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đPapers:

- Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
- Recent advances for quantum classifiers
- The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry
- Quantum algorithm for structure learning of Markov Random Fields
- Exploring variational quantum eigensolver ansatzes for the long-range XY model
- Photonic Quantum Policy Learning in OpenAI Gym
- A quantum-classical eigensolver using multiscale entanglement renormalization
- Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
- Monitoring fast superconducting qubit dynamics using a neural network
- Variational Quantum Reinforcement Learning via Evolutionary Optimization
- Optimal control of quantum thermal machines using machine learning
- Reinforcement learning-enhanced protocols for coherent population-transfer in three-level quantum systems
- Model-Independent Quantum Phases Classifier
- Investigating potential energy surfaces of noncollinear molecule using variational quantum circuit
- Quantum Walk to Train a Classical Artificial Neural Network
- Identifying optimal cycles in quantum thermal machines with reinforcement-learning
- Max-cut Clustering Utilizing Warm-Start QAOA and IBM Runtime
- On the effects of biased quantum random numbers on the initialization of artificial neural networks
- Photonic quantum computation by chiral quantun networks
- Classical Artificial Neural Network Training Using Quantum Walks as a Search Procedure

### Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Samson Wang,Piotr Czarnik,Andrew Arrasmith,M. Cerezo,Lukasz Cincio,Patrick J. ColesSep 03 2021Â quant-phcs.LGÂ arXiv:2109.01051v1

Variational Quantum Algorithms (VQAs) are widely viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.

### Recent advances for quantum classifiers

Weikang Li,Dong-Ling DengSep 01 2021Â quant-phcs.LGÂ arXiv:2108.13421v1

Machine learning has achieved dramatic success in a broad spectrum of applications. Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research and commercial applications, giving rise to an emergent research frontier of quantum machine learning. Along this line, quantum classifiers, which are quantum devices that aim to solve classification problems in machine learning, have attracted tremendous attention recently. In this review, we give a relatively comprehensive overview for the studies of quantum classifiers, with a focus on recent advances. First, we will review a number of quantum classification algorithms, including quantum support vector machine, quantum kernel methods, quantum decision tree, and quantum nearest neighbor algorithm. Then, we move on to introduce the variational quantum classifiers, which are essentially variational quantum circuits for classifications. We will review different architectures for constructing variational quantum classifiers and introduce the barren plateau problem, where the training of quantum classifiers might be hindered by the exponentially vanishing gradient. In addition, the vulnerability aspect of quantum classifiers in the setting of adversarial learning and the recent experimental progress on different quantum classifiers will also be discussed.

### The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry

Waheeda Saib,Petros Wallden,Ismail AkhalwayaAug 30 2021Â quant-phÂ arXiv:2108.12388v1

Variational quantum algorithms are suitable for use on noisy quantum systems. One of the most important use-cases is the quantum simulation of materials, using the variational quantum eigensolver (VQE). To optimize VQE performance, a suitable parameterized quantum circuit (ansatz) must be selected. We investigate a class of ansatze that incorporates knowledge of the quantum hardware, namely the hardware efficient ansatze. The performance of hardware efficient ansatze is affected differently by noise, and our goal is to study the effect of noise on evaluating which ansatz gives more accurate results in practice. First, we study the effect of noise on the different hardware efficient ansatze by benchmarking and ranking the performance of each ansatz family (i) on a chemistry application using VQE and (ii) by the recently established metric of “expressibility”. The results demonstrate the ranking of optimal circuits does not remain constant in the presence of noise. Second, we evaluate the suitability of the expressibility measure in this context by performing a correlation study between expressibility and the performance of the same circuits on a chemistry application using VQE. Our simulations reveal a weak correlation and therefore demonstrate that expressibility is not an adequate measure to quantify the effectiveness of parameterized quantum circuits for quantum chemistry. Third, we evaluate the effect of different quantum device noise models on the ordering of which ansatz family is best. Interestingly, we see that to decide which ansatz is optimal for use, one needs to consider the specific hardware used even within the same family of quantum hardware.

### Quantum algorithm for structure learning of Markov Random Fields

Liming Zhao,Siyi Yang,Patrick RebentrostSep 03 2021Â quant-phÂ arXiv:2109.01014v1

Markov random fields (MRFs) appear in many problems in machine learning and statistics. From a computational learning theory point of view, a natural problem of learning MRFs arises: given samples from an MRF from a restricted class, learn the structure of the MRF, that is the neighbors of each node of the underlying graph. In this work, we start at a known near-optimal classical algorithm for this learning problem and develop a modified classical algorithm. This classical algorithm retains the run time and guarantee of the previous algorithm and enables the use of quantum subroutines. Adapting a previous quantum algorithm, the Quantum Sparsitron, we provide a polynomial quantum speedup in terms of the number of variables for learning the structure of an MRF, if the MRF has bounded degree.

