arXiv subjects

Amara Katabarwa

Publications and source records attributed to Amara Katabarwa.

15 recordsLinked to original sources

arXiv2025

Detailed assessment of calculating drag force with quantum computers: Explicit time-evolution precludes exponential advantage for nonlinear differential equations

This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass classical computational limits by generating detailed quantum resource estimates (QREs) in terms of logical qubits and $T$-gate counts. Our analysis is based on a quantum algorithm leveraging Carleman linearization of the lattice Boltzmann method (LBM), which has been suggested to offer exponential speedup. We develop efficient block encodings for LBM matrices and a method for amplitude-encoding drag force. We apply the method to the simple case of fluid flow past a sphere across a range of Reynolds numbers ($\mathrm{Re}$). We estimate the required (logical qubits)$\times$($T$-gates), finding them to be prohibitively large, ranging from $10^{21}$ to $10^{39}$. While classical simulations scale as $O(\mathrm{Re}^3)$, our QREs exhibit a modest polynomial scaling of $O(\mathrm{Re}^{2.68})$, indicating no exponential quantum advantage. We attribute this limitation to an intrinsic power-law relationship between spatial grid resolution and time-stepping requirements that is a fundamental characteristic of explicit methods for evolving nonlinear differential equations. Thus, quantum computers are unlikely to provide utility in applications that require time-evolving fluids and other systems of nonlinear differential equations.

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arXiv2025

Constant-Factor Improvements in Quantum Algorithms for Linear Differential Equations

Finding the solution to linear ordinary differential equations of the form $\partial_t u(t) = -A(t)u(t)$ has been a promising theoretical avenue for \textit{asymptotic} quantum speedups. However, despite the improvements to existing quantum differential equation solvers over the years, little is known about \textit{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 $U_A$ that block encodes the generator $A$. 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 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 \textit{fast-forwardable}, these findings provide a 100-200x reduction in runtime costs. This analysis contributes towards establishing more promising applications for quantum computing.

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arXiv2025

On proving the robustness of algorithms for early fault-tolerant quantum computers

The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we anticipate an era of ''costly'' error correction, or early fault-tolerant quantum computing. Costly error correction might warrant settling for error-prone quantum computations. This motivates the development of quantum algorithms which are robust to some degree of error as well as methods to analyze their performance in the presence of error. Several such algorithms have recently been developed; what is missing is a methodology to analyze their robustness. To this end, we introduce a randomized algorithm for the task of phase estimation and give an analysis of its performance under two simple noise models. In both cases the analysis leads to a noise threshold, below which arbitrarily high accuracy can be achieved by increasing the number of samples used in the algorithm. As an application of this general analysis, we compute the maximum ratio of the largest circuit depth and the dephasing scale such that performance guarantees hold. We calculate that the randomized algorithm can succeed with arbitrarily high probability as long as the required circuit depth is less than 0.916 times the dephasing scale.

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arXiv2023

Early Fault-Tolerant Quantum Computing

Over the past decade, research in quantum computing has tended to fall into one of two camps: near-term intermediate scale quantum (NISQ) and fault-tolerant quantum computing (FTQC). Yet, a growing body of work has been investigating how to use quantum computers in transition between these two eras. This envisions operating with tens of thousands to millions of physical qubits, able to support fault-tolerant protocols, though operating close to the fault-tolerant threshold. Two challenges emerge from this picture: how to model the performance of devices that are continually improving and how to design algorithms to make the most use of these devices? In this work we develop a model for the performance of early fault-tolerant quantum computing (EFTQC) architectures and use this model to elucidate the regimes in which algorithms suited to such architectures are advantageous. As a concrete example, we show that, for the canonical task of phase estimation, in a regime of moderate scalability and using just over one million physical qubits, the ``reach'' of the quantum computer can be extended (compared to the standard approach) from 90-qubit instances to over 130-qubit instances using a simple early fault-tolerant quantum algorithm, which reduces the number of operations per circuit by a factor of 100 and increases the number of circuit repetitions by a factor of 10,000. This clarifies the role that such algorithms might play in the era of limited-scalability quantum computing.

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arXiv2023

Hypothesis Testing for Error Mitigation: How to Evaluate Error Mitigation

In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation will be a necessary tool to extract useful performance out of quantum devices. However, there is a big gap between the noise models often assumed by error mitigation techniques and the actual noise on quantum devices. As a consequence, there arises a gap between the theoretical expectations of the techniques and their everyday performance. Cloud users of quantum devices in particular, who often take the devices as they are, feel this gap the most. How should they parametrize their uncertainty in the usefulness of these techniques and be able to make judgement calls between resources required to implement error mitigation and the accuracy required at the algorithmic level? To answer the first question, we introduce hypothesis testing within the framework of quantum error mitigation and for the second question, we propose an inclusive figure of merit that accounts for both resource requirement and mitigation efficiency of an error mitigation implementation. The figure of merit is useful to weigh the trade-offs between the scalability and accuracy of various error mitigation methods. Finally, using the hypothesis testing and the figure of merit, we experimentally evaluate $16$ error mitigation pipelines composed of singular methods such as zero noise extrapolation, randomized compilation, measurement error mitigation, dynamical decoupling, and mitigation with estimation circuits. In total our data involved running $275,640$ circuits on two IBM quantum computers.

