arXiv subjects

Andrew Sornborger

Publications and source records attributed to Andrew Sornborger.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Magic State Factory Via Transversal Non-Clifford Gate

Magic-state preparation is a central component of fault-tolerant quantum computing. Recent theoretical and experimental successes in code-switch-based magic-state preparation have underscored the promise of these methods for quantum error correction. Similarly, magic-state cultivation has likewise been demonstrated in both numerical and experimental settings. However, a thorough comparison between magic-state cultivation and code-switch-based magic-state factories is still missing. In this work, we carry out end-to-end simulations of magic-state preparation using code switching and compare its resource requirements and performance against magic-state cultivation. As part of this analysis, we develop a lattice-surgery protocol for transfer between the doubled color code and the rotated surface code. We extend the complete code-switching protocol to the $d=5$ doubled color code and perform the corresponding end-to-end simulations. Finally, we propose two fault-tolerant magic-state preparation protocols that combine phase-kickback checks with a transversal non-Clifford gate.

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arXiv2026

Efficient Magic State Cultivation for $\sqrt{T}$ Gates

Recently, experimental and theoretical quantum error correction methodology has seen remarkable breakthroughs. In particular, magic state cultivation has been shown to simplify magic-state preparation and make it feasible for near-term devices. However, recent research on magic state cultivation has focused primarily on the cultivation of $T\left| + \right>_L$. Only a few other magic state cultivation methods beyond $T\left| + \right>_L$ have been investigated. Here, we generalize phase kickback checks for magic states at arbitrary Clifford hierarchy levels in specific codes. We provide an example of cultivation of $\sqrt{T}\left| + \right>_L$ in the doubled color code and the corresponding escape strategy using lattice surgery from the color code to large rotated surface codes. Using state vector simulation for un-grown cultivation, we observe a strong consistence between $S\left| + \right>_L$ and $\sqrt{T}\left| + \right>_L$ cultivation's performance on the doubled color code. Finally, we discuss the application of the corresponding $\sqrt{T}\left| + \right>_L$ cultivation, incorporating the STAR architecture and $T$ gates, for early fault-tolerant quantum computing and its potential to shorten gate synthesis in the fully fault-tolerant quantum computing era.

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arXiv2025

Transversal architecture for megaquop-scale quantum simulation with neutral atoms

Quantum computing experiments have made remarkable progress in demonstrating key components of quantum error correction, a prerequisite for scalable quantum computation. While we anticipate the arrival of early fault-tolerant quantum hardware capable of a million reliable quantum operations, the cost of preparing low-noise `magic resource states' presents a formidable challenge. The recently proposed partially-fault-tolerant architecture based on a space-time efficient analog rotation (STAR) approach attempts to address this challenge by using post-selection to prepare low-noise, small-angle magic states. Its proposed physical implementation, however, assumes fixed qubit connectivity, resulting in implementation costs closer to leading fully-fault-tolerant approaches. Here, we propose the transversal STAR architecture and co-design it with neutral-atom quantum hardware, deriving significant savings in logical layout, time, and space overhead. Through circuit-level simulations, we derive the logical noise model for surface-code-based transversal STAR gadgets and verify their composability. At its limit, the transversal STAR architecture can efficiently simulate local Hamiltonians with a total simulation volume exceeding 600. Achieving this limit would require approximately 10,000 physical qubits at a physical error rate of $10^{-3}$. This is equivalent to a fully-fault-tolerant computation requiring over $10^6$-$10^7$ $T$ gates. Finally, we extend the transversal STAR architecture to high-rate quantum codes, demonstrating how a limited set of highly parallel transversal Clifford gates and generalized small-angle magic injection can be utilized for effective quantum simulation. We anticipate that the co-designed transversal STAR architecture could substantially reduce the physical resources necessary for early-fault-tolerant quantum simulation at the megaquop scale.

