arXiv subjects

Jack S. Baker

Publications and source records attributed to Jack S. Baker.

At least 19 recordsLinked to original sources

arXiv2026

Stabilizer Statistical Mechanics: A Framework for Efficient Quantification and Classification of Magic States

The partition function is statistical mechanics' answer to an exponentially large spectrum, distilling it into a single analytic object whose temperature dependence resolves the full structure of the underlying ensemble. We show that magic, the resource separating universal quantum computation from classically simulable stabilizer dynamics, admits precisely such a description. Mapping the Pauli spectrum of a quantum state onto the energy levels of a fictitious many-body system, the Pauli gas, we construct its canonical partition function, the stabilizer partition function, and from its associated free energy a magic monotone that we call the stabilizer work. Both these objects are analytic functions of an inverse-temperature-like parameter and are efficiently estimable via Bell sampling. The framework is analytically tractable. We derive exact ensemble-averaged partition functions for Haar-random, $ν$-compressible, and pseudomagic states, together with concentration guarantees. We show that for every value of its parameter, the stabilizer work is a faithful, Subadditive magic monotone, while remaining efficiently accessible on quantum hardware and admitting an operational interpretation. Unlike measures that probe a single moment of the Pauli distribution, the stabilizer work is intrinsically moment-generating. As the temperature is tuned from high to low, it interpolates continuously between the stabilizer 2-Rényi entropy and the stabilizer nullity, revealing two previously disconnected monotones as limiting cases of a single object. We demonstrate the framework on low-rank stabilizer simulation, resource interconversion, molecular ground states, and quantum many-body systems. A thermodynamics of magic is therefore not merely an analogy but a working toolkit, opening a statistical-mechanical route to magic properties of quantum systems that no single measure can access.

quant-ph↗

arXiv2026

Universal initial state preparation for first quantized quantum simulations

Preparing symmetry-adapted initial states is a principal bottleneck in first-quantized quantum simulation. We present a universal approach that efficiently maps any polynomial-size superposition of occupation-number configurations to the first-quantized representation on a digital quantum computer. The method exploits the Jordan--Schwinger Lie algebra homomorphism, which identifies number-conserving second-quantized operators with their first-quantized action and induces an equivariant bijection between Fock occupations and $\mathfrak{su}(d)$ weight states within the Schur--Weyl decomposition. Operationally, we deterministically prepare an superposition of target Schur labels and apply the inverse quantum Schur transform. For $L$ configurations of $N$ particles over $d$ modes prepared to accuracy $ε$, the most efficient variant of the algorithm runs with non-Clifford gate complexity $\mathrm{poly}(L, N, \log d, \log ε^{-1})$. The protocol applies universally to fermions, bosons, and Green's paraparticles in arbitrary single-particle bases. Resource estimates establish practicality within leading first-quantized pipelines, with statistics-aware specializations promising further reductions.

quant-ph↗

arXiv2026

Designing quantum technologies with a quantum computer

Interacting spin systems in solids underpin a wide range of quantum technologies, from quantum sensors and single-photon sources to spin-defect-based quantum registers and processors. We develop a quantum-computer-aided framework for simulating such devices using a general many-body electron-spin-resonance Hamiltonian that incorporates zero-field splitting, the Zeeman effect, hyperfine interactions, dipole-dipole spin-spin interactions, and electron-phonon decoherence. Within this framework, we combine Gray-encoded qudit-to-qubit mappings, qubit-wise commuting aggregation, and a multi-reference selected quantum Krylov fast-forwarding hybrid algorithm, aiming to access extended-time dynamics within the constraints of NISQ and early fault-tolerant hardware. Numerical simulations demonstrate the computation of operationally useful quantities including autocorrelation functions up to $\sim100$ ns, together with microwave absorption spectra and the $\ell_1$-norm of coherence, achieving 18-30$\%$ reductions in gate counts and circuit depth for Trotterized time-evolution circuits compared to unoptimized implementations. Using the nitrogen vacancy center in diamond as a testbed, we benchmark the framework against classical simulations and identify the reference-state selection in sQKFF as the primary factor governing accuracy at fixed hardware cost. This methodology provides a flexible blueprint for using quantum computers to design, compare, and optimize solid-state spin-qubit technologies under experimentally realistic conditions.

quant-ph↗

arXiv2026

Efficient Quantum Circuits for Coherent Conversion Between General First- and Second-Quantized Many-Body Representations

