#29: July 3rd – July 9th

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Thermalization in Kitaev’s quantum double models via Tensor Network techniques

We show that the Davies generator associated to any 2D Kitaev’s quantum double model has a non-vanishing spectral gap in the thermodynamic limit. This validates rigorously the extended belief that those models are useless as self-correcting quantum memories, even in the non-abelian case. The proof uses recent ideas and results regarding the characterization of the spectral gap for parent Hamiltonians associated to Projected Entangled Pair States in terms of a bulk-boundary correspondence.

The Variational Power of Quantum Circuit Tensor Networks

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than 104104 parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for both the energy and correlation functions of the 1D Heisenberg and Fermi-Hubbard models in the gapless regime. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of quantum advantage with respect to expressiveness in the representation of physical ground-states.

Optimal metrology with variational quantum circuits on trapped ions

Cold atoms and ions exhibit unparalleled performance in frequency metrology epitomized in the atomic clock. More recently, such atomic systems have been used to implement programmable quantum computers and simulators with highest reported operational fidelities across platforms. Their strength in metrology and quantum information processing offers the opportunity to utilize tailored, programmable entanglement generation to approach the `optimal quantum sensor’ compatible with quantum mechanics. Here we report quantum enhancement in metrology beyond squeezing through low-depth, variational quantum circuits searching for optimal input states and measurement operators in a trapped ion platform. We perform entanglement-enhanced Ramsey interferometry finding optimal parameters for variational quantum circuits using a Bayesian approach to stochastic phase estimation tailored to the sensor platform capabilities and finite dynamic range of the interferometer. We verify the performance by both directly using theory predictions of optimal parameters, and performing online quantum-classical feedback optimization to `self-calibrate’ the variational parameters. In both cases we find that variational circuits outperform classical and direct spin squeezing strategies under realistic noise and imperfections. With 26 ions we achieve 2.02(8) dB of metrological gain over classical interferometers.

Combinatorial Optimization with Physics-Inspired Graph Neural Networks

We demonstrate how graph neural networks can be used to solve combinatorial optimization problems. Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum cut, minimum vertex cover, maximum independent set, as well as Ising spin glasses and higher-order generalizations thereof in the form of polynomial unconstrained binary optimization problems. We apply a relaxation strategy to the problem Hamiltonian to generate a differentiable loss function with which we train the graph neural network and apply a simple projection to integer variables once the unsupervised training process has completed. We showcase our approach with numerical results for the canonical maximum cut and maximum independent set problems. We find that the graph neural network optimizer performs on par or outperforms existing solvers, with the ability to scale beyond the state of the art to problems with millions of variables.

Quantum evolution kernel : Machine learning on graphs with programmable arrays of qubits

The rapid development of reliable Quantum Processing Units (QPU) opens up novel computational opportunities for machine learning. Here, we introduce a procedure for measuring the similarity between graph-structured data, based on the time-evolution of a quantum system. By encoding the topology of the input graph in the Hamiltonian of the system, the evolution produces measurement samples that retain key features of the data. We study analytically the procedure and illustrate its versatility in providing links to standard classical approaches. We then show numerically that this scheme performs well compared to standard graph kernels on typical benchmark datasets. Finally, we study the possibility of a concrete implementation on a realistic neutral-atom quantum processor.

Continuous Variable Quantum Algorithms: an Introduction

Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum properties of physical quantities, discrete or otherwise. It has been shown that physical quantities with continuous eigenvalue spectrum can be used for quantum computing as well. Currently, continuous variable quantum computing is a rapidly developing field both theoretically and experimentally. In this pedagogical introduction we present the basic theoretical concepts behind it and the tools for algorithm development. The paper targets readers with discrete quantum computing background, who are new to continuous variable quantum computing.

The fixed angle conjecture for QAOA on regular MaxCut graphs

The quantum approximate optimization algorithm (QAOA) is a near-term combinatorial optimization algorithm suitable for noisy quantum devices. However, little is known about performance guarantees for p>2p>2. A recent work computing MaxCut performance guarantees for 3-regular graphs conjectures that any dd-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for p<12p<12. We compute and provide these angles via numerical optimization and tensor networks. These fixed angles serve for an optimization-free version of QAOA, and have universally good performance on any 3 regular graph. Heuristic evidence is presented for the fixed angle conjecture on graph ensembles, which suggests that these fixed angles are “close” to global optimum. Under the fixed angle conjecture, QAOA has a larger performance guarantee than the Goemans Williamson algorithm on 3-regular graphs for p≥11p≥11, and is projected to beat special purpose classical algorithms for p∼30p∼30.

Digitized-counterdiabatic quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-counterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study.

