Quantum Resource Estimation Workshop

Sums of squares spectral amplification
Rolando D. Somma, Google

Abstract: I will present sum-of-squares spectral amplification (SOSSA), a framework for improving quantum simulation relevant to low-energy problems. I will show how SOSSA can be applied to problems like energy and phase estimation and provide fast quantum algorithms for these problems that significantly improve over prior art. To illustrate the power of SOSSA in applications, I will describe an application to real-world quantum chemistry systems, obtaining state of the art gate costs, and also the Sachdev-Ye-Kitaev model, where SOSSA gives asymptotic speedups over generic simulation methods by a factor of the square root of the system size. 

Dr. Rolando D. Somma is a research scientist at Google working on quantum computing. Prior to this appointment, Dr. Somma was a staff scientist, project leader, and principal investigator at Los Alamos National Laboratory (2009-2022), and a postdoctoral fellow at the Perimeter Institute for Theoretical Physics (2007-2009). Dr. Somma is recognized for his fundamental contributions to the theory of quantum computing and algorithms, having been elected as a fellow of the American Physical Society, Division of Quantum Information, in 2022.

A history of resource estimates for Shor's algorithm
Tom McCarthy, Project Eleven & Nebular

Abstract: When will Shor’s algorithm be capable of breaking cryptographically relevant problems such as RSA and elliptic-curve cryptography? Resource estimation techniques - quantifying the qubits, gates, and error-correction overhead required to run Shor's algorithm - help answer this question. Estimates for Shor’s algorithm have consistently declined over the past 30 years, which impacts quantum computing's relevance to cybersecurity and national security. Starting with Beckmann et al.’s 1996 analysis, this talk will trace the evolution of resource estimates for Shor's algorithm, highlighting the advances and optimizations that have driven the downward trend. 

Tom McCarthy is Head of Research and Company Formation at Nebular, an early-stage venture capital firm. He was on the Founding Team at Project Eleven, a post-quantum cryptography startup. He earned his degree in Theoretical Physics from Trinity College Dublin, where he was awarded a Foundation Scholarship in Physical Sciences. He is based in San Francisco.

Visualizing, Analyzing, and Verifying Quantum Programs with PennyLane and Qualtran
Josh Izaac, Xanadu

Abstract: Expand your quantum programming toolkit by integrating PennyLane and Qualtran, to leverage the best of both frameworks for end-to-end quantum programming and resource estimation workflows. Recent releases of both libraries have enabled full interoperability, making it easy to minimize resources, reason about and understand complex circuits, and verify their outputs via simulation. Learn how to simulate Qualtran’s circuits in PennyLane, estimate a PennyLane circuit’s resources using Qualtran, visualize circuits that mix components from both libraries, and more. We also present an industry use-case from an industry collaborator where we combine PennyLane and Qualtran to determine the resources (in terms of total number of qubits and gates) needed for quantum signal processing circuits for quantum Krylov methods, as introduced in arXiv:2501.05286. 

Josh Izaac is the Director of Product at Xanadu, leading roadmap planning for Xanadu’s open-source quantum programming frameworks, including PennyLane and Catalyst. His interests lie in enabling quantum research through novel quantum software. Prior to joining Xanadu, he earned his PhD in quantum computation at the University of Western Australia.

Constant-Factor Improvements in Quantum Algorithms for Linear Differential Equations
Matthew Pocrnic, University of Toronto