Quantum simulation at fixed particle number admits two equivalent descriptions, a first-quantized (particle) representation and a second-quantized (occupation-number) representation. Their quantum resource costs differ sharply across computational tasks, so the ability to convert coherently between them is valuable. We construct an explicit unitary $Q$, with inverse $Q^\dagger$, that maps a first-quantized state to its fixed-$N$ occupation-number form while diagnosing the input's particle-exchange symmetry. The conversion is therefore symmetry-agnostic at the input yet fully resolved at the output, and it applies uniformly to bosonic, fermionic, and parastatistical sectors. At its foundation lies a structural identification that we place at the center of this work: the quantum Schur transform supplied by Schur-Weyl duality is the non-abelian Fourier transform of the commuting pair $(S_N,U(d))$, and the occupation-number representation is its weight basis, retaining only the labels shared by both factors, the irrep $λ$ and the $\mathfrak{u}(d)$ weight. This reduction is lossless for bosons and fermions, while a canonical Gelfand-Tsetlin promise renders it one-to-one for the remaining sectors. Algorithmically, $Q$ composes the strong Schur transform with reversible arithmetic that computes occupations as successive row-sum differences of the Gelfand-Tsetlin pattern, yielding gate complexity $\mathrm{poly}(N,d,\log(1/ε))$. The converted state is prepared efficiently in quantum memory. Any classical algorithm that outputs it explicitly, however, pays a cost set by the sector dimension, which is polynomial of degree $N$ in $d$ at fixed $N$ and exponential in $N$ when $d=Θ(N)$. Finally, an efficient classical sampler for the induced occupation-number distribution would yield one for arbitrary quantum circuits, contrary to standard complexity assumptions.

quant-ph↗

arXiv2026

Physics-Inspired Extrapolation for efficient error mitigation and hardware certification

Quantum error mitigation (QEM) is essential for the noisy intermediate-scale quantum era, and will remain relevant for early fault-tolerant quantum computers, where logical error rates are still significant. However, most QEM methods incur an exponential sampling overhead to achieve unbiased estimates, limiting their practical applicability. Recently, error mitigation by restricted evolution (EMRE) was shown to estimate expectation values with constant sampling overhead, albeit with a small bias that grows with circuit size and noise level. Building upon the EMRE framework, here, we propose physics-inspired extrapolation (PIE), a linear circuit runtime protocol that achieves enhanced accuracy without incurring substantial overhead. Unlike traditional heuristic zero-noise extrapolation methods, PIE provides a theoretical foundation for the operational interpretation of its fitting parameters and demonstrates convergence to unbiased estimates as noise decreases. Distinctively, the slope of the extrapolation fit corresponds to the max-relative entropy between the ideal and noisy circuits, enabling quantitative hardware certification alongside error mitigation, with no additional computational overhead. We also demonstrate the efficacy of this method on IBMQ hardware and apply it to simulate 84-qubit quantum dynamics efficiently. Our results show that PIE yields accurate, low-variance error mitigated estimates, establishing it as a practical and scalable strategy for both error mitigation and hardware certification for near-term and early fault-tolerant quantum computers.

quant-ph↗

arXiv2025

Quantum algorithms to detect ODMR-active defects for quantum sensing applications

Spin defects in two-dimensional materials are a promising platform for quantum sensing. Simulating the defect's optical response and optically detected magnetic resonance (ODMR) contrast is key to identifying suitable candidates. However, existing simulation methods are typically unable to supply the required accuracy. Here, we propose two quantum algorithms to detect an imbalance in the triplet-to-singlet intersystem crossing (ISC) rates between excited states with the same and different spin projections -- a necessary condition for nonzero ODMR response. The lowest-cost approach evaluates whether the evolution of an $S=0$ state under the spin-orbit coupling induces ISC to $S=1$, and also whether there is an imbalance in its intensity depending on the final state spin projection. The second approach works by comparing the emission spectrum of a spin defect with and without the spin-orbit coupling operator, inferring ISC intensity for different spin transition channels from spectrum intensity changes. Additionally, we present an improved scheme to evaluate the defect's optical response, building upon previous work. We study these quantum algorithms in the context of the negatively charged boron vacancy in hexagonal boron nitride. We generate an embedded active space of 18 spatial orbitals using quantum defect embedding theory (QDET) and show that the ISC rate imbalance can be detected with as few as 105 logical qubits and $4.41 \times 10^8$ Toffoli gates. By avoiding direct and costly rate calculations, our methods enable faster screening of candidate defects for ODMR activity, advancing the prospect of using quantum simulations to aid the development of high-performing sensing devices.