Memory-Sample Lower Bounds for Learning Parity with Noise

In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn x=(x1,…,xn)∈{0,1}nx=(x1,…,xn)∈{0,1}n from a stream of random linear equations over F2F2 that are correct with probability 12+ε12+ε and flipped with probability 12−ε12−ε, that any learning algorithm requires either a memory of size Ω(n2/ε)Ω(n2/ε) or an exponential number of samples. In fact, we study memory-sample lower bounds for a large class of learning problems, as characterized by [GRT’18], when the samples are noisy. A matrix M:A×X→{−1,1}M:A×X→{−1,1} corresponds to the following learning problem with error parameter εε: an unknown element x∈Xx∈X is chosen uniformly at random. A learner tries to learn xx from a stream of samples, (a1,b1),(a2,b2)…(a1,b1),(a2,b2)…, where for every ii, ai∈Aai∈A is chosen uniformly at random and bi=M(ai,x)bi=M(ai,x) with probability 1/2+ε1/2+ε and bi=−M(ai,x)bi=−M(ai,x) with probability 1/2−ε1/2−ε (0<ε<120<ε<12). Assume that k,ℓ,rk,ℓ,r are such that any submatrix of MM of at least 2−k⋅|A|2−k⋅|A| rows and at least 2−ℓ⋅|X|2−ℓ⋅|X| columns, has a bias of at most 2−r2−r. We show that any learning algorithm for the learning problem corresponding to MM, with error, requires either a memory of size at least Ω(k⋅ℓε)Ω(k⋅ℓε), or at least 2Ω(r)2Ω(r) samples. In particular, this shows that for a large class of learning problems, same as those in [GRT’18], any learning algorithm requires either a memory of size at least Ω((log|X|)⋅(log|A|)ε)Ω((log⁡|X|)⋅(log⁡|A|)ε) or an exponential number of noisy samples. Our proof is based on adapting the arguments in [Raz’17,GRT’18] to the noisy case.

Optimal Control for Closed and Open System Quantum Optimization

We provide a rigorous analysis of the quantum optimal control problem in the setting of a linear combination s(t)B+(1−s(t))Cs(t)B+(1−s(t))C of two noncommuting Hamiltonians BB and CC. This includes both quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA). The target is to minimize the energy of the final “problem” Hamiltonian CC, for a time-dependent and bounded control schedule s(t)∈[0,1]s(t)∈[0,1] and t∈\mcI:=[0,tf]t∈\mcI:=[0,tf]. It was recently shown, in a purely closed system setting, that the optimal solution to this problem is a “bang-anneal-bang” schedule, with the bangs characterized by s(t)=0s(t)=0 and s(t)=1s(t)=1 in finite subintervals of \mcI\mcI, in particular s(0)=0s(0)=0 and s(tf)=1s(tf)=1, in contrast to the standard prescription s(0)=1s(0)=1 and s(tf)=0s(tf)=0 of quantum annealing. Here we extend this result to the open system setting, where the system is described by a density matrix rather than a pure state. This is the natural setting for experimental realizations of QA and QAOA. For finite-dimensional environments and without any approximations we identify sufficient conditions ensuring that either the bang-anneal, anneal-bang, or bang-anneal-bang schedules are optimal, and recover the optimality of s(0)=0s(0)=0 and s(tf)=1s(tf)=1. However, for infinite-dimensional environments and a system described by an adiabatic Redfield master equation we do not recover the bang-type optimal solution. In fact we can only identify conditions under which s(tf)=1s(tf)=1, and even this result is not recovered in the fully Markovian limit. The analysis, which we carry out entirely within the geometric framework of Pontryagin Maximum Principle, simplifies using the density matrix formulation compared to the state vector formulation.

A Quantum Convolutional Neural Network for Image Classification

Artificial neural networks have achieved great success in many fields ranging from image recognition to video understanding. However, its high requirements for computing and memory resources have limited further development on processing big data with high dimensions. In recent years, advances in quantum computing show that building neural networks on quantum processors is a potential solution to this problem. In this paper, we propose a novel neural network model named Quantum Convolutional Neural Network (QCNN), aiming at utilizing the computing power of quantum systems to accelerate classical machine learning tasks. The designed QCNN is based on implementable quantum circuits and has a similar structure as classical convolutional neural networks. Numerical simulation results on the MNIST dataset demonstrate the effectiveness of our model.

