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Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…
The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known…
Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Exploring quantum applications of near-term quantum devices is a rapidly growing field of quantum information science with both theoretical and practical interests. A leading paradigm to establish such near-term quantum applications is…
The randomized linear combination of unitaries (LCU) method with many applications to early fault-tolerant quantum computing algorithms has been proposed. This quantum algorithm computes the same expectation values as the original, fully…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit…
Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of…
Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in…
Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the…
In the context of Noisy Intermediate-Scale Quantum (NISQ) computing, parameterized quantum circuits (PQCs) represent a promising paradigm for tackling challenges in quantum sensing, optimal control, optimization, and machine learning on…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error of measurement outcome. While the uncertainty can be reduced by…
Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore…
With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short…