A5088973719- Quantum Computing Algorithms and Architecture
- Quantum Information and Cryptography
- Quantum Mechanics and Applications
- Quantum and electron transport phenomena
- Neural Networks and Reservoir Computing
- Quantum many-body systems
- Neural Networks and Applications
- Stochastic Gradient Optimization Techniques
- Advanced Thermodynamics and Statistical Mechanics
- Advancements in Semiconductor Devices and Circuit Design
- Atomic and Subatomic Physics Research
- Statistical Mechanics and Entropy
- Spectroscopy and Quantum Chemical Studies
- Computability, Logic, AI Algorithms
- Gaussian Processes and Bayesian Inference
- Advanced NMR Techniques and Applications
- Semiconductor Quantum Structures and Devices
- Quantum-Dot Cellular Automata
- Diamond and Carbon-based Materials Research
- Sparse and Compressive Sensing Techniques
- Model Reduction and Neural Networks
- Crystallography and Radiation Phenomena
- Advanced Control Systems Optimization
- Molecular spectroscopy and chirality
- Fault Detection and Control Systems
Los Alamos National Laboratory
2018-2024
Quantum Science Center
2021-2024
Oak Ridge National Laboratory
2023-2024
University of Waterloo
2014-2021
Centre for Quantum Technologies
2012-2014
National University of Singapore
2012-2014
Carnegie Mellon University
2010-2012
University of California, Berkeley
2005-2009
Abstract Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized circuit V ( ) to minimize cost function C . While VQAs may enable practical applications noisy computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming is an alternating layered ansatz composed blocks forming local 2-designs. Our first result states that defining in terms global observables leads exponentially vanishing gradients (i.e.,...
The Heisenberg uncertainty principle has a more precise formulation in terms of inequalities involving quantum entropies. Currently known entropic relations are presented; they capture and extend Heisenberg's idea the unpredictability outcomes incompatible measurements. Distinct results obtained for finite- infinite-dimensional Hilbert spaces. Applications surveyed, including entanglement witnesses, current ideas about wave-particle duality, analysis cryptography.
Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale (NISQ) computers. A natural question is whether noise NISQ devices places fundamental limitations VQA performance. We rigorously prove serious limitation for noisy VQAs, in that the causes training landscape have barren plateau (i.e., vanishing gradient). Specifically, local Pauli considered, we gradient vanishes exponentially number of qubits $n$ if depth ansatz grows linearly with $n$....
Parametrized quantum circuits serve as ansatze for solving variational problems and provide a flexible paradigm the programming of near-term computers. Ideally, such should be highly expressive, so that close approximation desired solution can accessed. On other hand, ansatz must also have sufficiently large gradients to allow training. Here, we derive fundamental relationship between these two essential properties: expressibility trainability. This is done by extending well-established...
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach discovering such algorithms. We apply our method to ubiquitous primitive: computing the overlap ${\rm Tr}(\rho\sigma)$ between two states $\rho$ $\sigma$. The standard algorithm this task, known as Swap Test, is used in many applications support vector machines, and, when specialized...
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized circuit on training data set, and subsequently making predictions testing set (i.e., generalizing). In this work, we provide comprehensive study of generalization performance in QML after limited number $N$ points. We show that the error model with $T$ trainable gates scales at worst as $\sqrt{T/N}$. When only $K \ll T$ have undergone substantial change optimization process, prove improves to...
Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this has been tempered by existence exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, Convolutional Neural Networks (QCNNs) proposed, involving a sequence convolutional and pooling layers that reduce number qubits while preserving information about relevant data features. In work we rigorously analyze gradient...
Abstract Variational hybrid quantum-classical algorithms (VHQCAs) are near-term that leverage classical optimization to minimize a cost function, which is efficiently evaluated on quantum computer. Recently VHQCAs have been proposed for compiling, where target unitary U compiled into short-depth gate sequence V . In this work, we report surprising form of noise resilience these algorithms. Namely, find one often learns the correct (i.e. variational parameters) despite various sources...