Abstract: Finding the solution to linear ordinary differential equations has been a promising theoretical avenue for asymptotic quantum speedups. However, despite the improvements to existing quantum differential equation solvers over the years, little is known about constant factor costs of such quantum algorithms. This makes it challenging to assess the prospects for using these algorithms in practice. In this work, we prove constant factor bounds for a promising new quantum differential equation solver, the linear combination of Hamiltonian simulation (LCHS) algorithm. Our bounds are formulated as the number of queries to a unitary that block encodes the generator. In doing so, we make several algorithmic improvements such as tighter truncation and discretization bounds on the LCHS kernel integral, a more efficient quantum compilation scheme for the SELECT operator in LCHS, as well as the use of a constant-factor bound for oblivious amplitude amplification, which may be of general interest. To the best of our knowledge, our new formulae improve over previous state of the art by at least two orders of magnitude, where the speedup can be far greater if state preparation has a significant cost. Accordingly, for any previous resource estimates of time-independent linear differential equations for the most general case whereby the dynamics are not fast-forwardable, these findings provide a 110x reduction in runtime costs. This analysis contributes towards establishing more promising applications for quantum computing.

Matthew Pocrnic is a graduate student entering the final year of his PhD at the University of Toronto, where he is supervised by Nathan Wiebe and Dvira Segal. His interests include quantum algorithms for simulating Hamiltonian dynamics, open quantum systems, and differential equations.

Potential applications of quantum computing in the study of magnetic materials and high temperature superconductivity
Sidhant Misra, Los Alamos National Laboratory 

Abstract: In this talk we present select computational tasks associated with two active areas of research at the Los Alamos National Laboratory. The first is the study of phase transitions and Hamiltonian identification for magnetic materials with special emphasis on the study of quantum spin liquids at the national high magnetic field laboratory (MAGLAB). The second involved computation of order parameters in the Fermi-Hubbard model used to model candidate materials for high temperature superconductivity. In each case, we provide a concrete formulation of the computational task, range of associated models and required tolerances, and highlight the major factors that affect the quantum resource estimates for quantum algorithms designed to perform these computations. 

Sidhant Misra is a staff scientist in the Applied Mathematics group at the Los Alamos National Laboratory. He obtained his PhD in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology in 2014. His research interests include statistical learning theory and algorithms, quantum algorithms and the applications of quantum computing and optimization methods and their applications.

Assessing the Fault-Tolerant Overhead for NMR Spectral Prediction
Justin Elenewski, MIT Lincoln Laboratory

Abstract: Recent experiments have sought to acquire nuclear magnetic resonance (NMR) spectra in zero to ultralow magnetic fields. This regime carries certain favorable tradeoffs, though it is challenging to interpret ultralow-field spectra without classically hard computations. Working by example, we demonstrate how NMR simulation is a promising target for fault-tolerant quantum computation. Our holistic analysis spans from input selection to the construction of explicit circuits for qubitized quantum dynamics. By maintaining parity with experimental requirements, we demonstrate how certain cases might be especially promising for early fault-tolerant architectures.

Dr. Justin Elenewski is a technical staff member in the Quantum-Enabled Computation group at MIT Lincoln Laboratory. His research interests include the design and analysis of quantum algorithms, classical algorithms for simulating physical systems, emerging applications for quantum computation, and a variety of topics in quantum information.

OQI's role in driving quantum innovation for human benefit
Francesca Schiavello, Open Quantum Institute

Abstract: The talk will begin by introducing the Open Quantum Institute (OQI), who we are, what our initiatives are, how we plan to bring them forward, and what space we occupy in the quantum eco-system. It will then delve into our use case applications for tackling real-world problems, specifically aimed at the UN's sustainable development goals (SDGs), and vetted by UN agencies. The different phases of the use case applications will be covered, from conceptualization, to methodology development, resource estimation, formalizing justification, running on simulators and real hardware. Lastly, it will delve deeper in a couple of specific use cases to conclude the presentation.

Francesca Schiavello is a Quantum Applications Advisor at the Open Quantum Institute (OQI). She takes on a technical role, aiding and supporting teams to bring forward quantum computing use-case applications. She has a Bachelors in Mathematics, and a Masters in Computational Science. Before OQI she worked at Hartree Centre, a UK national supercomputing center, as a Quantum and High Performance Software Engineer, working on the integration of emerging technologies in the industry.