Noisy Devices Research Articles

Quantum self-supervised learning

The resurgence of self-supervised learning, whereby a deep learning model generates its own supervisory signal from the data, promises a scalable way to tackle the dramatically increasing size of real-world data sets without human annotation. However, the staggering computational complexity of these methods is such that for state-of-the-art performance, classical hardware requirements represent a significant bottleneck to further progress. Here we take the first steps to understanding whether quantum neural networks (QNNs) could meet the demand for more powerful architectures and test its effectiveness in proof-of-principle hybrid experiments. Interestingly, we observe a numerical advantage for the learning of visual representations using small-scale QNN over equivalently structured classical networks, even when the quantum circuits are sampled with only 100 shots. Furthermore, we apply our best quantum model to classify unseen images on the ibmq_paris quantum computer and find that current noisy devices can already achieve equal accuracy to the equivalent classical model on downstream tasks.

High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits

The development of noisy intermediate-scale quantum (NISQ) devices has extended the scope of executable quantum circuits with high-fidelity single- and two-qubit gates. Equipping NISQ devices with three-qubit gates will enable the realization of more complex quantum algorithms and efficient quantum error correction protocols with reduced circuit depth. Several three-qubit gates have been implemented for superconducting qubits, but their use in gate synthesis has been limited due to their low fidelity. Here, using fixed-frequency superconducting qubits, we demonstrate a high-fidelity iToffoli gate based on two-qubit interactions, the so-called cross-resonance effect. As with the Toffoli gate, this three-qubit gate can be used to perform universal quantum computation. The iToffoli gate is implemented by simultaneously applying microwave pulses to a linear chain of three qubits, revealing a process fidelity as high as 98.26(2)%. Moreover, we numerically show that our gate scheme can produce additional three-qubit gates which provide more efficient gate synthesis than the Toffoli and iToffoli gates. Our work not only brings a high-fidelity iToffoli gate to current superconducting quantum processors but also opens a pathway for developing multi-qubit gates based on two-qubit interactions.

Noise-Induced Entanglement Transition in One-Dimensional Random Quantum Circuits

A random quantum circuit is a minimally structured model to study entanglement dynamics of many-body quantum systems. We consider a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we find that, as the physical error rate is decreased below a critical value p c ≈ 0.056, the logarithmic entanglement negativity changes from the area law to the volume law, giving rise to an entanglement transition. The critical exponent of the correlation length can be determined from the finite-size scaling analysis, revealing the universal dynamic property of the noisy intermediate-scale quantum devices.

Non-adiabatic quantum wavepacket dynamics simulation based on electronic structure calculations using the variational quantum eigensolver

A non-adiabatic nuclear wavepacket dynamics simulation of the H$_2$O$^+$ de-excitation process is performed based on electronic structure calculations using the variational quantum eigensolver. The adiabatic potential energy surfaces and non-adiabatic coupling vectors are computed with algorithms for noisy intermediate-scale quantum devices, and time propagation is simulated with conventional methods for classical computers. The results of non-adiabatic transition dynamics from the $\tilde{B}$ state to $\tilde{A}$ state reproduce the trend reported in previous studies, which suggests that this quantum-classical hybrid scheme may be a useful application for noisy intermediate-scale quantum devices.

Testing quantum foundations with quantum computers

We present two complementary viewpoints for combining quantum computers and the foundations of quantum mechanics. On the one hand, ideal devices can be used as test beds for experimental tests of the foundations of quantum mechanics: We provide algorithms for the Peres test for complex numbers in quantum superpositions and the Sorkin test of Born's rule. On the other hand, noisy intermediate-scale quantum devices can be benchmarked using these same tests. These are deep quantum benchmarks based on the foundations of quantum theory itself. We present test data from Rigetti hardware.Received 28 November 2021Accepted 23 February 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L022001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum benchmarkingQuantum computationQuantum foundationsQuantum simulationPhysical SystemsSuperconducting qubitsQuantum InformationGeneral Physics

On the Robustness of Quantum Algorithms for Blockchain Consensus.

