Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing

We formalize a rigorous connection between barren plateaus (BP) in variational quantum algorithms and exponential concentration of quantum kernels for machine learning. Our results imply that recently proposed strategies to build BP-free quantum circuits can be utilized to construct useful quantum kernels for machine learning. This is illustrated by a numerical example employing a provably BP-free quantum neural network to construct kernel matrices for classification datasets...

Variational quantum algorithms (VQAs) are expected to establish valuable applications on near-term quantum computers. However, recent works have pointed out that the performance of VQAs greatly relies on the expressibility of the ansatzes and is seriously limited by optimization issues such as barren plateaus (i.e., vanishing gradients). This work proposes the state efficient ansatz (SEA) for accurate ground state preparation with improved trainability. We show that the SEA c...

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 variational quantum algorithms (VQAs). These algorithms use a classical optimizer to train a parameterized quantum circuit to accomplish certain tasks, where the circuits are usually randomly initialized. In this work, we prove that for a broad...

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 potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function land...

This review investigates the landscapes of prevalent hybrid quantum-classical optimization algorithms in many rapidly developing quantum technologies, where the objective function is either computed by a natural quantum system or a quantum ansatz that is engineered, but the optimizer is classical. In any particular case, the nature of the underlying control landscape is fundamentally important for systematic optimization of the objective. In early studies on the optimal contr...

Quantum compilation provides a method to translate quantum algorithms at a high level of abstraction into their implementations as quantum circuits on real hardware. One approach to quantum compiling is to design a parameterised circuit and to use techniques from optimisation to find the parameters that minimise the distance between the parameterised circuit and the target circuit of interest. While promising, such an approach typically runs into the obstacle of barren platea...

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", particularly for ensuring that a prohibitively flat landscape -- a so-called "barren plateau" -- is avoided. For a model of such ans\"{a}tze, we relate the typical landscape flatness to a certain family of random walks, enabling us to derive a M...

This paper presents a new hybrid Quantum Machine Learning (QML) model composed of three elements: a classical computer in charge of the data preparation and interpretation; a Gate-based Quantum Computer running the Variational Quantum Algorithm (VQA) representing the Quantum Neural Network (QNN); and an adiabatic Quantum Computer where the optimization function is executed to find the best parameters for the VQA. As of the moment of this writing, the majority of QNNs are be...

We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hami...

We provide several quantum algorithms for continuous optimization that do not require any gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. This allows us, in certain cases, to obtain exponentially better query upper bounds relative to the best known upper bounds for gradient-based optimization schemes which utilize quantum computers only for the evaluation of gradients. Our firs...