Quantum Hardware Research Articles

Improved clinical data imputation via classical and quantum determinantal point processes

Imputing data is a critical issue for machine learning practitioners, including in the life sciences domain, where missing clinical data is a typical situation and the reliability of the imputation is of great importance. Currently, there is no canonical approach for imputation of clinical data and widely used algorithms introduce variance in the downstream classification. Here we propose novel imputation methods based on determinantal point processes (DPP) that enhance popular techniques such as the multivariate imputation by chained equations and MissForest. Their advantages are twofold: improving the quality of the imputed data demonstrated by increased accuracy of the downstream classification and providing deterministic and reliable imputations that remove the variance from the classification results. We experimentally demonstrate the advantages of our methods by performing extensive imputations on synthetic and real clinical data. We also perform quantum hardware experiments by applying the quantum circuits for DPP sampling since such quantum algorithms provide a computational advantage with respect to classical ones. We demonstrate competitive results with up to 10 qubits for small-scale imputation tasks on a state-of-the-art IBM quantum processor. Our classical and quantum methods improve the effectiveness and robustness of clinical data prediction modeling by providing better and more reliable data imputations. These improvements can add significant value in settings demanding high precision, such as in pharmaceutical drug trials where our approach can provide higher confidence in the predictions made.

Improved financial forecasting via quantum machine learning

Quantum algorithms have the potential to enhance machine learning across a variety of domains and applications. In this work, we show how quantum machine learning can be used to improve financial forecasting. First, we use classical and quantum Determinantal Point Processes to enhance Random Forest models for churn prediction, improving precision by almost 6%. Second, we design quantum neural network architectures with orthogonal and compound layers for credit risk assessment, which match classical performance with significantly fewer parameters. Our results demonstrate that leveraging quantum ideas can effectively enhance the performance of machine learning, both today as quantum-inspired classical ML solutions, and even more in the future, with the advent of better quantum hardware.

Quantum Fourier networks for solving parametric PDEs

Many real-world problems, like modelling environment dynamics, physical processes, time series etc involve solving partial differential equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture called Fourier neural operator (FNO) proved to be capable of learning solutions of given PDE families for any initial conditions as input. However, it results in a time complexity linear in the number of evaluations of the PDEs while testing. Given the advancements in quantum hardware and the recent results in quantum machine learning methods, we exploit the running efficiency offered by these and propose quantum algorithms inspired by the classical FNO, which result in time complexity logarithmic in the number of evaluations and are expected to be substantially faster than their classical counterpart. At their core, we use the unary encoding paradigm and orthogonal quantum layers and introduce a new quantum Fourier transform in the unary basis. We propose three different quantum circuits to perform a quantum FNO. The proposals differ in their depth and their similarity to the classical FNO. We also benchmark our proposed algorithms on three PDE families, namely Burgers’ equation, Darcy’s flow equation and the Navier–Stokes equation. The results show that our quantum methods are comparable in performance to the classical FNO. We also perform an analysis on small-scale image classification tasks where our proposed algorithms are at par with the performance of classical convolutional neural networks, proving their applicability to other domains as well.

Minimizing readout-induced noise for early fault-tolerant quantum computers

Quantum error correcting code can diagnose potential errors and correct them based on measured outcomes by leveraging syndrome measurement. However, mid-circuit measurement has been technically challenging for early fault-tolerant quantum computers and the readout-induced noise acts as a main contributor to the logical infidelity. We present a different method for syndrome extraction, namely , that requires only a single-shot measurement on a single ancilla, while the canonical syndrome measurement requires multiple measurements to extract the eigenvalue for each stabilizer generator. As such, we can detect the error in the logical state with minimized readout-induced noise. By adopting our method as a precheck routine for quantum error correcting cycles, we can significantly reduce the readout overhead, the idling time, and the logical error rate during syndrome measurement. We numerically analyze the performance of our protocol using Iceberg code and Steane code under realistic noise parameters based on superconducting hardware and demonstrate the advantage of our protocol in the near-term scenario. As mid-circuit measurements are still error-prone for near-term quantum hardware, our method could boost the applications of early fault-tolerant quantum computing. Published by the American Physical Society 2024

A Perspective on Protein Structure Prediction Using Quantum Computers.

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

Quantum-Informed Recursive Optimization Algorithms

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component (e.g., locality) and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We showcase the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow circuits of the quantum approximate optimization algorithm, solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a template for a broader class of hybrid quantum-classical algorithms for combinatorial optimization. Published by the American Physical Society 2024

Near-term distributed quantum computation using mean-field corrections and auxiliary qubits

Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such exchange of quantum information itself poses unique engineering challenges, requiring high gate fidelity and costly non-local operations. To mitigate this, we propose near-term distributed quantum computing, focusing on approximate approaches that involve limited information transfer and conservative entanglement production. We first devise an approximate distributed computing scheme for the time evolution of quantum systems split across any combination of classical and quantum devices. Our procedure harnesses mean-field corrections and auxiliary qubits to link two or more devices classically, optimally encoding the auxiliary qubits to both minimize short-time evolution error and extend the approximate scheme’s performance to longer evolution times. We then expand the scheme to include limited quantum information transfer through selective qubit shuffling or teleportation, broadening our method’s applicability and boosting its performance. Finally, we build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms. To characterize our technique, we introduce a non-linear perturbation theory that discerns the critical role of our mean-field corrections in optimization and may be suitable for analyzing other non-linear quantum techniques. This fragmented pre-training is remarkably successful, reducing algorithmic error by orders of magnitude while requiring fewer iterations.