Blockchain has revolutionized many fields, such as distributed sensor networks, finance, and cryptocurrency. Consensus between distributed network nodes is at the core of such blockchain technologies. The three primary performance measures for any consensus algorithm are scalability, security, and decentralization. This paper evaluates the usefulness and practicality of quantum consensus algorithms for blockchain-enhanced sensor, and computing networks and evaluates them against the aforementioned performance measures. In particular, we investigate their noise robustness against quantum decoherence in quantum processors and over fiber-optic channels. We observe that the quantum noise generally increases the error rate in the list distribution. However, the effect is variable on different quantum consensus schemes. For example, the entanglement-free scheme is more affected than entanglement-based schemes for the local noise cases, while in the case of noisy optical fiber links, the effect is prominent on all quantum consensus schemes. We infer that the current quantum protocols with noisy intermediate-scale quantum devices and noisy quantum communication can only be employed for modular units in intraenterprise-level blockchain, such as Zilliqa, for sensor, and computing networks.

Calculating the Green’s function of two-site fermionic Hubbard model in a photonic system

The Green’s function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of the Green’s function impedes the research of many-body systems. The appearance of the noisy intermediate-scale quantum devices and quantum–classical hybrid algorithm inspire a new method to calculate the Green’s function. Here we design a programmable quantum circuit for photons with utilizing the polarization and the path degrees of freedom to construct a highly-precise variational quantum state of a photon, and first report the experimental realization for calculating the Green’s function of the two-site fermionic Hubbard model, a prototypical model for strongly-correlated materials, in photonic systems. We run the variational quantum eigensolver to obtain the ground state and excited states of the model, and then evaluate the transition amplitudes among the eigenstates. The experimental results present the spectral function of the Green’s function, which agrees well with exact results. Our demonstration provides the further possibility of the photonic system in quantum simulation and applications in solving complicated problems in many-body systems, biological science and so on.

Decomposing the generalized Toffoli gate with qutrits

The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we propose a decomposition scheme for a generalized $N$-qubit Toffoli gate with the use of $2N-3$ two-qutrit gates for arbitrary connectivity. The fixed number of the required additional levels (the choice of qutrits is optimal) and the use of the iSWAP gate as a native operation make our approach directly applicable for ongoing experiments with superconducting quantum processors. Specifically, we present a blueprint of the realization of the proposed scheme for the Aspen-9 processor supporting quantum operations with qutrits.

Automatic depth optimization for a quantum approximate optimization algorithm

Quantum approximate optimization algorithm (QAOA) is a hybrid algorithm whose control parameters are classically optimized. In addition to the variational parameters, the right choice of hyperparameter is crucial for improving the performance of any optimization model. Control depth, or the number of variational parameters, is considered as the most important hyperparameter for QAOA. In this paper we investigate the control depth selection with an automatic algorithm based on proximal gradient descent. The performances of the automatic algorithm are demonstrated on seven-node and ten-node max-cut problems, which show that the control depth can be significantly reduced during the iteration whereas achieving an sufficient level of optimization accuracy. With theoretical convergence guarantee, the proposed algorithm can be used as an efficient tool for choosing the appropriate control depth as a replacement of random search or empirical rules. Moreover, the reduction of control depth will induce a significant reduction in the number of quantum gates in circuit, which improves the applicability of QAOA on noisy intermediate-scale quantum devices.

Calculation of Core-Excited and Core-Ionized States Using Variational Quantum Deflation Method and Applications to Photocatalyst Modeling.

The possibility of performing quantum-chemical calculations using quantum computers has attracted much interest. Variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum devices. Although the validity of this method has been demonstrated, there have been few practical applications, primarily because of the uncertain effect of calculation conditions on the results. In the present study, calculations of the core-excited and core-ionized states for common molecules based on the VQD method were examined using a classical computer, focusing on the effects of the weighting coefficients applied in the penalty terms of the cost function. Adopting a simplified procedure for estimating the weighting coefficients based on molecular orbital levels allowed these core-level states to be successfully calculated. The O 1s core-ionized state for a water molecule was calculated with various weighting coefficients, and the resulting ansatz states were systematically examined. The application of this technique to functional materials was demonstrated by calculating the core-level states for titanium dioxide (TiO2) and nitrogen-doped TiO2 models. The results demonstrate that VQD calculations employing an appropriate cost function can be applied to the analysis of functional materials in conjunction with an experimental approach.

