Tufts Quantum Computing Seminar

Talks:

June 20, 2024

Title: Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements

Speaker: Rahul Sahay, Harvard University

Abstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk, we go beyond this, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. Focusing on 1D, a framework is developed for the case where a single round of measurements is the only entangling operation. We show this creates matrix product states and identify necessary and sufficient tensor conditions for preparability, which uniquely determine the preparation protocol. We use these conditions to both classify preparable quantum states and characterize their physical constraints. Intriguingly, we find a trade-off between the richness of the preparable entanglement spectrum and correlation functions, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover, we connect properties of the preparation protocol to the resulting phase of matter. At a high level, our work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter, away from their fixed points, in quantum devices. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].

June 6, 2024

Title: Functional quantum algorithms: a mélange of methods for matrix functions

Speaker: Zane Rossi, MIT

Abstract: The study of quantum algorithms is stymied by a lack of human intuition-many of these algorithms appear to rely on non-intuitive attributes unique to quantum mechanics, and as such 'good' quantum algorithms are often sporadic, requiring bespoke analysis. The quantum algorithmist is up against a triple headwind: they must (1) be delusion-hardened against non-generalizing classical heuristics, (2) have understanding of disparate classical algorithms with which to compare their work, and (3) do this all largely without access the high-level programming abstractions ubiquitous in classical computer science for over seventy years.

A partial remedy for these problems has emerged with the development of a new class of quantum algorithms, quantum signal processing (QSP) and quantum singular value transformation (QSVT), which have had success in unifying, simplifying, and improving most known quantum algorithms. QSP/QSVT transform the spectrum of linear operators encoded in unitary processes by near arbitrary continuous functions, and this simple ability-computing matrix functions quantum mechanically-has been shown to subsume diverse tasks with comparatively simple complexity analysis.

This work claims and provides a series of constructions supporting that QSP and QSVT should not be viewed solely as subroutines for transforming linear systems, but as limited examples among an extensive class of quantum algorithms converting algorithmic problems to simpler algebraic ones. We construct an array of algorithms in this class, which we call 'functional quantum algorithms', and show they ought to and can be manipulated and combined purely at the level of this algebraic reduction to constitute useful, composite quantum algorithms.

We emphasize three constructions (among a collection of auxiliary results), ordered by complexity: (a) a limited extension of QSP/QSVT-like circuit ansätze to the multivariable matrix function setting, (b) a construction of recursively composable univariate QSP/QSVT-like subroutines, and (c) a construction of modular quantum subroutines (gadgets) that can approximate generic multivariable continuous matrix functions. We provide necessary and sufficient conditions under which these algorithms can be analyzed and combined functionally, i.e., purely at the level of the scalar transformations applied, and show these assertions require significant doing given our constructions' violation of basic assumptions of standard QSP and QSVT, necessitating alternative proof techniques and quantum subroutines of independent interest. We also show how our results situate functional quantum algorithms among existing constructions of classical functional programming, identifying our constructions as instances of monads, suggesting concrete directions for high-level, flexible quantum algorithmic design and analysis.

May 30, 2024

Title: Bounding Trotter Error in the Context of Quantum Phase Estimation

Speaker: William Simon, Tufts University 

Abstract: Trotterization refers to a group of techniques for constructing quantum circuits that approximate the time-evolution operator of a particular Hamiltonian. One application of these Trotterized time-evolution operators is to implement the Quantum Phase Estimation (QPE) algorithm and estimate the eigenvalues of the underlying Hamiltonian. As the magnitude of the Trotter error scales, the quantum resources needed to compensate for this error in QPE must also grow. In this talk, I will give an overview of how Trotterized time-evolution operators are used in the context of QPE and discuss standard, state-independent bounds on the Trotter error. I will also introduce state-dependent error bounds and discuss what happens when the initial quantum state is close to the target eigenstate. Finally, I will introduce an efficient quantum algorithm for estimating these state-dependent error bounds on any initial state and discuss the implications of these bounds on the associated quantum resource estimates for running QPE.