quant-ph↗

arXiv2025

Error-Mitigation Enabled Multicomponent Quantum Simulations Beyond the Born-Oppenheimer Approximation

We introduce a multicomponent unitary coupled cluster framework for quantum simulations of molecular systems that incorporate both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation. Using the nuclear-electronic orbital formalism, we construct mcUCC ansätze for positronium hydride and molecular hydrogen with a quantum proton, and analyze hardware requirements for different excitation truncations. To further reduce resource costs effectively, we employ the local unitary cluster Jastrow ansatz and implement it experimentally on IBM Q's Heron superconducting hardware. With the Physics-Inspired Extrapolation error mitigation protocol, the computed ground-state energies remain within chemical accuracy, consistent with the stated uncertainty level. These results provide the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware and outline a path toward scalable algorithms unifying electronic and nuclear degrees of freedom.

quant-ph↗

arXiv2025

Quantum Resilience: Canadian Innovations in Quantum Error Correction and Quantum Error Mitigation

In celebration of the 2025 International Year of Quantum Science and Technology, this article highlights the pioneering achievements and ongoing innovations in quantum error correction and quantum error mitigation by Canadian institutions, academia and industry alike. Emphasizing Canada's central role in advancing these two related areas, we summarize landmark theoretical breakthroughs, cutting-edge experiments, and emerging techniques aimed at reducing and/or eliminating errors incurred when using a quantum computer. This community-focused overview underscores Canada's leadership in addressing the critical challenge of noise in quantum information science.

quant-ph↗

arXiv2024

Simulating optically-active spin defects with a quantum computer

There is a pressing need for more accurate computational simulations of the opto-electronic properties of defects in materials to aid in the development of quantum sensing platforms. In this work, we explore how quantum computers could be effectively utilized for this purpose. Specifically, we develop fault-tolerant quantum algorithms to simulate optically active defect states and their radiative emission rates. We employ quantum defect embedding theory to translate the Hamiltonian of a defect-containing supercell into a smaller, effective Hamiltonian that accounts for dielectric screening effects. Our approach integrates block-encoding of the dipole operator with quantum phase estimation to selectively sample the optically active excited states that exhibit the largest dipole transition amplitudes. We also provide estimates of the quantum resources required to simulate a negatively-charged boron vacancy in a hexagonal boron nitride cluster. We conclude by offering a forward-looking perspective on the potential of quantum computers to enhance quantum sensor capabilities and identify specific scenarios where quantum computing can resolve problems traditionally challenging for classical computers.

quant-ph↗

arXiv2024

Parallel hybrid quantum-classical machine learning for kernelized time-series classification

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. In this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a time-series Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.

quant-ph↗

arXiv2023

Grad DFT: a software library for machine learning enhanced density functional theory

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when dealing with strongly correlated systems. To address these shortcomings, recent work has begun to explore how machine learning can expand the capabilities of DFT; an endeavor with many open questions and technical challenges. In this work, we present Grad DFT: a fully differentiable JAX-based DFT library, enabling quick prototyping and experimentation with machine learning-enhanced exchange-correlation energy functionals. Grad DFT employs a pioneering parametrization of exchange-correlation functionals constructed using a weighted sum of energy densities, where the weights are determined using neural networks. Moreover, Grad DFT encompasses a comprehensive suite of auxiliary functions, notably featuring a just-in-time compilable and fully differentiable self-consistent iterative procedure. To support training and benchmarking efforts, we additionally compile a curated dataset of experimental dissociation energies of dimers, half of which contain transition metal atoms characterized by strong electronic correlations. The software library is tested against experimental results to study the generalization capabilities of a neural functional across potential energy surfaces and atomic species, as well as the effect of training data noise on the resulting model accuracy.

physics.chem-ph↗

arXiv2023

Quantum-Classical Multiple Kernel Learning

As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the near future. Paired with kernel methods like support-vector machines, small and noisy quantum computers can evaluate classically-hard quantum kernels that capture unique notions of similarity in data. Taking inspiration from techniques in classical machine learning, this work investigates simulated quantum kernels in the context of multiple kernel learning (MKL). We consider pairwise combinations of several classical-classical, quantum-quantum, and quantum-classical kernels in an empirical investigation of their classification performance with support-vector machines. We also introduce a novel approach, which we call QCC-net (quantum-classical-convex neural network), for optimizing the weights of base kernels together with any kernel parameters. We show this approach to be effective for enhancing various performance metrics in an MKL setting. Looking at data with an increasing number of features (up to 13 dimensions), we find parameter training to be important for successfully weighting kernels in some combinations. Using the optimal kernel weights as indicators of relative utility, we find growing contributions from trainable quantum kernels in quantum-classical kernel combinations as the number of features increases. We observe the opposite trend for combinations containing simpler, non-parametric quantum kernels.