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arXiv2025

Roadblocks and Opportunities in Quantum Algorithms -- Insights from the National Quantum Initiative Joint Algorithms Workshop, May 20--22, 2024

The National Quantum Initiative Joint Algorithms Workshop brought together researchers across academia, national laboratories, and industry to assess the current landscape of quantum algorithms and discuss roadblocks to progress. The workshop featured discussions on emerging algorithmic techniques, resource constraints in near-term hardware, and opportunities for co-design across software and systems. Presented here are seven topics from the workshop, each highlighting a critical challenge or promising opportunity discussed during the event. Together, they offer a snapshot of the field's evolving priorities and a shared vision for what is needed to advance quantum computational capabilities.

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arXiv2025

Variational optical phase learning on a continuous-variable quantum compiler

Quantum process learning is a fundamental primitive that draws inspiration from machine learning with the goal of better studying the dynamics of quantum systems. One approach to quantum process learning is quantum compilation, whereby an analog quantum operation is digitized by compiling it into a series of basic gates. While there has been significant focus on quantum compiling for discrete-variable systems, the continuous-variable (CV) framework has received comparatively less attention. We present an experimental implementation of a CV quantum compiler that uses two mode-squeezed light to learn a Gaussian unitary operation. We demonstrate the compiler by learning a parameterized linear phase unitary through the use of target and control phase unitaries to demonstrate a factor of 5.4 increase in the precision of the phase estimation and a 3.6-fold acceleration in the time-to-solution metric when leveraging quantum resources. Our results are enabled by the tunable control of our cost landscape via variable squeezing, thus providing a critical framework to simultaneously increase precision and reduce time-to-solution.

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arXiv2024

SymBreak: Mitigating Quantum Degeneracy Issues in QLDPC Code Decoders by Breaking Symmetry

Quantum error correction (QEC) is critical for scalable and reliable quantum computing, but existing solutions, such as surface codes, incur significant qubit overhead. Quantum low-density parity check (qLDPC) codes have recently emerged as a promising alternative, requiring fewer qubits. However, the lack of efficient decoders remains a major barrier to their practical implementation. In this work, we introduce SymBreak, a novel decoder for qLDPC codes that adaptively modifies the decoding graph to improve the performance of state-of-the-art belief propagation (BP) decoders. Our key contribution is identifying quantum degeneracy as a root cause of the convergence issues often encountered in BP decoding of quantum LDPC codes. We propose a solution that mitigates this issue at the decoding graph level, achieving both fast and accurate decoding. Our results demonstrate that SymBreak outperforms BP and BP+OSD-a more complex variant of BP-with a $16.17\times$ reduction in logical error rate compared to BP and $3.23\times$ compared to BP+OSD across various qLDPC code families. With only an $18.97$% time overhead compared to BP, SymBreak provides significantly faster decoding times than BP+OSD, representing a major advancement in efficient and accurate decoding for qLDPC-based QEC architectures.

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arXiv2024

CaliScalpel: In-Situ and Fine-Grained Qubit Calibration Integrated with Surface Code Quantum Error Correction

Quantum Error Correction (QEC) is a cornerstone of fault-tolerant, large-scale quantum computing. However, qubit error drift significantly degrades QEC performance over time, necessitating periodic calibration. Traditional calibration methods disrupt quantum states, requiring system downtime and making in situ calibration infeasible. We present CaliScalpel, an innovative framework for in situ calibration in surface codes. The core idea behind CaliScalpel is leveraging code deformation to isolate qubits undergoing calibration from logical patches. This allows calibration to proceed concurrently with computation, while code enlargement maintains error correction capabilities with minimal qubit overhead. Additionally, CaliScalpel incorporates optimized calibration schedules derived from detailed device characterization, effectively minimizing physical error rates. Our results show that CaliScalpel achieves concurrent calibration and computation with modest qubit overhead and negligible execution time impact, marking a significant step toward practical in situ calibration in surface-code-based quantum computing systems.

