Noisy Intermediate-scale Quantum Research Articles

Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems.

Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the noisy intermediate scale quantum era, it is imperative to develop compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop a disentangled Ansatz construction protocol that can dynamically tailor an optimal Ansatz using the one- and two-body cluster operators and a selection of rank-two scatterers. The construction of the Ansatz may potentially be performed in parallel over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.

Self-correcting quantum many-body control using reinforcement learning with tensor networks

Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and, consequently, to devise reliable and robust optimal control protocols. Here we present a framework for efficiently controlling quantum many-body systems based on reinforcement learning (RL). We tackle the quantum-control problem by leveraging matrix product states (1) for representing the many-body state and (2) as part of the trainable machine learning architecture for our RL agent. The framework is applied to prepare ground states of the quantum Ising chain, including states in the critical region. It allows us to control systems far larger than neural-network-only architectures permit, while retaining the advantages of deep learning algorithms, such as generalizability and trainable robustness to noise. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states and of adapting control protocols on the fly when the quantum dynamics is subject to stochastic perturbations. Furthermore, we map our RL framework to a hybrid quantum–classical algorithm that can be performed on noisy intermediate-scale quantum devices and test it under the presence of experimentally relevant sources of noise.

Stereoscopic scalable quantum convolutional neural networks

As the noisy intermediate-scale quantum (NISQ) era has begun, a quantum neural network (QNN) is definitely a promising solution to many problems that classical neural networks cannot solve. In addition, a quantum convolutional neural network (QCNN) is now receiving a lot of attention because it can process high dimensional inputs comparing to QNN. However, due to the nature of quantum computing, it is difficult to scale up the QCNN to extract a sufficient number of features due to barren plateaus. This is especially challenging in classification operations with high-dimensional data input. However, due to the nature of quantum computing, it is difficult to scale up the QCNN to extract a sufficient number of features due to barren plateaus. This is especially challenging in classification operations with high dimensional data input. Motivated by this, a novel stereoscopic 3D scalable QCNN (sQCNN-3D) is proposed for point cloud data processing in classification applications. Furthermore, reverse fidelity training (RF-Train) is additionally considered on top of sQCNN-3D for diversifying features with a limited number of qubits using the fidelity of quantum computing. Our data-intensive performance evaluation verifies that the proposed algorithm achieves desired performance.

FV-Train: Quantum Convolutional Neural Network Training with a Finite Number of Qubits by Extracting Diverse Features (Student Abstract)

Quantum convolutional neural network (QCNN) has just become as an emerging research topic as we experience the noisy intermediate-scale quantum (NISQ) era and beyond. As convolutional filters in QCNN extract intrinsic feature using quantum-based ansatz, it should use only finite number of qubits to prevent barren plateaus, and it introduces the lack of the feature information. In this paper, we propose a novel QCNN training algorithm to optimize feature extraction while using only a finite number of qubits, which is called fidelity-variation training (FV-Training).

Quantum Bilinear Interpolation Algorithms Based on Geometric Centers

Bilinear interpolation is widely used in classical signal and image processing. Quantum algorithms have been designed for efficiently realizing bilinear interpolation. However, these quantum algorithms have limitations in circuit width and garbage outputs, which block the quantum algorithms applied to noisy intermediate-scale quantum devices. In addition, the existing quantum bilinear interpolation algorithms cannot keep the consistency between the geometric centers of the original and target images. To save the above questions, we propose quantum bilinear interpolation algorithms based on geometric centers using fault-tolerant implementations of quantum arithmetic operators. Proposed algorithms include the scaling-up and scaling-down for signals (grayscale images) and signals with three channels (color images). Simulation results demonstrate that the proposed bilinear interpolation algorithms obtain the same results as their classical counterparts with an exponential speedup. Performance analysis reveals that the proposed bilinear interpolation algorithms keep the consistency of geometric centers and significantly reduce circuit width and garbage outputs compared to the existing works.

