we will attempt to map out the magnetic field throughout TJ and use subsequent data for positioning within the campus. This application will serve as a proof-of-concept for a larger scale implementation of the device.

The intellectual merit of this experiment stems from a recent paper by Bulau, Walter, and Fritz published in August of 2025 that details the creation of a low-cost CW-ODMR Magnetometer. A typical Magnetometer requires a light source, color filter, TIA (Transimpedance amplifier), a microwave structure, and microwave generator. Bulau et al. opted to use an LED (instead of the traditional laser) as a light source, a single stage TIA from Texas Instruments, and a low cost microwave generator. Their results prove promising for a low cost ,lightweight, and compact contraption to serve as a magnetometer. The researchers have also proposed various strategies to improve the measurements and capacity of the setup, including by using higher quality diamonds, using a smaller microwave resonator, and possibly adding shielding around the device. The magnetometer produced through this project will then be put to use in a magnetic mapping algorithm via Gaussian Processes to interpolate discrete measurements over a continuous field. This will allow a measurement at any single place in the field to be placed on the magnetic field map. Meanwhile, one of the diamonds to be used in the magnetometer will be a seed diamond grown in the lab. The growth of a seed diamond in the lab will be cheaper than if a fully grown NV diamond were obtained from an outside source, making it an appealing option. The seed diamond will be grown using either methods detailed by Kunuku, which utilize high pressure and temperature chambers to bombard the seed diamond with CH4 or with methods detailed by Karki, which involves using an alternative method with UV radiation instead. The intellectual merit of growing and fabricating our own NV diamond from a seed diamond would allow us to learn and gain more experience with baking carbon in an oven; then, we can publish on it so that the greater public will also be able to take advantage of our newly gained knowledge.

The broader impacts of NV-diamond production method is its instrumental applications in CW- ODRM detection, while keeping NV-diamond production costs low. Additionally, reliably being able to grow and cut seed NV diamonds into ones usable for experiment and application will allow for more affordable NV diamond experiments, increasing accessibility in educational programs around the world. Meanwhile, the broader impacts of a lightweight magnetometer and sensitive measurement of Earth’s magnetic fields cannot be overstated. This research has particularly promising applications for navigation in areas without satellite signals or data access. Xuezhi Wang et al. devised a mathematical model for fitting the Earth’s magnetic fields to a position on the globe using magnetometry. Their algorithm, though error prone, shows a promising, relatively accurate method to apply magnetometry to navigation. A system similar to that described in this research would be compatible with their algorithm, if implemented correctly. The resulting overall system would allow positioning on the globe via sensitive detection of the Earth’s magnetic field, allowing any user to place themselves on the globe without access to traditional satellite based systems.

A Hybrid Quantum-Classical Attention Mechanism for Efficient Large Language Models

Smaran, Ansh

Our proposed research aims to explore new methods that improve efficiency in large language models by designing a hybrid quantum-classical attention mechanism. The attention layer acts as the mechanism that dynamically weights and highlights relevant parts while generating each output token. Self-attention, a core component, enables these models to capture long-range relations yet creates quadratic computational cost [1]. This project will test whether a quantum module inside the attention mechanism reduces this bottleneck while preserving accuracy and stability. By testing feasibility, our research seeks to identify practical applications that integrate quantum computation and modern natural language processing systems.

Intellectual Merit The intellectual merit of this project lies in advancing efficient architectures for large language models (LLMs) by exploring a hybrid quantum-classical attention mechanism. While LLMs achieved remarkable success in translation, dialogue, and reasoning, reliance on quadratic-cost self-attention creates severe efficiency bottlenecks. Recent quantum self-attention approaches, such as QSANN and QMSAN, show the potential of quantum circuits to compute similarity across exponentially large Hilbert spaces [2–4]. However, they remain limited by noise and low qubit counts in near-term devices. By offloading the query-key similarity step, which stands as the most computationally intensive, to quantum modules while preserving classical value and residual pathways, this project aims to combine the power of quantum systems with the scalability and robustness of classical deep learning.

Broader Impact The potential broader impacts of our work extend to the computing community and other fields that rely on language models. By improving efficiency in attention mechanisms, this research reduces environmental and economic costs linked to training and deploying LLMs, a major concern as model sizes continue to grow [5]. The hybrid approach also creates new opportunities for specialized domain-specific LLMs. For example, these models could operate under constrained settings such as onboard medical devices, educational platforms, and edge computing. More generally, developing methods that merge quantum and classical computing builds the foundation for future high-performance AI systems.

Hybrid Quantum-Classical Pipeline for Identifying Higher Order Correlations in Neurons

Caroline, Jennifer

Introduction

The proposed research aims to develop a hybrid quantum-classical pipeline to identify higher-order, or motif-level, correlations in neurons populations. We will analyze two-photon calcium imaging data collected from the mouse auditory cortex when mice are given auditory stimuli of different frequencies. Currently, we plan to use the data collected by Bowen et al. 2024. We will begin by pre-processing the data: identifying neuronal spikes, reducing dimensionality, and calculating correlation between neurons. The output will be a neuronal graph that is both directional and weighted: neurons are expressed as nodes, connections between neurons are expressed as edges, directionality indicates whether neuron A affected neuron B or vice versa, and the weights inform relatedness or possible motifs among neurons.

Intellectual Merit

The intellectual merit of this experiment is rooted in previously developed methods for analyzing calcium imaging data and constructing neuronal graphs. In the brain, neurons often form connected circuits where a firing event in one neuron can either activate or suppress firing in another neuron, or even a group of neurons (often called a functional subcircuit). An accepted method to represent these connections in this field is in the form of neuronal graphs. There are several approaches to creating these graphs classically, and the most recent papers follow the steps listed below:

• Data structure: Convert the calcium imaging data to a matrix where the rows represent neurons and the columns represent time points.