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arXiv2024

Neuromorphic on-chip reservoir computing with spiking neural network architectures

Reservoir computing is a promising approach for harnessing the computational power of recurrent neural networks while dramatically simplifying training. This paper investigates the application of integrate-and-fire neurons within reservoir computing frameworks for two distinct tasks: capturing chaotic dynamics of the Hénon map and forecasting the Mackey-Glass time series. Integrate-and-fire neurons can be implemented in low-power neuromorphic architectures such as Intel Loihi. We explore the impact of network topologies created through random interactions on the reservoir's performance. Our study reveals task-specific variations in network effectiveness, highlighting the importance of tailored architectures for distinct computational tasks. To identify optimal network configurations, we employ a meta-learning approach combined with simulated annealing. This method efficiently explores the space of possible network structures, identifying architectures that excel in different scenarios. The resulting networks demonstrate a range of behaviors, showcasing how inherent architectural features influence task-specific capabilities. We study the reservoir computing performance using a custom integrate-and-fire code, Intel's Lava neuromorphic computing software framework, and via an on-chip implementation in Loihi. We conclude with an analysis of the energy performance of the Loihi architecture.

cs.NE↗

arXiv2024

Probabilistic Flux Limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters has been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Moreover, while aleatoric (inherent randomness) and epistemic (lack of knowledge) uncertainty is commonplace in fluid dynamical systems, these effects are generally ignored in the design of flux limiters. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. This new, {\it probabilistic flux limiter}, learned with high-resolution data, consists of a set of flux limiting functions with associated probabilities, which define the frequencies of selection for their use. Using the example of Burgers' equation, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters, and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

physics.flu-dyn↗

arXiv2024

A Search for Classical Subsystems in Quantum Worlds

Decoherence and einselection have been effective in explaining several features of an emergent classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into constituent system and environment subsystems, as well as specially constructed Hamiltonians. In this work, we take a systematic approach to discover, given a fixed Hamiltonian, (potentially) several factorizations (or tensor product structures) of a global Hilbert space that admit a quasi-classical description of subsystems in the sense that certain states (the "pointer states") are robust to entanglement. We show that every Hamiltonian admits a pointer basis in the factorization where the energy eigenvectors are separable. Furthermore, we implement an algorithm that allows us to discover a multitude of factorizations that admit pointer states and use it to explore these quasi-classical "realms" for both random and structured Hamiltonians. We also derive several analytical forms that the Hamiltonian may take in such factorizations, each with its unique set of features. Our approach has several implications: it enables us to derive the division into quasi-classical subsystems, demonstrates that decohering subsystems do not necessarily align with our classical notion of locality, and challenges ideas expressed by some authors that the propensity of a system to exhibit classical dynamics relies on minimizing the interaction between subsystems. From a quantum foundations perspective, these results lead to interesting ramifications for relative-state interpretations. From a quantum engineering perspective, these results may be useful in characterizing decoherence free subspaces and other passive error avoidance protocols.

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arXiv2023

High-fidelity dimer excitations using quantum hardware

Many-body entangled quantum spin systems exhibit emergent phenomena such as topological quantum spin liquids with distinct excitation spectra accessed in inelastic neutron scattering (INS) experiments. Here we simulate the dynamics of a quantum spin dimer, the basic quantum unit of emergent many-body spin systems. While canonical Trotterization methods require deep circuits precluding long time-scale simulations, we demonstrate 'direct' Resource-Efficient Fast-forwarding (REFF) measurements with short-depth circuits that can be used to capture longer time dynamics on quantum hardware. The temporal evolution of the 2-spin correlation coefficients enabled the calculation of the dynamical structure factor $S(\mathbf{Q},ω)$ - the key component of the neutron scattering cross-section. We simulate the triplet gap and the triplet splitting of the quantum dimer with sufficient fidelity to compare to experimental neutron data. Our results on current circuit hardware pave an important avenue to benchmark, or even predict, the outputs of the costly INS experiments.