Entangled phase of simultaneous fermion and exciton condensations realized

Fermion-exciton condensates (FECs)---computationally and theoretically predicted states that simultaneously exhibit the character of superconducting states and exciton condensates---are novel quantum states whose properties may involve a hybridization of superconductivity and the dissipationless flow of energy. Here, we exploit prior investigations of superconducting states and exciton condensates on quantum devices to identify a tuneable quantum state preparation entangling the wave functions of the individual condensate states. Utilizing this state preparation, we prepare a variety of FEC states on quantum computers---realizing strongly correlated FEC states on current, noisy intermediate-scale quantum devices---and verify the presence of the dual condensate via postmeasurement analysis. This confirmation of the previously predicted condensate state on quantum devices as well as the form of its wave function motivates further theoretical and experimental exploration of the properties, applications, and stability of FECs.

Variational Ansatz preparation to avoid CNOT-gates on noisy quantum devices for combinatorial optimizations

The variational quantum eigensolver (VQE), which is a quantum–classical hybrid approach, has latent powers to leverage near-term quantum devices by effectively managing a limited number of qubits with finite coherent lifetimes. While it is generally argued that the quantum approximate optimization algorithm (QAOA), which is a special case of VQE with a variational Ansatz based on the adiabatic theorem, may enable practical applications of noisy quantum devices for classical combinatorial optimizations, the strategy to improve the performance of this algorithm by increasing the circuit depth conflicts with the limited coherence time of near-term quantum devices. Here, we introduce strategies involving the VQE to reduce the circuit resources required for solving combinatorial optimizations. Our concept of a parameterized quantum circuit allows the Ansatz preparation to be achieved by only single-qubit operation. We find that the variational Ansatz without controlled X-gates leads to quick convergence in a classical subroutine used to determine the variational parameters. In addition, the variational Ansatz with optimized parameters maintains performance over the problem sizes both on the numerical simulation and IBM 27-qubit processor “ibm_kawasaki.” Therefore, the variational Ansatz introduced in this study has several advantages considering the total calculation time and performance scaling over the problem sizes. We also show that the variational Ansatz consisting of a lower number of gate operations than that of QAOA can approximate the eigenstates of diagonal Hamiltonians with high accuracy. We illustrate our ideas with a maximum-cut problem and show that near-term quantum applications may be feasible using short-depth circuits.

Gate-based circuit designs for quantum adder-inspired quantum random walks on superconducting qubits

Quantum random walks, which drew much attention over the past few decades for their distinctly nonclassical behavior, are a promising subfield within quantum computing. Theoretical framework and applications for these walks have seen many great mathematical advances, with experimental demonstrations now catching up. In this study, we examine the viability of implementing coin quantum random walks using a Quantum Adder-based Shift Operator, with quantum circuit designs specifically for superconducting qubits. We focus on the strengths and weaknesses of these walks, particularly circuit depth, gate count, connectivity requirements and scalability. We propose and analyze a novel approach to implementing boundary conditions for these walks, demonstrating the technique explicitly in one and two dimensions. Finally, we present several fidelity results from running our circuits on IBM’s quantum volume 32 ‘Toronto’ chip, showcasing the extent to which these noisy intermediate-scale quantum devices can currently handle quantum walks.

Toward Robust Autotuning of Noisy Quantum dot Devices

The current autotuning approaches for quantum dot (QD) devices, while showing some success, lack an assessment of data reliability. This leads to unexpected failures when noisy or otherwise low-quality data is processed by an autonomous system. In this work, we propose a framework for robust autotuning of QD devices that combines a machine learning (ML) state classifier with a data quality control module. The data quality control module acts as a "gatekeeper" system, ensuring that only reliable data are processed by the state classifier. Lower data quality results in either device recalibration or termination. To train both ML systems, we enhance the QD simulation by incorporating synthetic noise typical of QD experiments. We confirm that the inclusion of synthetic noise in the training of the state classifier significantly improves the performance, resulting in an accuracy of 95.0(9) % when tested on experimental data. We then validate the functionality of the data quality control module by showing that the state classifier performance deteriorates with decreasing data quality, as expected. Our results establish a robust and flexible ML framework for autonomous tuning of noisy QD devices.

Variational quantum reinforcement learning via evolutionary optimization

Recent advances in classical reinforcement learning (RL) and quantum computation point to a promising direction for performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in modern quantum devices. Here, we present two frameworks for deep quantum RL tasks using gradient-free evolutionary optimization. First, we apply the amplitude encoding scheme to the Cart-Pole problem, where we demonstrate the quantum advantage of parameter saving using amplitude encoding. Second, we propose a hybrid framework where the quantum RL agents are equipped with a hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs of dimensions exceeding the number of qubits. This allows us to perform quantum RL in the MiniGrid environment with 147-dimensional inputs. 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.

