arXiv subjects

Thomas E. Baker

Publications and source records attributed to Thomas E. Baker.

At least 19 recordsLinked to original sources

arXiv2026

Intro2QC: An Approachable Introduction to Quantum Computing for STEM Education in High Schools

In recent years, quantum computing has gained strong traction on the global stage. Pioneering developments in quantum engineering, algorithms and software reinforce the view that quantum computation will eventually catalyze transformative technological advancements across diverse sectors. In anticipation of the future impact of quantum computing, many governments, universities and tech organizations have invested heavily into advancing quantum science, boosting quantum readiness, and building a diverse, talented workforce through quantum education initiatives. Specialized university programs, public awareness campaigns and STEM outreach activities all serve a critical function in fostering a deeper understanding of quantum physics and quantum technologies among non-experts. At the level of high school, a major vision is for these initiatives to reshape the teaching of 20th century physics in STEM classrooms, and inspire the future generation of quantum scientists and professionals. In the current paper, we are presenting the materials we have created for an outreach workshop introducing quantum computing to high school students in an approachable and engaging way. Intro2QC is an exploration of quantum computing's relevance to solving real-world challenges by relating how the unintuitive behaviours of quantum systems can be useful in providing computational advantage. The workshop materials include an online interactive quantum programming tutorial hosted on the Intro2QC website, along with the full lesson plan for STEM instructors and the presentation slides available on the Github repository. This single-session 90-minute workshop has been delivered to approximately 160 students in multiple school groups from Grades 9-12 in British Columbia Canada in the highlight of the International Year of Quantum Science and Technology.

physics.ed-ph↗

arXiv2026

Quantum computation with the eigenstate thermalization hypothesis instead of wavefunction preparation

It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum systems to produce an equal superposition of eigenstates. The quantum phase estimation subroutine then allows for the computations of functions of the input operator, leading to a variety of methods in linear algebra. The algorithm circumvents the need for elaborate wavefunction preparation on the quantum computer to find the solution of the linear algebra problem in poly-logarithmic time.

quant-ph↗

arXiv2026

Basic linear algebra methods for quantum problems

Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic routines would be highly time-consuming. We aim in this article to review those basic routines and provide a knowledge foundation for how to perform basic operations on a computer that would be inaccessible with pen and paper. Elementary details on the solutions to linear algebra problems and computational complexity are reviewed. The focus is on solving eigenvalue problems for quantum systems, but the discussion is generic to many other applications. Common matrix forms relevant to quantum systems and their solution strategies are covered. The discussion extends to computational numerical methods for which the most efficient functions exist in freely available libraries. These include eigenvalue, Schur, QR, LU, LDL, Cholesky, and singular value decompositions. The algorithms for obtaining some of these decompositions are discussed, with focus being placed on those used in modern libraries.

physics.comp-ph↗

arXiv2025

Quantum algorithm for the gradient of a logarithm-determinant

The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories, as well as the inverses of matrices. A multi-variable version of the quantum gradient algorithm is developed here to evaluate the derivative of the logarithm-determinant. From this, the inverse of a sparse-rank input operator may be determined efficiently. Measuring an expectation value of the quantum state--instead of all $N^2$ elements of the input operator--can be accomplished in $O(k/\varepsilon^2)$ time in the idealized case for $k$ relevant eigenvectors of the input matrix with precision $\varepsilon$. A practical implementation of the required operator will likely need $\log_2N$ overhead, giving an overall complexity of $O((k\log_2 N)/\varepsilon^2)$. The method applies widely and converges super-linearly in $k$ when the condition number is high. The best classical method we are aware of scales as $N$. Given the same resource assumptions as other algorithms, such that an equal superposition of eigenvectors is available efficiently, the algorithm is evaluated in the practical case as $O(\log_2 N/\varepsilon^2)$. The output is given in $O(1)$ queries of oracle, which is given explicitly here and only relies on time-evolution operators that can be implemented with arbitrarily small error. The algorithm is envisioned for fully error-corrected quantum computers but may be implementable on near-term machines. We discuss how this algorithm can be used for kernel-based quantum machine-learning.