### Exploring variational quantum eigensolver ansatzes for the long-range XY model

Jia-Bin You,Dax Enshan Koh,Jian Feng Kong,Wen-Jun Ding,Ching Eng Png,Lin WuSep 02 2021Â quant-phÂ arXiv:2109.00288v1

Finding the ground state energy and wavefunction of a quantum many-body system is a key problem in quantum physics and chemistry. We study this problem for the long-range XY model by using the variational quantum eigensolver (VQE) algorithm. We consider VQE ansatzes with full and linear entanglement structures consisting of different building gates: the CNOT gate, the controlled-rotation (CRX) gate, and the two-qubit rotation (TQR) gate. We find that the full-entanglement CRX and TQR ansatzes can sufficiently describe the ground state energy of the long-range XY model. In contrast, only the full-entanglement TQR ansatz can represent the ground state wavefunction with a fidelity close to one. In addition, we find that instead of using full-entanglement ansatzes, restricted-entanglement ansatzes where entangling gates are applied only between qubits that are a fixed distance from each other already suffice to give acceptable solutions. Using the entanglement entropy to characterize the expressive powers of the VQE ansatzes, we show that the full-entanglement TQR ansatz has the highest expressive power among them.

### Photonic Quantum Policy Learning in OpenAI Gym

DĂĄniel Nagy,Zsolt Tabi,PĂŠter HĂĄga,ZsĂłfia Kallus,ZoltĂĄn ZimborĂĄsAug 31 2021Â quant-phcs.LGstat.MLÂ arXiv:2108.12926v1

In recent years, near-term noisy intermediate scale quantum (NISQ) computing devices have become available. One of the most promising application areas to leverage such NISQ quantum computer prototypes is quantum machine learning. While quantum neural networks are widely studied for supervised learning, quantum reinforcement learning is still just an emerging field of this area. To solve a classical continuous control problem, we use a continuous-variable quantum machine learning approach. We introduce proximal policy optimization for photonic variational quantum agents and also study the effect of the data re-uploading. We present performance assessment via empirical study using Strawberry Fields, a photonic simulator Fock backend and a hybrid training framework connected to an OpenAI Gym environment and TensorFlow. For the restricted CartPole problem, the two variations of the photonic policy learning achieve comparable performance levels and a faster convergence than the baseline classical neural network of same number of trainable parameters.

### A quantum-classical eigensolver using multiscale entanglement renormalization

Qiang Miao,Thomas BarthelAug 31 2021Â quant-phÂ arXiv:2108.13401v1

Hybrid quantum-classical algorithms promise to be practical for near-term quantum computing. We propose a variational quantum eigensolver (VQE) for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. This quantum MERA has substantially lower computation costs than corresponding classical algorithms. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale (NISQ) devices and still describe very large systems. It is particularly attractive for ion-trap devices with ion-shuttling capabilities. While the total number of required qubits grows logarithmically in the size of the simulated system, the number of qubits needed in the interaction region is system-size independent. Translation invariance of the simulated systems can be used to make computation costs logarithmic in the system size and describe the thermodynamic limit. We demonstrate the approach numerically for a MERA with Trotterized disentanglers and isometries. With a few Trotter steps, one recovers the accuracy of the full MERA.

### Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model

Andy C. Y. Li,M. Sohaib Alam,Thomas Iadecola,Ammar Jahin,Doga Murat Kurkcuoglu,Richard Li,Peter P. Orth,A. BarÄąĹ ĂzgĂźler,Gabriel N. PerdueAug 31 2021Â quant-phÂ arXiv:2108.13375v1Scite!3PDFQuantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require error-corrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to find energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational ansatz (HVA). We further demonstrate the implementation of an HVA circuit on Rigetti’s Aspen-9 chip with error mitigation.

### Monitoring fast superconducting qubit dynamics using a neural network

G. Koolstra,N. Stevenson,S. Barzili,L. Burns,K. Siva,S. Greenfield,W. Livingston,A. Hashim,R. K. Naik,J. M. Kreikebaum,K. P. O’Brien,D. I. Santiago,J. Dressel,I. SiddiqiAug 30 2021Â quant-phÂ arXiv:2108.12023v1

Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments. Monitoring rapid qubit dynamics, e.g. during quantum gates, requires more complicated methods with increased demand for prior information. Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a Long-Short Term Memory (LSTM) artificial neural network with minimal prior information. Despite few training assumptions, the LSTM produces trajectories that include qubit-readout resonator correlations due to a finite detection bandwidth. In addition to revealing rotated measurement eigenstates and a reduced measurement rate in agreement with theory for a fixed drive, the trained LSTM also correctly reconstructs evolution for an unknown drive with rapid modulation. Our work enables new applications of weak measurements with faster or initially unknown qubit dynamics, such as the diagnosis of coherent errors in quantum gates.