Branching quantum convolutional neural networks

Neural-network-based algorithms have garnered considerable attention for their ability to learn complex patterns from very-high-dimensional data sets towards classifying complex long-range patterns of entanglement and correlations in many-body quantum systems, and towards processing high-dimensional classical data sets. Small-scale quantum computers are already showing potential gains in learning tasks on large quantum and very large classical data sets. A particularly interesting class of algorithms, the quantum convolutional neural networks (QCNNs) could learn features of a quantum data set by performing a binary classification task on a nontrivial phase of quantum matter. Inspired by this promise, we present a generalization of QCNN, the ``branching quantum convolutional neural network,'' or bQCNN, with substantially higher expressibility. A key feature of bQCNN is that it leverages midcircuit (intermediate) measurement results, realizable on several current quantum devices, obtained in pooling layers to determine which sets of parameters will be used in the subsequent convolutional layers of the circuit. This results in a ``branching'' structure, which allows for a greater number of trainable variational parameters in a given circuit depth. This is of particular use in current-day noisy intermediate-scale quantum devices, where circuit depth is limited by gate noise. We present an overview of the Ansatz structure and scaling and provide evidence of its enhanced expressibility compared with QCNN. Using artificially constructed large data sets of training states as a proof of concept, we demonstrate the existence of training tasks in which bQCNN far outperforms an ordinary QCNN. We provide an explicit example of such a task in the recognition of the transition from a symmetry protected topological to a trivial phase induced by multiple, distinct perturbations. Finally, we present future directions where the classical branching structure and increased density of trainable parameters in bQCNN would be particularly valuable.

Estimating Gibbs partition function with quantum Clifford sampling

The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum–classical algorithm to estimate the partition function, utilising a novel quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require -depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112–22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δ is the minimum spectral gap of stochastic matrices and ϵ is the multiplicative error. Our algorithm requires only a shallow -depth quantum circuit, repeated times, to provide a comparable ϵ approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.

Solving quantum master equations with deep quantum neural networks

Deep quantum neural networks may provide a promising way to achieve a quantum learning advantage with noisy intermediate-scale quantum devices. Here, we use deep quantum feed-forward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems and introduce a variational method with quantum derivatives to solve the master equation for dynamics and stationary states. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including an efficient quantum analog of the back-propagation algorithm, resource-saving reuse of hidden qubits, general applicability independent of dimensionality and entanglement properties, as well as the convenient implementation of symmetries. As proof-of-principle demonstrations, we apply this approach to both one-dimensional transverse field Ising and two-dimensional ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ models with dissipation, and show that it can efficiently capture their dynamics and stationary states with a desired accuracy.

Quantum Noise Sensing by Generating Fake Noise

Noisy intermediate-scale quantum (NISQ) devices are nowadays starting to become available to the final user, hence potentially allowing the quantum speedups predicted by quantum-information theory to be shown. However, before implementing any quantum algorithm, it is crucial to have at least a partial or possibly full knowledge on the type and amount of noise affecting the quantum machine. Here, by generalizing quantum generative adversarial learning from quantum states (QGANs) to quantum operations, superoperators, and channels (here named super QGANs), we propose a very promising framework to characterize noise in a realistic quantum device, even in the case of spatially and temporally correlated noise (memory channels) affecting quantum circuits. The key idea is to learn about the noise by mimicking it in a way that one cannot distinguish between the real (to be sensed) and the fake (generated) one. We find that, when applied to the benchmarking case of Pauli channels, the super-QGAN protocol is able to learn the associated error rates even in the case of spatially and temporally correlated noise. Moreover, we also show how to employ it for quantum metrology applications. We believe our super QGANs pave the way for the development of hybrid quantum-classical machine-learning protocols for a better characterization and control of the current and future unavoidably noisy quantum devices.

Quantum algorithm for credit valuation adjustments

Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases, credit valuation adjustment (CVA), and identify opportunities and challenges towards quantum advantage for practical instances. To build a NISQ-friendly quantum circuit able to solve such problem, we draw on various heuristics that indicate the potential for significant improvement over well-known techniques such as reversible logical circuit synthesis. In minimizing the resource requirements for amplitude amplification while maximizing the speedup gained from the quantum coherence of a noisy device, we adopt a recently developed Bayesian variant of quantum amplitude estimation using engineered likelihood functions. We perform numerical analyses to characterize the prospect of quantum speedup in concrete CVA instances over classical Monte Carlo simulations.