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arXiv2022

Noise tailoring for Robust Amplitude Estimation

A universal fault-tolerant quantum computer holds the promise to speed up computational problems that are otherwise intractable on classical computers; however, for the next decade or so, our access is restricted to noisy intermediate-scale quantum (NISQ) computers and, perhaps, early fault tolerant (EFT) quantum computers. This motivates the development of many near-term quantum algorithms including robust amplitude estimation (RAE), which is a quantum-enhanced algorithm for estimating expectation values. One obstacle to using RAE has been a paucity of ways of getting realistic error models incorporated into this algorithm. So far the impact of device noise on RAE is incorporated into one of its subroutines as an exponential decay model, which is unrealistic for NISQ devices and, maybe, for EFT devices; this hinders the performance of RAE. Rather than trying to explicitly model realistic noise effects, which may be infeasible, we circumvent this obstacle by tailoring device noise to generate an effective noise model, whose impact on RAE closely resembles that of the exponential decay model. Using noisy simulations, we show that our noise-tailored RAE algorithm is able to regain improvements in both bias and precision that are expected for RAE. Additionally, on IBM's quantum computer our algorithm demonstrates advantage over the standard estimation technique in reducing bias. Thus, our work extends the feasibility of RAE on NISQ computers, consequently bringing us one step closer towards achieving quantum advantage using these devices.

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arXiv2022

Connecting geometry and performance of two-qubit parameterized quantum circuits

Parameterized quantum circuits (PQCs) are a central component of many variational quantum algorithms, yet there is a lack of understanding of how their parameterization impacts algorithm performance. We initiate this discussion by using principal bundles to geometrically characterize two-qubit PQCs. On the base manifold, we use the Mannoury-Fubini-Study metric to find a simple equation relating the Ricci scalar (geometry) and concurrence (entanglement). By calculating the Ricci scalar during a variational quantum eigensolver (VQE) optimization process, this offers us a new perspective to how and why Quantum Natural Gradient outperforms the standard gradient descent. We argue that the key to the Quantum Natural Gradient's superior performance is its ability to find regions of high negative curvature early in the optimization process. These regions of high negative curvature appear to be important in accelerating the optimization process.

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arXiv2022

Generation of High-Resolution Handwritten Digits with an Ion-Trap Quantum Computer

Generating high-quality data (e.g. images or video) is one of the most exciting and challenging frontiers in unsupervised machine learning. Utilizing quantum computers in such tasks to potentially enhance conventional machine learning algorithms has emerged as a promising application, but poses big challenges due to the limited number of qubits and the level of gate noise in available devices. In this work, we provide the first practical and experimental implementation of a quantum-classical generative algorithm capable of generating high-resolution images of handwritten digits with state-of-the-art gate-based quantum computers. In our quantum-assisted machine learning framework, we implement a quantum-circuit based generative model to learn and sample the prior distribution of a Generative Adversarial Network. We introduce a multi-basis technique that leverages the unique possibility of measuring quantum states in different bases, hence enhancing the expressivity of the prior distribution. We train this hybrid algorithm on an ion-trap device based on $^{171}$Yb$^{+}$ ion qubits to generate high-quality images and quantitatively outperform comparable classical Generative Adversarial Networks trained on the popular MNIST data set for handwritten digits.

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arXiv2021

Reducing runtime and error in VQE using deeper and noisier quantum circuits

The rapid development of noisy intermediate-scale quantum (NISQ) devices has raised the question of whether or not these devices will find commercial use. Unfortunately, a major shortcoming of many proposed NISQ-amenable algorithms, such as the variational quantum eigensolver (VQE), is coming into view: the algorithms require too many independent quantum measurements to solve practical problems in a reasonable amount of time. This motivates the central question of our work: how might we speed up such algorithms in spite of the impact of error on NISQ computations? We demonstrate on quantum hardware that the estimation of expectation values, a core subroutine of many quantum algorithms including VQE, can be improved in terms of precision and accuracy by using a technique we call Robust Amplitude Estimation. Consequently, this method reduces the runtime to achieve the same mean-squared error compared to the standard prepare-and-measure estimation method. The surprising result is that by using deeper, and therefore more error-prone, quantum circuits, we realize more accurate quantum computations in less time. As the quality of quantum devices improves, this method will provide a proportional reduction in estimation runtime. This technique may be used to speed up quantum computations into the regime of early fault-tolerant quantum computation and aid in the realization of quantum advantage.