### Variational Quantum Reinforcement Learning via Evolutionary Optimization

Samuel Yen-Chi Chen,Chih-Min Huang,Chia-Wei Hsing,Hsi-Sheng Goan,Ying-Jer KaoSep 03 2021Â quant-phcs.AIcs.ETcs.LGcs.NEÂ arXiv:2109.00540v1

Recent advance in classical reinforcement learning (RL) and quantum computation (QC) points to a promising direction of performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in the modern quantum devices. Here we present two frameworks of deep quantum RL tasks using a gradient-free evolution optimization: First, we apply the amplitude encoding scheme to the Cart-Pole problem; Second, we propose a hybrid framework where the quantum RL agents are equipped with hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs with dimensions exceeding the number of qubits. This allows us to perform quantum RL on the MiniGrid environment with 147-dimensional inputs. We demonstrate the quantum advantage of parameter saving using the amplitude encoding. The hybrid TN-VQC architecture provides a natural way to perform efficient compression of the input dimension, enabling further quantum RL applications on noisy intermediate-scale quantum devices.

### Optimal control of quantum thermal machines using machine learning

Ilia Khait,Juan Carrasquilla,Dvira SegalAug 31 2021Â quant-phcond-mat.dis-nncond-mat.stat-mechÂ arXiv:2108.12441v1

Identifying optimal thermodynamical processes has been the essence of thermodynamics since its inception. Here, we show that differentiable programming (DP), a machine learning (ML) tool, can be employed to optimize finite-time thermodynamical processes in a quantum thermal machine. We consider the paradigmatic quantum Otto engine with a time-dependent harmonic oscillator as its working fluid, and build upon shortcut-to-adiabaticity (STA) protocols. We formulate the STA driving protocol as a constrained optimization task and apply DP to find optimal driving profiles for an appropriate figure of merit. Our ML scheme discovers profiles for the compression and expansion strokes that are superior to previously-suggested protocols. Moreover, using our ML algorithm we show that a previously-employed, intuitive energetic cost of the STA driving suffers from a fundamental flaw, which we resolve with an alternative construction for the cost function. Our method and results demonstrate that ML is beneficial both for solving hard-constrained quantum control problems and for devising and assessing their theoretical groundwork.

### Reinforcement learning-enhanced protocols for coherent population-transfer in three-level quantum systems

Jonathon Brown,Pierpaolo Sgroi,Luigi Giannelli,Gheorghe Sorin Paraoanu,Elisabetta Paladino,Giuseppe Falci,Mauro Paternostro,Alessandro FerraroSep 03 2021Â quant-phÂ arXiv:2109.00973v1

We deploy a combination of reinforcement learning-based approaches and more traditional optimization tech- niques to identify optimal protocols for population transfer in a multi-level system. We constraint our strategy to the case of fixed coupling rates but time-varying detunings, a situation that would simplify considerably the implementation of population transfer in relevant experimental platforms, such as semiconducting and super- conducting ones. Our approach is able to explore the space of possible control protocols to reveal the existence of efficient protocols that, remarkably, differ from (and can be superior to) standard Raman, STIRAP or other adiabatic schemes. The new protocols that we identify are robust against both energy losses and dephasing.

### Model-Independent Quantum Phases Classifier

Felipe Mahlow,FabrĂcio S. Luiz,AndrĂŠ L. Malvezzi,Felipe F. FanchiniSep 03 2021Â quant-phÂ arXiv:2109.00625v1

Machine learning has revolutionized many fields of science and technology. Through theÂ kk-Nearest Neighbors algorithm, we develop a model-independent classifier, where the algorithm can classify phases of a model to which it has never had access. For this, we study three distinct spin-11Â models with some common phases: the XXZ chains with uniaxial single-ion-type anisotropy, the bound alternating XXZ chains, and the bilinear biquadratic chain. We show that, with high probability, algorithms trained with two of these models can determine common phases with the third. It is the first step toward a universal classifier, where an algorithm is able to detect any phase with no knowledge about the Hamiltonian, only knowing partial information about the quantum state.

### Investigating potential energy surfaces of noncollinear molecule using variational quantum circuit

Anh Pham,Daniel BeaulieuSep 02 2021Â quant-phcond-mat.mtrl-sciÂ arXiv:2109.00401v1

We demonstrate the simulation of a noncollinear molecule, e.g. H2O molecule using Variational Quantum Eigensolver (VQE) with high chemical accuracy. The 2D and 3D potential energy surface (PES) were reported. Taking advantage of the potential speedup in Qiskit runtime program, the optimal initial parameters for the variational quantum circuits were obtained after several consecutive iterations, thus resulting in accurate prediction of water’s PES matching result obtained from exact diagonalization of the full Hamiltonian.