Near term algorithms for linear systems of equations

Finding solutions to systems of linear equations is a common problem in many areas of science and engineering, with much potential for a speed up on quantum devices. While the Harrow–Hassidim–Lloyd (HHL) quantum algorithm yields up to an exponential speed up over classical algorithms in some cases, it requires a fault-tolerant quantum computer, which is unlikely to be available in the near-term. Thus, attention has turned to the investigation of quantum algorithms for noisy intermediate-scale quantum (NISQ) devices where several near-term approaches to solving systems of linear equations have been proposed. This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods and adaptions. Several contributions are made in this paper, which include: the first application of the Evolutionary Ansatz to the VQLS (EAVQLS), the first implementation of the Logical Ansatz VQLS (LAVQLS), based on the Classical Combination of Quantum States (CQS) method, a proof of principle demonstration of the CQS method on real quantum hardware and a method for the implementation of the Adiabatic Ansatz on the VQLS (AAVQLS). These approaches are implemented and contrasted. The CQS method is run with moderate success on a real quantum device. The EAVQLS and AAVQLS show promise as possible improvements to the standard VQLS algorithm once refined.

Machine learning aided dimensionality reduction toward a resource efficient projective quantum eigensolver: Formal development and pilot applications.

In recent times, a variety of hybrid quantum-classical algorithms have been developed that aim to calculate the ground state energies of molecular systems on Noisy Intermediate-Scale Quantum (NISQ) devices. Albeit the utilization of shallow depth circuits in these algorithms, the optimization of ansatz parameters necessitates a substantial number of quantum measurements, leading to prolonged runtimes on the scantly available quantum hardware. Through our work, we lay the general foundation for an interdisciplinary approach that can be used to drastically reduce the dependency of these algorithms on quantum infrastructure. We showcase these pertinent concepts within the framework of the recently developed Projective Quantum Eigensolver (PQE) that involves iterative optimization of the nonlinearly coupled parameters through repeated residue measurements on quantum hardware. We demonstrate that one may perceive such a nonlinear optimization problem as a collective dynamic interplay of fast and slow relaxing modes. As such, the synergy among the parameters is exploited using an on-the-fly supervised machine learning protocol that dynamically casts the PQE optimization into a smaller subspace by reducing the effective degrees of freedom. We demonstrate analytically and numerically that our proposed methodology ensures a drastic reduction in the number of quantum measurements necessary for the parameter updates without compromising the characteristic accuracy. Furthermore, the machine learning model may be tuned to capture the noisy data of NISQ devices, and thus the predicted energy is shown to be resilient under a given noise model.

Quantum neural network cost function concentration dependency on the parametrization expressivity

Although we are currently in the era of noisy intermediate scale quantum devices, several studies are being conducted with the aim of bringing machine learning to the quantum domain. Currently, quantum variational circuits are one of the main strategies used to build such models. However, despite its widespread use, we still do not know what are the minimum resources needed to create a quantum machine learning model. In this article, we analyze how the expressiveness of the parametrization affects the cost function. We analytically show that the more expressive the parametrization is, the more the cost function will tend to concentrate around a value that depends both on the chosen observable and on the number of qubits used. For this, we initially obtain a relationship between the expressiveness of the parametrization and the mean value of the cost function. Afterwards, we relate the expressivity of the parametrization with the variance of the cost function. Finally, we show some numerical simulation results that confirm our theoretical-analytical predictions. To the best of our knowledge, this is the first time that these two important aspects of quantum neural networks are explicitly connected.

Scaling superconducting quantum chip with highly integratable quantum building blocks

Designing and fabricating large-scale superconducting quantum chips with increasing number of qubits is a pressing challenge for the quantum computing. Here, we propose a three-dimensional stacked chip architecture comprised with quantum building blocks. In which, two primary types of blocks are the qubit block and the coupling block. They are designed as functional parts that can be utilized within the same footprint across multiple levels of the chip stack in the vertical direction. Common technological problems, such as the sensitivity of capacitors and coupling strengths to fabrication parameters, and dielectric losses from interfaces, can be addressed at the intra-block or block level efficiently. Once a library of standard blocks is designed and verified, they can be selected and arranged into arrays on chips at the placing stage of the design flow for specific quantum applications. Such chip structure and design protocol will reduce the design difficulty, and promote the reuse of standard blocks, thus paving the way for chips for noisy intermediate-scale quantum computing and quantum error correction.