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arXiv2021

Quantum algorithm for credit valuation adjustments

Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases, credit valuation adjustment (CVA), and identify opportunities and challenges towards quantum advantage for practical instances. To improve the depths of quantum circuits for solving such problem, we draw on various heuristics that indicate the potential for significant improvement over well-known techniques such as reversible logical circuit synthesis. In minimizing the resource requirements for amplitude amplification while maximizing the speedup gained from the quantum coherence of a noisy device, we adopt a recently developed Bayesian variant of quantum amplitude estimation using engineered likelihood functions (ELF). We perform numerical analyses to characterize the prospect of quantum speedup in concrete CVA instances over classical Monte Carlo simulations.

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arXiv2021

Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor

In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms could provide a quantum advantage. In this work, we study a QAOA-based quantum optimization algorithm by implementing the Variational Quantum Factoring (VQF) algorithm. We execute experimental demonstrations using a superconducting quantum processor and investigate the trade-off between quantum resources (number of qubits and circuit depth) and the probability that a given biprime is successfully factored. In our experiments, the integers 1099551473989, 3127, and 6557 are factored with 3, 4, and 5 qubits, respectively, using a QAOA ansatz with up to 8 layers and we are able to identify the optimal number of circuit layers for a given instance to maximize success probability. Furthermore, we demonstrate the impact of different noise sources on the performance of QAOA and reveal the coherent error caused by the residual ZZ-coupling between qubits as a dominant source of error in the superconducting quantum processor.

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arXiv2018

Measurement of GHZ and cluster state entanglement monotones in transmon qubits

Experimental detection of entanglement in superconducting qubits has been mostly limited, for more than two qubits, to witness-based and related approaches that can certify the presence of some entanglement, but not rigorously quantify how much. Here we measure the entanglement of three- and four-qubit GHZ and linear cluster states prepared on the 16-qubit IBM Rueschlikon (ibmqx5) chip, by estimating their entanglement monotones. GHZ and cluster states not only have wide application in quantum computing, but also have the convenient property of having similar state preparation circuits and fidelities, allowing for a meaningful comparison of their degree of entanglement. We also measure the decay of the monotones with time, and find in the GHZ case that they actually oscillate, which we interpret as a drift in the relative phase between the $|0\rangle^{\otimes n}$ and $|1\rangle^{\otimes n}$ components, but not an oscillation in the actual entanglement. After experimentally correcting for this drift with virtual Z rotations we find that the GHZ states appear to be considerably more robust than cluster states, exhibiting higher fidelity and entanglement at later times. Our results contribute to the quantification and understanding of the strength and robustness of multi-qubit entanglement in the noisy environment of a superconducting quantum computer.

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arXiv2017

A dynamical interpretation of the Pauli Twirling Approximation and Quantum Error Correction

One of simplest and most widely used error model in working with quantum circuits is the Pauli Twirling Approximation (PTA). Restricting ourselves to analysis of free dynamics of qubits we show explicitly how application of PTA is equivalent to ignoring most of the quantum back action of the system and give a general argument as to why this approximation leads to low logical error rates in fault tolerant stabilizer circuits as compared to other quantum channels. We provide numerical evidence that PTA's performance in modeling noise gets worse as number of qubits increase.

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arXiv2017

Quantum Projective Simulation with Hamiltonian Evolution: A study in reinforcement learning

Projective Simulation was introduced as a novel approach to Artificial Intelligence. It involves a deliberation procedure that consists of a random walk on a graph of clips and allows for the learning agent to project itself into the future before committing to an action. Here we study and analyze a quantum mechanical version in which the random walk is performed by two kinds of Hamiltonians. The first kind is implemented by naively embedding the classical model in a quantum model by turning the clips into qubits. The other allows for storing clips in superpositions of qubits allowing for a potentially purely quantum mechanical learning procedure in which the perception of the environment is purely quantum mechanical but the action is classical. We lastly introduce the concept of interacting projective agents for both the classical and quantum mechanical case.

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arXiv2015

Three-step implementation of any nxn unitary with a complete graph of n qubits

Quantum computation with a complete graph of superconducting qubits has been recently proposed, and applications to amplitude amplification, phase estimation, and the simulation of realistic atomic collisions given [Phys. Rev. A 91, 062309 (2015)]. This single-excitation subspace (SES) approach does not require error correction and is practical now. Previously it was shown how to implement symmetric nxn unitaries in a single step, but not general unitaries. Here we show that any element in the unitary group U(n) can be executed in no more than three steps, for any n. This enables the implementation of highly complex operations in constant time, and in some cases even allows for the compilation of an entire algorithm down to only three operations. Using this protocol we show how to prepare any pure state of an SES chip in three steps, and also how to compute, for a given SES state rho, the expectation value of any nxn Hermitian observable O in a constant number of steps.

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