Identifying quantum phases via disentanglement based on deep reinforcement learning

Identifying phases of matter is a complicated process, especially in quantum theory, where the complexity of the ground state appears to rise exponentially with system size. Typically, physicists have been responsible for identifying suitable order parameters for the identification of the various phases. The entanglement of quantum many-body systems exhibits rich structures and can be determined over the phase diagram. The intriguing question of the relationship between entanglement and quantum phase change has recently been addressed. As a method that works directly on the entanglement structure, disentanglement can provide factual information on the entanglement structure. In this work, we follow a radically different approach to identifying quantum phases: we utilize reinforcement learning (RL) approaches to develop an efficient variational quantum circuit that disentangles the ground-state of Ising spin chain systems. We show that the specified quantum circuit structure of the tested models correlates to a phase transition in the behaviour of the entanglement. We show a similar universal quantum circuit structure for ground states in the same phase to reduce entanglement entropy. This study sheds light on characterizing quantum phases with the types of entanglement structures of the ground states.

Machine Learning-Derived Entanglement Witnesses

In this work, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states. An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target entangled state; this hyperplane is a weighted sum of observables (`features’) whose coefficients are optimized during the training of the SVM. In contrast to other methods such as deep neural networks, the training of an SVM is a convex optimization problem and always yields an `optimal’ solution. We demonstrate with this method the ability to obtain witnesses that require only local measurements even when the target state is a non-stabilizer state. Furthermore, we show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This programmatic approach will allow us to streamline the detection of entangled states in experiment.

Quadratic and Higher-Order Unconstrained Binary Optimization of Railway Dispatching Problem for Quantum Computing

The consequences of disruptions in railway traffic are the primary cause of passengers’ dissatisfaction. Hence, appropriate dispatching decisions are necessary (e.g., by assigning the order of trains), given the numerous restrictions of traffic nature. The latter is perceived as an NP-hard problem. This paper outlines QUBO (quadratic unconstrained binary optimization) and HOBO (higher-order binary optimization) representations for dispatching problems of railway traffic management. Specifically, we consider minimal span between trains, minimal stay on stations, station/track occupation, and rolling stock circulation. The main result is the hybrid algorithm to deal with disturbances in rail traffic on single-, double- and multi-track lines; the demonstrative model illustrates the issue briefly. This algorithm can solve railway dispatching problems using the quantum annealer or any other QUBO-based optimization device.

Pixel identification in an image using Grover Search Algorithm

Quantum Computing offers an entirely new way of doing computation governed by the rules of quantum mechanics like Superposition and Entanglement. These rules allow us to do computation over all the possible states simultaneously. Hence, offering exponentially higher computation power than the present classical computers. Quantum computing algorithms are entirely different from classical algorithms due to quantum parallel computing derived from quantum state superposition and entanglement, which has natural advantages over classical image processing. Grover algorithm is a quantum-based search algorithm used to find the correct answer from an unsorted database by computing all the inputs simultaneously. Thus, giving us a quadratic speed-up of order O(n) 1/2 in comparison to the classical algorithm which offers speedup with order O(n). We used the Grover algorithm for identifying the black pixel in a (2×2) classical image by first converting it into a quantum state and then running the Grover algorithm for identifying the pixel with 0 value maximum gray-scale intensity. This technique has applications in areas like steganography offering data encryption between users, image segmentation.

Quantum Annealing Formulation for Binary Neural Networks

Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been profoundly successful in pushing the boundaries of AI. It is thus natural to investigate potentially game changing technologies such as quantum annealers to augment the capabilities of deep learning. In this work, we explore binary neural networks, which are lightweight yet powerful models typically intended for resource constrained devices. Departing from current training regimes for binary networks that smooth/approximate the activation functions to make the network differentiable, we devise a quadratic unconstrained binary optimization formulation for the training problem. While the problem is intractable, i.e., the cost to estimate the binary weights scales exponentially with network size, we show how the problem can be optimized directly on a quantum annealer, thereby opening up to the potential gains of quantum computing. We experimentally validated our formulation via simulation and testing on an actual quantum annealer (D-Wave Advantage), the latter to the extent allowable by the capacity of current technology.

QKSA: Quantum Knowledge Seeking Agent

In this article we present the motivation and the core thesis towards the implementation of a Quantum Knowledge Seeking Agent (QKSA). QKSA is a general reinforcement learning agent that can be used to model classical and quantum dynamics. It merges ideas from universal artificial general intelligence, constructor theory and genetic programming to build a robust and general framework for testing the capabilities of the agent in a variety of environments. It takes the artificial life (or, animat) path to artificial general intelligence where a population of intelligent agents are instantiated to explore valid ways of modelling the perceptions. The multiplicity and survivability of the agents are defined by the fitness, with respect to the explainability and predictability, of a resource-bounded computational model of the environment. This general learning approach is then employed to model the physics of an environment based on subjective observer states of the agents. A specific case of quantum process tomography as a general modelling principle is presented. The various background ideas and a baseline formalism are discussed in this article which sets the groundwork for the implementations of the QKSA that are currently in active development.

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