Reducing the CNOT Count for Clifford+T Circuits on NISQ Architectures

While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit operations, such as CNOT, to "connected" qubits. SWAP gates can be used to place the logical qubits on admissible physical qubits, but they entail a significant increase in CNOT-count. In this paper we consider the problem of reducing the CNOT-count in Clifford+T circuits on connectivity constrained architectures, like noisy intermediate-scale quantum (NISQ) computing devices. We "slice" the circuit at the position of Hadamard gates and "build" the intermediate {CNOT,T} sub-circuits using Steiner trees, significantly improving on previous methods. We compared the performance of our algorithms while mapping different benchmark and random circuits to some well-known architectures such as 9-qubit square grid, 16-qubit square grid, Rigetti 16-qubit Aspen, 16-qubit IBM QX5 and 20-qubit IBM Tokyo. Our methods give less CNOT-count compared to Qiskit and TKET transpiler as well as using SWAP gates. Assuming most of the errors in a NISQ circuit implementation are due to CNOT errors, then our method would allow circuits with few times more CNOT gates be reliably implemented than the previous methods would permit.

Scalable and Flexible Classical Shadow Tomography with Tensor Networks

Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of a quantum state with few measurements. Two classical shadow protocols have been extensively studied in the literature: the single-qubit (local) Pauli measurement, which is well suited for predicting local operators but inefficient for large operators; and the global Clifford measurement, which is efficient for low-rank operators but infeasible on near-term quantum devices due to the extensive gate overhead. In this work, we demonstrate a scalable classical shadow tomography approach for generic randomized measurements implemented with finite-depth local Clifford random unitary circuits, which interpolates between the limits of Pauli and Clifford measurements. The method combines the recently proposed locally-scrambled classical shadow tomography framework with tensor network techniques to achieve scalability for computing the classical shadow reconstruction map and evaluating various physical properties. The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead and is friendly to noisy intermediate-scale quantum (NISQ) devices. We show that the shallow-circuit measurement protocol provides immediate, exponential advantages over the Pauli measurement protocol for predicting quasi-local operators. It also enables a more efficient fidelity estimation compared to the Pauli measurement.

Entanglement entropy production in Quantum Neural Networks

Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several QNN architectures have been proposed and successfully tested on benchmark datasets for machine learning. However, quantitative studies of the QNN-generated entanglement have been investigated only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. Here, we employ matrix product states to characterize recently studied QNN architectures with random parameters up to fifty qubits showing that their entanglement, measured in terms of entanglement entropy between qubits, tends to that of Haar distributed random states as the depth of the QNN is increased. We certify the randomness of the quantum states also by measuring the expressibility of the circuits, as well as using tools from random matrix theory. We show a universal behavior for the rate at which entanglement is created in any given QNN architecture, and consequently introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Our results characterise the entanglement properties of quantum neural networks, and provides new evidence of the rate at which these approximate random unitaries.

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.

Parameter-parallel distributed variational quantum algorithm

Variational quantum algorithms (VQAs) have emerged as a promising near-term technique to explore practical quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, the inefficient parameter training process due to the incompatibility with backpropagation and the cost of a large number of measurements, posing a great challenge to the large-scale development of VQAs. Here, we propose a parameter-parallel distributed variational quantum algorithm (PPD-VQA), to accelerate the training process by parameter-parallel training with multiple quantum processors. To maintain the high performance of PPD-VQA in the realistic noise scenarios, a alternate training strategy is proposed to alleviate the acceleration attenuation caused by noise differences among multiple quantum processors, which is an unavoidable common problem of distributed VQA. Besides, the gradient compression is also employed to overcome the potential communication bottlenecks. The achieved results suggest that the PPD-VQA could provide a practical solution for coordinating multiple quantum processors to handle large-scale real-word applications.

Quantum Neural Networks for a Supply Chain Logistics Application

AbstractProblem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate‐scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical‐quantum algorithms have potential, however, to achieve good performance on much larger problem instances. One such hybrid algorithm on a problem of substantial importance: vehicle routing for supply chain logistics with multiple trucks and complex demand structure is investigated. Reinforcement learning with neural networks with embedded quantum circuits is used. In such neural networks, projecting high‐dimensional feature vectors down to smaller vectors is necessary to accommodate restrictions on the number of qubits of NISQ hardware. However, a multi‐head attention mechanism is used where, even in classical machine learning, such projections are natural and desirable. Data from the truck routing logistics of a company in the automotive sector is considered, and the methodology is applied by decomposing into small teams of trucks and results are found comparable to human truck assignment.