quant-ph↗

arXiv2023

A Quantum-Inspired Binary Optimization Algorithm for Representative Selection

Advancements in quantum computing are fuelling emerging applications across disciplines, including finance, where quantum and quantum-inspired algorithms can now make market predictions, detect fraud, and optimize portfolios. Expanding this toolbox, we propose the selector algorithm: a method for selecting the most representative subset of data from a larger dataset. The selected subset includes data points that simultaneously meet the two requirements of being maximally close to neighboring data points and maximally far from more distant data points where the precise notion of distance is given by any kernel or generalized similarity function. The cost function encoding the above requirements naturally presents itself as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which is well-suited for quantum optimization algorithms - including quantum annealing. While the selector algorithm has applications in multiple areas, it is particularly useful in finance, where it can be used to build a diversified portfolio from a more extensive selection of assets. After experimenting with synthetic datasets, we show two use cases for the selector algorithm with real data: (1) approximately reconstructing the NASDAQ 100 index using a subset of stocks, and (2) diversifying a portfolio of cryptocurrencies. In our analysis of use case (2), we compare the performance of two quantum annealers provided by D-Wave Systems.

quant-ph↗

arXiv2022

Quantum Variational Rewinding for Time Series Anomaly Detection

Electron dynamics, financial markets and nuclear fission reactors, though seemingly unrelated, all produce observable characteristics evolving with time. Within this broad scope, departures from normal temporal behavior range from academically interesting to potentially catastrophic. New algorithms for time series anomaly detection (TAD) are therefore certainly in demand. With the advent of newly accessible quantum processing units (QPUs), exploring a quantum approach to TAD is now relevant and is the topic of this work. Our approach - Quantum Variational Rewinding, or, QVR - trains a family of parameterized unitary time-devolution operators to cluster normal time series instances encoded within quantum states. Unseen time series are assigned an anomaly score based upon their distance from the cluster center, which, beyond a given threshold, classifies anomalous behavior. After a first demonstration with a simple and didactic case, QVR is used to study the real problem of identifying anomalous behavior in cryptocurrency market data. Finally, multivariate time series from the cryptocurrency use case are studied using IBM's Falcon r5.11H family of superconducting transmon QPUs, where anomaly score errors resulting from hardware noise are shown to be reducible by as much as 20% using advanced error mitigation techniques.

quant-ph↗

arXiv2022

Wasserstein Solution Quality and the Quantum Approximate Optimization Algorithm: A Portfolio Optimization Case Study

Optimizing of a portfolio of financial assets is a critical industrial problem which can be approximately solved using algorithms suitable for quantum processing units (QPUs). We benchmark the success of this approach using the Quantum Approximate Optimization Algorithm (QAOA); an algorithm targeting gate-model QPUs. Our focus is on the quality of solutions achieved as determined by the Normalized and Complementary Wasserstein Distance, $η$, which we present in a manner to expose the QAOA as a transporter of probability. Using $η$ as an application specific benchmark of performance, we measure it on selection of QPUs as a function of QAOA circuit depth $p$. At $n = 2$ (2 qubits) we find peak solution quality at $p=5$ for most systems and for $n = 3$ this peak is at $p=4$ on a trapped ion QPU. Increasing solution quality with $p$ is also observed using variants of the more general Quantum Alternating Operator Ansätz at $p=2$ for $n = 2$ and $3$ which has not been previously reported. In identical measurements, $η$ is observed to be variable at a level exceeding the noise produced from the finite number of shots. This suggests that variability itself should be regarded as a QPU performance benchmark for given applications. While studying the ideal execution of QAOA, we find that $p=1$ solution quality degrades when the portfolio budget $B$ approaches $n/2$ and increases when $B \approx 1$ or $n-1$. This trend directly corresponds to the binomial coefficient $nCB$ and is connected with the recently reported phenomenon of reachability deficits. Derivative-requiring and derivative-free classical optimizers are benchmarked on the basis of the achieved $η$ beyond $p=1$ to find that derivative-free optimizers are generally more effective for the given computational resources, problem sizes and circuit depths.