quant-ph↗

arXiv2024

Bundled matrix product states represent low-energy excitations faithfully

We consider a set of density matrices. All of which are written in the same orbital basis, but the orbital basis size is less than the total Hilbert space size. We ask how each density matrix is related to each of the others by establishing a norm between density matrices based on the truncation error in a partial trace for a small set of orbitals. We find that states with large energy differences must have large differences in their density matrices. Small energy differences are divided into two groups, one where two density matrices have small differences and another where they are very different, as is the case of symmetry. We extend these ideas to a bundle of matrix product states and show that bond dimension of the wavefunction ansatz for two states with large energy differences are larger. Meanwhile, low energy differences can have nearly the same bond dimensions for similar states.

quant-ph↗

arXiv2023

Direct solution of multiple excitations in a matrix product state with block Lanczos

Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a bundled matrix product state, holding many excitations. The use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations. The method is demonstrated on a Heisenberg model and other cases of interest. A large of number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain.

cond-mat.str-el↗

arXiv2021

DMRjulia: Tensor recipes for entanglement renormalization computations

Detailed notes on the functions included in the DMRjulia library are included here. This discussion of how to program functions for a tensor network library are intended to be a supplement to the other documentation dedicated to explaining the high level concepts. The chosen language used here is the high-level julia language that is intended to provide an introduction to provide a concise introduction and show transparently some best practices for the functions. This document is best used as a supplement to both the internal code notes and introductions to the subject to both inform the user about other functions available and also to clarify some design choices and future directions. This document presently covers the implementation of the functions in the tensor network library for dense tensors. The algorithms implemented here is the density matrix renormalization group. The document will be updated periodically with new features to include the latest developments.

quant-ph↗

arXiv2021

Block Lanczos method for excited states on a quantum computer

The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is in principle capable of obtaining excitations, the extension to a block Lanczos routine can resolve degeneracies with better precision and only costs $\mathcal{O}(d^2)$ for $d$ excitations on top of the previously introduced quantum Lanczos recursion method. The formal complexity in applying all operators to the system at once with oblivious amplitude amplification is exponential, but this cost can be kept small to obtain the ground state by incrementally adding operators. The error of the ground state energy based on the accuracy of the Lanczos coefficients is investigated and the error of the ground state energy. It is demonstrated to scale linearly with the uncertainty of the Lanczos coefficients. Extension to non-Hermitian operators is also discussed.

quant-ph↗

arXiv2021

Build your own tensor network library: DMRjulia I. Basic library for the density matrix renormalization group

An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia library. Algorithmic complexity, measurements from the matrix product state, convergence to the ground state, and other relevant features are also discussed. The present document covers the implementation of operations for dense tensors into the Julia language. The code can be used as an educational tool to understand how tensor network computations are done in the context of entanglement renormalization or as a template for other codes in low level languages. A comprehensive Supplemental Material is meant to be a "Numerical Recipes" style introduction to the core functions and a simple implementation of them. The code is fast enough to be used in research and can be used to make new algorithms.

quant-ph↗

arXiv2021

Méthodes de calcul avec réseaux de tenseurs en physique (Basic tensor network computations in physics)

Cet article se veut un survol des réseaux de tenseurs et s'adresse aux débutants en la matière. Nous y mettons l'accent sur les outils nécessaires à l'implémentation concrète d'algorithmes. Quatre opérations de base (remodelage, permutation d'indices, contraction et décomposition) qui sont couramment utilisées dans les algorithmes de réseaux de tenseurs y sont décrites. Y seront aussi couverts la notation diagrammatique, les états en produit de matrices (MPS), les opérateurs en produit de matrices (MPO), état projeté de paires intriquées (PEPS), l'approche par renormalisation d'enchevêtrement multi-échelle (MERA), la décimation par bloc d'évolution temporelle (TEBD) et le groupe de renormalisation de tenseurs (TRG). This article is intended as an overview of tensor networks for beginners looking to perform computations. We focus on the tools necessary for the concrete implementation of algorithms. Four basic operations (reshaping, permutation, contraction, and decomposition) that are commonly used in tensor network algorithms are covered. The article also briefly reviews diagrammatic notation, matrix product states (MPS), matrix product operators (MPO), projected entangled pair states (PEPS), multi-scale entanglement renormalization ansatz (MERA), time evolution block decimation (TEBD), and tensor renormalization group (TRG).

quant-ph↗

arXiv2021

Lanczos recursion on a quantum computer for the Green's function and ground state

A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an interacting Green's function for use in condensed matter, particle physics, and other areas. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining the ground state is also discussed.