• Noise reduction: Denoise the calcium imaging data to separate the signal from complex physiological noise (there are a variety of methods for this, but we have yet to synthesize possible approaches).

• Similarity and correlation: Compare the similarity between neurons using a variety of metrics, such as Pearson correlation coefficients or transfer entropy values (accounts for temporality, and therefore enables the creation of directional graphs).

• Cluster analysis: Perform cluster analysis with k-means, Louvain community detection, or DBSCAN.

• Network analysis: If the data is represented as a network, statistics such as modularity, small-worldness, and calculated clustering coefficients can also be derived from the adjacency matrix of the neuronal graph.

However, motif identification within networks is an NP-hard algorithm and becomes slower with multiple constraints such as activation and suppression. We propose a neuroscience application of the QOMIC (quantum optimization for motif identification) algorithm developed by Ngo et al. 2025. Using QOMIC, we hope to outperform classical algorithms by identifying more motifs and reducing the computational expense. With the knowledge gained from the QOMIC implementation, we will develop our own quantum algorithm that aims to address QOMIC's weaknesses. Identifying more functional subcircuits and motifs in the brain can enable a better understanding of how different neurons interact with each other and respond to sound stimuli.

Broader Impact

Our research may indicate functional subcircuits in the brain. These dynamics are critical for understanding how groups of neurons collectively encode information and transition between neural states. Importantly, the patterns we identify may be extrapolated beyond the auditory system and reflect the general organizational motifs of the cerebral cortex. Many cortical regions share a similar layered architecture and exhibit comparable population-level computations, suggesting that higher-order coactivation patterns and network structures observed within the auditory cortex may also underlie processes in visual, somatosensory, and association cortices. Identifying recurring activation motifs and community structures in these areas could offer a deeper, systems-level understanding of how the brain encodes sensory information, supports memory, and produces complex cognitive functions such as decision-making and conscious perception. This approach thus provides a scalable and generalizable framework for exploring collective neural behavior across the brain.

Quantum Simulation of Elliptic Curve Crytography Arithmetic

Sophia, Luv

Introduction:

Our proposed research aims to explore the implementation of elliptic curve cryptography (ECC) arithmetic on quantum computers by developing quantum circuits for group operations across multiple elliptic curve models. Building on prior work that optimized affine Weierstrass addition formulas for Shor’s algorithm, we extend these approaches to alternative curve models, including Montgomery curves, Twisted Edwards curves, and curves defined over binary fields. Our main hypothesis is that while all these models yield functionally equivalent group laws, their quantum circuit cost, in terms of qubit width, depth, and $T$-gate count, will vary substantially. By systematically comparing models, we aim to identify which curve representations present the lowest-cost path for quantum cryptanalysis of ECC.

Intellectual Merit:

The intellectual merit of this project lies in broadening the resource estimates for quantum attacks on ECC beyond the standard Weierstrass form. While previous studies have primarily focused on affine Weierstrass coordinates over prime fields, classical cryptography routinely employs Montgomery and Edwards curves for their efficiency and complete addition laws. Moreover, binary fields $\mathbb{F}_{2^m}$ remain in use in certain standards, yet quantum resource estimates for these settings remain scarce. By constructing and analyzing reversible arithmetic circuits for these models, our work contributes new insight into the comparative security of different ECC families under quantum adversaries. The results will not only test the universality of previous findings but also advance the methodology for designing and evaluating quantum circuits for algebraic structures beyond integer modular arithmetic.

Broader Impact:

Evaluating quantum circuit costs across multiple elliptic curve models will provide the cryptography community with a clearer picture of which ECC variants are most vulnerable to quantum attacks, thereby guiding future cryptographic standardization and migration to post-quantum schemes. Beyond cryptography, our work develops reusable building blocks for reversible polynomial arithmetic (for binary fields) and modular inversion circuits, both of which can be leveraged in other domains of quantum simulation and number-theoretic algorithms.

Ansatz significance in sample-based quantum diagonalization

Olivia

EXTERNAL MENTOR: Dr. Jason Saroni, Virginia Tech

Introduction

The proposed research aims to answer a key quantum chemistry question in finding ground states of many-body systems. Sample-based quantum diagonalization (SQD) methods are an alternative approach to traditional Variational Quantum Eigensolvers (VQEs) for approximating ground states by projecting the Hamiltonian into a sampled subspace. As VQE is an iterative process, it can be computationally expensive as opposed to SQD. However, a requirement of SQD is that the circuit from which the subspace is created must be able to sample the ground-state wave function. We will explore the guidelines of such a circuit in hopes of making SQD a more efficient solution to finding the ground state of molecular systems.

Intellectual Merit

The intellectual merit of this experiment rests on choosing an appropriate ansatz such that sampling circuit electronic configurations creates a subspace that contains the Hamiltonian's ground state. This will allow us to diagonalize the Hamiltonian. There is already research on neural network-enhanced SQD approaches, sampling with time-evolution circuits, and on extending the use of SQD to find excited states rather than ground states of electronic systems, but this research will focus solely on SQD itself and sampling driven by variational ansatz.

Broader Impact

So far, scientists have shown that SQD succeeds in approximating ground states in active spaces of up to 36 orbitals and 77 qubits. By improving SQD, we can use this algorithm on more complex systems that take up more orbitals and qubits. SQD is critical to solvation modeling efforts, in which solutes and solvents are considered together in the same system. Ultimately, research on SQD can make leaps in efficiently solving for ground states of many-body systems, aiding in drug discovery and modern electronics development.

Quantum Agent-Based Modeling for Disease Dynamics

Ryan

abstract