quant-ph↗

arXiv2021

Origin of ferroelectric domain wall alignment with surface trenches in ultrathin films

Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films and superlattices promises control over the orientation and direction of FE domain walls (DWs). Through exploiting the phenomenon of DW-surface trench (ST) parallel alignment, systems where DWs are known for becoming electrical conductors could now become useful nanocircuits using only standard lithographical techniques. Despite this clear application, the microscopic mechanism responsible for the alignment phenomenon has remained elusive. Using ultrathin PbTiO$_3$ films as a model system, we explore this mechanism with large scale density functional theory simulations on as many as 5,136 atoms. Although we expect multiple contributing factors, we show that parallel DW-ST alignment can be well explained by this configuration giving rise to an arrangement of electric dipole moments which best restore polar continuity to the film. These moments preserve the polar texture of the pristine film, thus minimizing ST-induced depolarizing fields. Given the generality of this mechanism, we suggest that STs could be used to engineer other exotic polar textures in a variety of FE nanostructures as supported by the appearance of ST-induced polar cycloidal modulations in this letter. Our simulations also support experimental observations of ST-induced negative strains which have been suggested to play a role in the alignment mechanism.

cond-mat.mtrl-sci↗

arXiv2020

Polar morphologies from first principles: PbTiO$_3$ films on SrTiO$_3$ substrates and the $p(2 \times Λ)$ surface reconstruction

Low dimensional structures comprised of ferroelectric (FE) PbTiO$_3$ (PTO) and quantum paraelectric SrTiO$_3$ (STO) are hosts to complex polarization textures such as polar waves, flux-closure domains and polar skyrmion phases. Density functional theory (DFT) simulations can provide insight into this order, but, are limited by the computational effort needed to simulate the thousands of required atoms. To relieve this issue, we use the novel multi-site support function (MSSF) method within DFT to reduce the solution time for the electronic groundstate whilst preserving high accuracy. Using MSSFs, we simulate thin PTO films on STO substrates with system sizes $>2000$ atoms. In the ultrathin limit, the polar wave texture with cylindrical chiral bubbles emerges as an intermediate phase between full flux closure domains and in-plane polarization. This is driven by an internal bias field born of the compositionally broken inversion symmetry in the [001] direction. Since the exact nature of this bias field depends sensitively on the film boundary conditions, this informs a new principle of design for manipulating chiral order on the nanoscale through the careful choice of substrate, surface termination or use of overlayers. Antiferrodistortive (AFD) order locally interacts with these polar textures giving rise to strong FE/AFD coupling at the PbO terminated surface driving a $p(2 \times Λ)$ surface reconstruction. This offers another pathway for the local control of ferroelectricity.

cond-mat.mtrl-sci↗

arXiv2020

The pseudoatomic orbital basis: electronic accuracy and soft-mode distortions in ABO$_3$ perovskites

The perovskite oxides are known to be susceptible to structural distortions over a long wavelength when compared to their parent cubic structures. From an ab initio simulation perspective, this requires accurate calculations including many thousands of atoms; a task well beyond the remit of traditional plane wave-based density functional theory (DFT). We suggest that this void can be filled using the methodology implemented in the large-scale DFT code, CONQUEST, using a local pseudoatomic orbital (PAO) basis. Whilst this basis has been tested before for some structural and energetic properties, none have treated the most fundamental quantity to the theory, the charge density $n(\mathbf{r})$ itself. An accurate description of $n(\mathbf{r})$ is vital to the perovskite oxides due to the crucial role played by short-range restoring forces (characterised by bond covalency) and long range coulomb forces as suggested by the soft-mode theory of Cochran and Anderson. We find that modestly sized basis sets of PAOs can reproduce the plane-wave charge density to a total integrated error of better than 0.5% and provide Bader partitioned ionic charges, volumes and average charge densities to similar degree of accuracy. Further, the multi-mode antiferroelectric distortion of PbZrO$_3$ and its associated energetics are reproduced by better than 99% when compared to plane-waves. This work suggests that electronic structure calculations using efficient and compact basis sets of pseudoatomic orbitals can achieve the same accuracy as high cutoff energy plane-wave calculations. When paired with the CONQUEST code, calculations with high electronic and structural accuracy can now be performed on many thousands of atoms, even on systems as delicate as the perovskite oxides.

physics.comp-ph↗