quant-ph↗

arXiv2020

Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer

One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory. We demonstrate a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer. Only existing assumptions for the current feasibility of solutions on the quantum computer are used. Several known algorithms including quantum phase estimation, quantum amplitude estimation, and quantum gradient methods are used to train a machine learned model. One advantage of this combination of algorithms is that the quantum wavefunction does not need to be completely re-prepared at each step, lowering a sizable pre-factor. Using the assumptions for solutions of the ground-state algorithms on a quantum computer, we demonstrate that finding the Kohn-Sham potential is not necessarily more difficult than the ground state density. Once constructed, a classical user can use the resulting machine learned functional to solve for the ground state of a system self-consistently, provided the machine learned approximation is accurate enough for the input system. It is also demonstrated how the classical user can access commonly used time- and temperature-dependent approximations from the ground state model. Minor modifications to the algorithm can learn other types of functional theories including exact time- and temperature-dependence. Several other algorithms--including quantum machine learning--are demonstrated to be impractical in the general case for this problem.

quant-ph↗

arXiv2020

On two phases inside the Bose condensation dome of Yb$_2$Si$_2$O$_7$

Recent experimental data on Bose-Einstein Condensation (BEC) of magnons in the spin-gap compound Yb$_2$Si$_2$O$_7$ revealed an asymmetric BEC dome arXiv:1810.13096v2. We examine modifications to the Heisenberg model on a breathing honeycomb lattice, showing that this physics can be explained by competing forms of weak anisotropy. We employ a gamut of analytical and numerical techniques to show that the anisotropy yields a field driven phase transition from a state with broken Ising symmetry to a phase which breaks no symmetries and crosses over to the polarized limit.

cond-mat.str-el↗

arXiv2019

Efficient modeling of superconducting quantum circuits with tensor networks

We introduce an efficient tensor network toolbox to compute the low-energy excitations of large-scale superconducting quantum circuits up to a desired accuracy. We benchmark this algorithm on the fluxonium qubit, a superconducting quantum circuit based on a Josephson junction array with over a hundred junctions. As an example of the possibilities offered by this numerical tool, we compute the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips, taking into account the array degrees of freedom corresponding to a Hilbert space as large as$~15^{180}$. Our algorithm is applicable to the wide variety of circuit-QED systems and may be a useful tool for scaling up superconducting-qubit technologies.

quant-ph↗

arXiv2018

The role of canting and depleted-triplet minima in superconducting spin valve structures

The trilayer and pentalayer spin valve structures are revisited to determine the behavior of pair correlations and Josephson current when the magnetic layers are canted at arbitrary angle. The two systems display markedly different behaviors in the center magnetic layer. While the trilayer generates a triplet component that is weakly affected by canting, the pentalayer tunes in singlet pair correlations depending heavily on canting. We also show that a minimum with depleted $m=\pm1$ triplet components, rather than a $0-π$ transition, may be observed in the current profile $I_c(d_F)$ of a trilayer spin valve. The depleted-triplet minimum (DTM) is directly attributable to a decrease of $m=\pm1$ triplet correlations with increased thickness of the central ferromagnet, accompanied by a hidden, simultaneous sign change of the Gor'kov functions contributed from the left and right superconductors. We introduce a toy model for superconducting-magnetic proximity systems to better illuminate the behavior of individual components of the Gor'kov function and compare with a full numerical calculation.

cond-mat.supr-con↗

arXiv2018

Chemical accuracy from small, system-adapted basis functions

We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2-3 basis functions per electron to achieve chemical accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many atoms. We discuss the promise and challenges for realistic quantum chemical calculations.

physics.chem-ph↗

arXiv2018

Selecting Initial States from Genetic Tempering for Efficient Monte Carlo Sampling

An alternative to Monte Carlo techniques requiring large sampling times is presented here. Ideas from a genetic algorithm are used to select the best initial states from many independent, parallel Metropolis-Hastings iterations that are run on a single graphics processing unit. This algorithm represents the idealized limit of the parallel tempering method and, if the threads are selected perfectly, this algorithm converges without any Monte Carlo iterations--although some are required in practice. Models tested here (Ising, anti-ferromagnetic Kagome, and random-bond Ising) are sampled on a time scale of seconds and with a small uncertainty that is free from auto-correlation.

cond-mat.stat-mech↗

arXiv2016

Pure density functional for strong correlations and the thermodynamic limit from machine learning

We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to $F[n]$, the universal part of the electronic density functional, to within quantum chemical accuracy. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly-stretched bonds without any specific difficulty (unlike all standard DFT approximations) and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.

cond-mat.str-el↗