May 23, 2024

Title: Tensile-strained self-assembly: Nanoscale stretching for novel quantum light sources

Speaker: Paul Simmonds, Tufts University

Abstract: Since the early 1990s, self-assembled quantum dots (QDs) have been the subject of intensive research for technologies ranging from high-stability lasers, to intermediate band solar cells. Driven by compressive strain, semiconductor QDs form spontaneously on the (001) surfaces of both III-V and group IV materials. However, QDs grown on non-(001) surfaces, and QDs grown under tensile rather than compressive strain, are becoming increasingly desirable for a variety of applications. The low fine-structure splitting of (111) QDs should make them ideal entangled photon sources; tensile-strained QDs would have dramatically reduced semiconductor band gaps, with implications for infrared optoelectronics and nanoscale band structure engineering. The issue is however, that until recently it has been enormously challenging to synthesize QDs on non-(001) surfaces, or under tensile strain, that are free from crystallographic defects. I will discuss a robust approach to QD self-assembly that overcomes these difficulties, and explain how using molecular beam epitaxy we can reliably and controllably grow defect-free, tensile-strained QDs on (111) surfaces. I will describe the application of tensile-strained self-assembly to several different material systems, and discuss data confirming the promising properties of these novel QDs for use as deterministic single- and entangled-photon light sources. Our results indicate that tensile-strained self-assembly represents a powerful new tool for the synthesis of highly symmetric QDs and the development of novel quantum materials.

May 16, 2024

Title: Quantum simulation of quantum field theory on the light-front

Speaker: Peter Love, Tufts University

Abstract: Quantum simulation is a leading future application of quantum computation. Quantum field theory poses novel challenges because of the need to regulate and renormalize the theories in order to extract physically meaningful results. Quantum simulation algorithms also require a Hamiltonian formulation of the theory. Dirac showed that relativistic theories admit three Hamiltonian formulations. The equal time formulation is commonly used for quantum field theory, whereas the front form offers several advantages for the computation of properties of composite particles. In this talk I will review work on quantum simulation of quantum field theory in the light front formulation, including questions of renormalization, simulation of scattering processes and quantum resources on the light front.

May 9, 2024

Title: The Space Below BQP

Speaker: Saeed Mehraban, Tufts University

Abstract: I will give an overview of models of quantum computing intermediate between classical polynomial time (BPP) and quantum polynomial time (BQP) and describe connections with near-term implementations of quantum computers.

May 2, 2024

Title: Intentionally Designing Models for Learning Tasks with Quantum Mechanics

Speaker: Kaitlin Gili, University of Oxford

Abstract: Classical generative machine learning research now extends far beyond general neural networks, we have models designed with specific features (focused attention, flexible sequencing, etc.) that are intentionally useful for correspondingly relevant learning tasks. In this seminar talk, the speaker will begin with a brief overview of how quantum computation has led to an exciting new set of features for designing generative models, emphasizing that these features should be utilized with intention to help researchers obtain a better understanding of how quantum is useful and for what specific learning tasks. She will walk through an example of an investigation that utilizes such an approach, demonstrating her latest results on how we can use the quantum feature of non-commutativity measurements of a quantum system generating different results when taken in a different order to design a model that can learn order effects in human psychology datasets. She will conclude with insights for conducting future research in quantum generative learning, specifically how we can combine theoretical knowledge from the fields of quantum foundations and quantum cognition to build generative models for learning tasks where classical methods are not currently excelling.

April 25, 2024

Title: Linear Combination of Unitary, How Widely Can We Use it?

Speaker: Sultana Hadi, Tufts University

Abstract: I will discuss the block encoding method which probabilistically implements a linear combination of unitary. The nature of the probabilistic method leads to using the oblivious amplitude amplification (OAA) method to increase the success probability. However, things are not that simple, and the question is to explore how close the linear combination of unitary should be for OAA to be workable.

April 18, 2024

No meeting.

April 11, 2024

Title: Calculating Energies in the Contextual Subspace

Speaker: Alexis Ralli, Tufts University

The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground-state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground-state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with solving the full Hamiltonian via traditional VQE. We showcase the CS-VQE algorithm and present different improvements to the method.

April 4, 2024

Title: What is Quantum Noise?

Speaker: Oliver Maupin, Tufts University

Abstract: Quantum noise is the largest obstacle in the field of quantum computing. But what is noise? Why is it bad for quantum circuits? What physical mechanisms cause noise in today's NISQ devices? In this talk I will answer these questions as I present an overview of quantum noise as it impacts the results of quantum algorithms. We will cover some ways to quantify noise using quality metrics, how we can model noise at the circuit level using noise channels, and how we can differentiate between stochastic and coherent noise.