Achieving near-term quantum advantage will require accurate estimation of observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based computers. The generates training data $\{X_i^{\text{noisy}},X_i^{\text{exact}}\}$ via circuits composed largely Clifford gates, which can be efficiently simulated classically, where $X_i^{\text{noisy}}$ and $X_i^{\text{exact}}$ are noisy noiseless respectively. Fitting...
Compiling quantum algorithms for near-term computers (accounting connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry academia. Avoiding the exponential overhead of classical simulation dynamics will allow compilation larger algorithms, strategy this to evaluate an algorithm's cost on computer. To end, we propose variational hybrid quantum-classical algorithm called quantum-assisted compiling (QAQC). In QAQC, use overlap...
Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on data. Rigorous scaling results are urgently needed specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze gradient (and hence trainability) recently architecture that call dissipative QNNs (DQNNs), where input qubits each layer discarded layer's output. We find DQNNs can exhibit barren plateaus,...
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed understand scalability. One known scaling result VQAs barren plateaus, where certain circumstances lead exponentially vanishing gradients. It common folklore that problem-inspired ansatzes avoid but in fact, very little about gradient scaling. In this we employ tools from optimal control develop a framework can diagnose the...
As quantum computers become available to the general public, need has arisen train a cohort of programmers, many whom have been developing classical computer programs for most their careers. While currently less than 100 qubits, computing hardware is widely expected grow in terms qubit count, quality, and connectivity. This review aims explain principles programming, which are quite different from with straightforward algebra that makes understanding underlying fascinating mechanical...
Abstract Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application near-term quantum computers. The variational eigensolver (VQE) treats the case when matrix is a Hamiltonian. Here, we address density ρ . We introduce state (VQSE), which analogous to VQE in that it variationally learns largest as well gate sequence V prepares corresponding eigenvectors. VQSE exploits connection between diagonalization majorization define cost function...
Abstract Quantum neural networks (QNNs) offer a powerful paradigm for programming near-term quantum computers and have the potential to speed up applications ranging from data science chemistry materials science. However, possible obstacle realizing that speed-up is barren plateau (BP) phenomenon, whereby gradient vanishes exponentially in system size n certain QNN architectures. The question of whether high-order derivative information such as Hessian could help escape BP was recently posed...
The impact of hardware noise on quantum circuits is circumvented using a machine learning strategy that outputs the best circuit design for optimizing performance given algorithmic task under noisy environment.
Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but relevant chaos and thermalization. In this Letter, we ask if machine learning (QML) could be used such processes. We prove a no-go theorem for an unknown scrambling process with QML, showing that it is highly probable any variational Ansatz have barren plateau landscape, i.e., cost gradients vanish exponentially in the system size. This...
Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term computers. However, very little known about cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate connection between three different features that have been observed PQCs: (1) exponentially vanishing gradients (called barren plateaus), (2) exponential concentration mean, and (3) narrowness minina narrow gorges). We analytically...
Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that with little to no inductive biases (i.e., assumptions about the problem embedded model) likely have trainability and generalization issues, especially for large sizes. As such, is fundamental develop schemes encode as much information available hand. In this work we present a simple, yet powerful, framework where underlying invariances used build QML that, by...
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum Linear Solver (VQLS), on near-term computers. VQLS seeks variationally prepare <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>x</mml:mi><mml:mo fence="false"...
Abstract A new paradigm for data science has emerged, with quantum data, models, and computational devices. This field, called machine learning (QML), aims to achieve a speedup over traditional analysis. However, its success usually hinges on efficiently training the parameters in neural networks, field of QML is still lacking theoretical scaling results their trainability. Some trainability have been proven closely related variational algorithms (VQAs). While both fields involve...
Quantum neural network architectures that have little to no inductive biases are known face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge creating models encoding the symmetries of task. This is materialized through usage equivariant networks action which commutes with symmetry. In work, we import these ideas quantum realm presenting comprehensive theoretical framework design (EQNNs) for essentially any...