### Quantum Walk to Train a Classical Artificial Neural Network

Luciano S. de Souza,Jonathan H. A. Carvalho,Tiago A. E. FerreiraSep 02 2021Â quant-phÂ arXiv:2109.00128v1

This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to simulate a quantum machine to execute the quantum walk. In this way, to minimize the computational cost, the methodology employed to train the neural network will adjust the synaptic weights of the output layer, not altering the weights of the hidden layer, inspired in the method of Extreme Learning Machine. The quantum walk algorithm as a search algorithm is quadratically faster than its classic analog. The quantum walk variance isÂ O(t)O(t)Â while the variance of its classic analog isÂ O(tâ)O(t), whereÂ ttÂ is the time or iteration. In addition to computational gain, another advantage of the proposed procedure is to be possible to know \textita priori the number of iterations required to obtain the solutions, unlike the classical training algorithms based on gradient descendent.

### Identifying optimal cycles in quantum thermal machines with reinforcement-learning

Paolo Andrea Erdman,Frank NoĂŠSep 01 2021Â quant-phcond-mat.mes-hallcs.LGÂ arXiv:2108.13525v1

The optimal control of open quantum systems is a challenging task but has a key role in improving existing quantum information processing technologies. We introduce a general framework based on Reinforcement Learning to discover optimal thermodynamic cycles that maximize the power of out-of-equilibrium quantum heat engines and refrigerators. We apply our method, based on the soft actor-critic algorithm, to three systems: a benchmark two-level system heat engine, where we find the optimal known cycle; an experimentally realistic refrigerator based on a superconducting qubit that generates coherence, where we find a non-intuitive control sequence that outperform previous cycles proposed in literature; a heat engine based on a quantum harmonic oscillator, where we find a cycle with an elaborate structure that outperforms the optimized Otto cycle. We then evaluate the corresponding efficiency at maximum power.

### Max-cut Clustering Utilizing Warm-Start QAOA and IBM Runtime

Daniel Beaulieu,Anh PhamSep 01 2021Â quant-phÂ arXiv:2108.13464v1

Quantum optimization algorithms can be used to recreate unsupervised learning clustering of data by mapping the problem to a graph optimization problem and finding the minimum energy for a MaxCut problem formulation. This research tests the “Warm Start” variant of Quantum Approximate Optimization Algorithm (QAOA) versus the standard implementation of QAOA for unstructured clustering problems. The performance for IBM’s new Qiskit Runtime API for speeding up optimization algorithms is also tested in terms of speed up and relative performance compared to the standard implementation of optimization algorithms. Warm-start QAOA performs better than any other optimization algorithm, though standard QAOA runs the fastest. This research also used a non-convex optimizer to relax the quadratic program for the Warm-start QAOA.

### On the effects of biased quantum random numbers on the initialization of artificial neural networks

Raoul Heese,Moritz Wolter,Sascha MĂźcke,Lukas Franken,Nico PiatkowskiAug 31 2021Â quant-phstat.MLÂ arXiv:2108.13329v1

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

### Photonic quantum computation by chiral quantun networks

Wei-Bin Yan,Ying-Jie Zhang,Zhong-Xiao Man,Heng Fan,Yun-Jie XiaAug 31 2021Â quant-phÂ arXiv:2108.13213v1

Inspired by the excellent control of single photons realized by the atom-photon-chiral couplings, we propose a novel potential photonic-quantum-computation scheme. The single-photon rotating and phase-shift operations, which can be controlled by another single photon, are realized by properly designed atom-photon-chiral couplings. The operations can be integrated into a chiral quantum network to realize photonic quantum computation. Based on the proposal, an algorithm to perform the machine learning tasks is developed, in which the essential nonlinearities come from the appropriately designed operations.

### Classical Artificial Neural Network Training Using Quantum Walks as a Search Procedure

Luciano S. de Souza,Jonathan H. A. de Carvalho,Tiago A. E. FerreiraAug 31 2021Â quant-phÂ arXiv:2108.12448v1

This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic weights of a classical artificial neural network. Each vertex of this complete graph represents a possible synaptic weight set in theÂ ww-dimensional search space, whereÂ wwÂ is the number of weights of the neural network. To know the number of iterations required \textita priori to obtain the solutions is one of the main advantages of the procedure. Another advantage is that the proposed method does not stagnate in local minimums. Thus, it is possible to use the quantum walk search procedure as an alternative to the backpropagation algorithm. The proposed method was employed for aÂ XORXORÂ problem to prove the proposed concept. To solve this problem, the proposed method trained a classical artificial neural network with nine weights. However, the procedure can find solutions for any number of dimensions. The results achieved demonstrate the viability of the proposal, contributing to machine learning and quantum computing researches.

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