Related papers: The Adjoint Is All You Need: Characterizing Barren…
Dynamical Lie algebras (DLAs) have emerged as a valuable tool in the study of parameterized quantum circuits, helping to characterize both their expressiveness and trainability. In particular, the absence or presence of barren plateaus…
Barren plateaus have emerged as a pivotal challenge for variational quantum computing. Our understanding of this phenomenon underwent a transformative shift with the recent introduction of a Lie algebraic theory capable of explaining most…
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is…
Advances in quantum computing over the last two decades have required sophisticated mathematical frameworks to deepen the understanding of quantum algorithms. In this review, we introduce the theory of Lie groups and their algebras to…
Quantum algorithms based on the variational principle have found applications in diverse areas with a huge flexibility. But as the circuit size increases the variational landscapes become flattened, causing the so-called Barren plateau…
We develop a framework for analyzing layered quantum algorithms such as quantum alternating operator ans\"atze. Our framework relates quantum cost gradient operators, derived from the cost and mixing Hamiltonians, to classical cost…
Variational quantum algorithms (VQAs) optimize the parameters $\vec{\theta}$ of a parametrized quantum circuit $V(\vec{\theta})$ to minimize a cost function $C$. While VQAs may enable practical applications of noisy quantum computers, they…
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these…
Parameterized quantum circuits serve as ans\"{a}tze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers. Ideally, such ans\"{a}tze should be highly expressive so that a close…
We investigate the barren plateau (BP) phenomenon in variational quantum algorithms using a statistical approach. Using Gaussian function models, we identify three distinct types of BPs. The first type, which we called localized-dip BPs,…
Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge…
Determining the physically accessible unitary dynamics of a quantum system under finite Hamiltonian resources is a central problem in quantum control and Hamiltonian engineering. Dynamical Lie algebras (DLAs) provide the fundamental link…
Variational Quantum Algorithms (VQAs) are critically threatened by the Barren Plateau (BP) phenomenon. In this work, we introduce the H-EFT Variational Ansatz (H-EFT-VA), an architecture inspired by Effective Field Theory (EFT). By…
The Quantum Approximate Optimization Algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ans\"atze for…
The XY-mixer has widespread utilization in modern quantum computing, including in variational quantum algorithms, such as Quantum Alternating Operator Ansatz (QAOA). The XY ansatz is particularly useful for solving Cardinality Constrained…
Variational quantum computing offers a flexible computational paradigm with applications in diverse areas. However, a key obstacle to realizing their potential is the Barren Plateau (BP) phenomenon. When a model exhibits a BP, its parameter…
Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. While this approach reduces the number of qubits and operations required from the quantum…
Quantifying the flatness of the objective-function landscape associated with unstructured parameterized quantum circuits is important for understanding the performance of variational algorithms utilizing a "hardware-efficient ansatz",…
Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and…
The QAOA has been the subject of intense study over recent years, yet the corresponding Dynamical Lie Algebra (DLA)--a key indicator of the expressivity and trainability of VQAs--remains poorly understood beyond highly symmetric instances.…