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arXiv2023

Machine Learning Changes the Rules for Flux Limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations (DNSs) has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock capturing methods. Focusing on flux limiters provides a specific plug-and-play component for existing numerical methods. Since their introduction, an array of flux limiters has been designed. Using the coarse-grained Burgers' equation, we show that flux-limiters may be rank-ordered in terms of their log-error relative to high-resolution data. We then develop theory to find an optimal flux-limiter and present flux-limiters that outperform others tested for integrating Burgers' equation on lattices with $2\times$, $3\times$, $4\times$, and $8\times$ coarse-grainings. We train a continuous piecewise linear limiter by minimizing the mean-squared misfit to 6-grid point segments of high-resolution data, averaged over all segments. While flux limiters are generally designed to have an output of $ϕ(r) = 1$ at a flux ratio of $r = 1$, our limiters are not bound by this rule, and yet produce a smaller error than standard limiters. We find that our machine learned limiters have distinctive features that may provide new rules-of-thumb for the development of improved limiters. Additionally, we use our theory to learn flux-limiters that outperform standard limiters across a range of values (as opposed to at a specific fixed value) of coarse-graining, number of discretized bins, and diffusion parameter. This demonstrates the ability to produce flux limiters that should be more broadly useful than standard limiters for general applications.

physics.flu-dyn↗

arXiv2022

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number $N$ of training data points. We show that the generalization error of a quantum machine learning model with $T$ trainable gates scales at worst as $\sqrt{T/N}$. When only $K \ll T$ gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $\sqrt{K / N}$. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

quant-ph↗

arXiv2022

Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets

The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training data set. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process (the quantum analog of a function) with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this work, we show that entangled data sets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our work establishes that entanglement is a commodity in quantum machine learning.

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arXiv2021

Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete variable hardware, less has been paid to compiling in the continuous variable paradigm. Here we motivate several, closely related, short depth continuous variable algorithms for quantum compilation. We analyse the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr non-linearities. We further make connections between this framework and quantum learning theory in the continuous variable setting by deriving No-Free-Lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using Two-Mode-Squeezed states.

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arXiv2021

The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardware

The capabilities of natural neural systems have inspired new generations of machine learning algorithms as well as neuromorphic very large-scale integrated (VLSI) circuits capable of fast, low-power information processing. However, it has been argued that most modern machine learning algorithms are not neurophysiologically plausible. In particular, the workhorse of modern deep learning, the backpropagation algorithm, has proven difficult to translate to neuromorphic hardware. In this study, we present a neuromorphic, spiking backpropagation algorithm based on synfire-gated dynamical information coordination and processing, implemented on Intel's Loihi neuromorphic research processor. We demonstrate a proof-of-principle three-layer circuit that learns to classify digits from the MNIST dataset. To our knowledge, this is the first work to show a Spiking Neural Network (SNN) implementation of the backpropagation algorithm that is fully on-chip, without a computer in the loop. It is competitive in accuracy with off-chip trained SNNs and achieves an energy-delay product suitable for edge computing. This implementation shows a path for using in-memory, massively parallel neuromorphic processors for low-power, low-latency implementation of modern deep learning applications.

cs.NE↗

arXiv2021

Long-time simulations with high fidelity on quantum hardware

Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems. However, while rapidly improving, these devices have short coherence times, limiting the depth of algorithms that may be successfully implemented. Here we demonstrate that, despite these limitations, it is possible to implement long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on the Rigetti and IBM quantum computers, maintaining a fidelity of at least 0.9 for over 600 time steps. This is a factor of 150 longer than is possible using the iterated Trotter method. Our simulations are performed using a new algorithm that we call the fixed state Variational Fast Forwarding (fsVFF) algorithm. This algorithm decreases the circuit depth and width required for a quantum simulation by finding an approximate diagonalization of a short time evolution unitary. Crucially, fsVFF only requires finding a diagonalization on the subspace spanned by the initial state, rather than on the total Hilbert space as with previous methods, substantially reducing the required resources. We further demonstrate the viability of fsVFF through large numerical implementations of the algorithm, as well as an analysis of its noise resilience and the scaling of simulation errors.

quant-ph↗

arXiv2021

Quantum simulation of operator spreading in the chaotic Ising model

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a 4-spin Ising model as a function of space, time, and integrability. Reaching 4 spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.

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