Solving Graph Problems Using Gaussian Boson Sampling.

Gaussian boson sampling (GBS) is not only a feasible protocol for demonstrating quantum computational advantage, but also mathematically associated with certain graph-related and quantum chemistry problems. In particular, it is proposed that the generated samples from the GBS could be harnessed to enhance the classical stochastic algorithms in searching some graph features. Here, we use Jiǔzhāng, a noisy intermediate-scale quantum computer, to solve graph problems. The samples are generated from a 144-mode fully connected photonic processor, with photon click up to 80 in the quantum computational advantage regime. We investigate the open question of whether the GBS enhancement over the classical stochastic algorithms persists-and how it scales-with an increasing system size on noisy quantum devices in the computationally interesting regime. We experimentally observe the presence of GBS enhancement with a large photon-click number and a robustness of the enhancement under certain noise. Our work is a step toward testing real-world problems using the existing noisy intermediate-scale quantum computers and hopes to stimulate the development of more efficient classical and quantum-inspired algorithms.

Analog Quantum Variational Embedding Classifier

Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy, intermediate-scale quantum (NISQ) computers, various quantum-classical hybrid algorithms have been proposed. One such previously proposed hybrid algorithm is a gate-based variational embedding classifier, which is composed of a classical neural network and a parameterized gate-based quantum circuit. We propose a quantum variational embedding classifier based on an analog quantum computer, where control signals vary continuously in time. In our algorithm, the classical data is transformed into the parameters of the time-varying Hamiltonian of the analog quantum computer by a linear transformation. The nonlinearity needed for a nonlinear classification problem is purely provided by the analog quantum computer through the nonlinear dependence of the final quantum state on the control parameters of the Hamiltonian. We performed numerical simulations that demonstrate the effectiveness of our algorithm for performing binary and multi-class classification on linearly inseparable datasets such as concentric circles and MNIST digits. Our classifier can reach accuracy comparable with the best classical classifiers. We find the performance of our classifier can be increased by increasing the number of qubits until the performance saturates and fluctuates. Moreover, the number of optimization parameters of our classifier scales linearly with the number of qubits. The increase of number of training parameters when the size increases is therefore not as fast as that of neural network. Our algorithm presents the possibility of using current quantum annealers for solving practical machine-learning problems, and it could also be useful to explore quantum advantage in quantum machine learning.

Implementation of Quantum Key Distribution Algorithm in Real Time IBM Quantum Computers

Abstract: We are Currently in the NISQ(noisy intermediate scale quantum) era. Current Quantum computers have a high noise error rate. With the increasing number of qubits every year we can develop fault tolerant quantum systems which have immense power to change our current computing power. Current quantum systems have shown to have the potential to break the classical RSA algorithm using shors algorithm. With more development and increase in number of qubits available it could easily break the current security systems of our computing. In future we could transmit data safely using the same quantum principles in the post quantum cryptography era. Quantum key distribution could be the future protocol used to transfer our secure information without getting hacked even by using quantum computing and break other quantum principles like shors algorithm which can break current encryption techniques like the RSA algorithms. We need to develop Quantum network infrastructure so we can implement the quantum key distribution algorithm in the future to enable secure transmission of data.

QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer

Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware. In this paper, we present results on the first NLP experiments conducted on Noisy Intermediate-Scale Quantum (NISQ) computers for datasets of size greater than 100 sentences. Exploiting the formal similarity of the compositional model of meaning by Coecke, Sadrzadeh, and Clark (2010) with quantum theory, we create representations for sentences that have a natural mapping to quantum circuits. We use these representations to implement and successfully train NLP models that solve simple sentence classification tasks on quantum hardware. We conduct quantum simulations that compare the syntax-sensitive model of Coecke et al. with two baselines that use less or no syntax; specifically, we implement the quantum analogues of a “bag-of-words” model, where syntax is not taken into account at all, and of a word-sequence model, where only word order is respected. We demonstrate that all models converge smoothly both in simulations and when run on quantum hardware, and that the results are the expected ones based on the nature of the tasks and the datasets used. Another important goal of this paper is to describe in a way accessible to AI and NLP researchers the main principles, process and challenges of experiments on quantum hardware. Our aim in doing this is to take the first small steps in this unexplored research territory and pave the way for practical Quantum Natural Language Processing.

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)--style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.