Experimental Virtual Distillation of Entanglement and Coherence.

Noise is, in general, inevitable and detrimental to practical and useful quantum communication and computation. Under the resource theory framework, resource distillation serves as a generic tool to overcome the effect of noise. Yet, conventional resource distillation protocols generally require operations on multiple copies of resource states, and strong limitations exist that restrict their practical utilities. Recently, by relaxing the setting of resource distillation to only approximating the measurement statistics instead of the quantum state, a resource-frugal protocol, "virtual resource distillation," is proposed, which allows more effective distillation of noisy resources. Here, we report its experimental implementation on a photonic quantum system for the distillation of quantum coherence (up to dimension four) and bipartite entanglement. We show the virtual distillation of the maximal superposed state of dimension four from the state of dimension two, an impossible task in conventional coherence distillation. Furthermore, we demonstrate the virtual distillation of entanglement with operations acting only on a single copy of the noisy Einstein-Podolsky-Rosen (EPR) pair and showcase the quantum teleportation task using the virtually distilled EPR pair with a significantly improved fidelity of the teleported state. These results illustrate the feasibility of the virtual resource distillation method and pave the way for accurate manipulation of quantum resources with noisy quantum hardware.

Low-depth simulations of fermionic systems on square-grid quantum hardware

We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen low-depth fermion-to-qubit mappings and allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a 70% improvement upon previous state-of-the-art. Our compression technique also results in significant reduction of two-qubit gates. We find the lowest gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.

FragQC: An efficient quantum error reduction technique using quantum circuit fragmentation

Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of sub-circuits that can be executed on the smaller noisy quantum hardware available. However, the process of quantum circuit fragmentation involves finding an ideal cut that has exponential time complexity and also the classical post-processing required to reconstruct the output. In this paper, we represent a quantum circuit using a weighted graph and propose a novel classical graph partitioning algorithm for selecting an efficient fragmentation that reduces the entanglement between the sub-circuits along with balancing the estimated error in each sub-circuit. We also demonstrate a comparative study of different classical and quantum approaches to graph partitioning for finding such a cut. We present FragQC, a software tool that cuts a quantum circuit into sub-circuits when its error probability exceeds a certain threshold. With this proposed approach, we achieve an increase in fidelity of 13.38% compared to direct execution without cutting the circuit, and 7.88% over the state-of-the-art ILP-based method for the benchmark circuits.The code for FragQC is available at https://github.com/arnavdas88/FragQC.

Hybrid quantum neural network structures for image multi-classification

Image classification is a fundamental problem in computer vision, and neural networks provide an effective solution. With the advancement of quantum technology, quantum neural networks have attracted a lot of attention. However, they are only suitable for low-dimensional data and require dimensionality reduction and quantum encoding. Two image classification methods have recently emerged: one employs PCA for dimensionality reduction and angular encoding, and the other integrates QNN into a CNN to improve performance. Despite numerous algorithms, the differences between them remain unclear. This study explores these algorithms’ performance in multi-class image classification and proposes an optimized hybrid quantum neural network suitable for the current environment. As the number of classes increases, research on PCA-based quantum algorithms reveals the barren plateau problem of QNN, which is not suitable for multiple classes in a hybrid setting. Our proposed model combining traditional CNN with QNN addresses QNN’s multi-class training difficulties to some extent and achieves satisfactory classification results. Nevertheless, its accuracy remains below that of the top-performing CNN models. Furthermore, we investigate transfer learning in hybrid quantum neural network models and assess the performance of our models on the quantum hardware from IBM. In conclusion, quantum neural networks show promise but require further research and optimization, facing challenges ahead.

Dynamic optimization on quantum hardware: Feasibility for a process industry use case

The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable computations are critical. Conventional methods can struggle to surmount the complexities of such tasks. Quantum computing and quantum annealing emerge as avant-garde contenders to transcend conventional computational constraints. We convert a dynamic optimization problem, characterized by an optimization problem with a system of differential–algebraic equations embedded, into a Quadratic Unconstrained Binary Optimization problem, enabling quantum computational approaches. The empirical findings synthesized from classical methods, simulated annealing, quantum annealing via D-Wave’s quantum annealer, and hybrid solver methodologies, illuminate the intricate landscape of computational prowess essential for tackling complex and high-dimensional dynamic optimization problems. Our findings suggest that while quantum annealing is a maturing technology that currently does not outperform state-of-the-art classical solvers, continuous improvements could eventually aid in increasing efficiency within the chemical process industry.

Probing entanglement in a 2D hard-core Bose-Hubbard lattice.

Entanglement and its propagation are central to understanding many physical properties of quantum systems1-3. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour4-7. However, a universal understanding remains challenging owing to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems8-14. Here we use a controllable 4 × 4 array of superconducting qubits to emulate a 2D hard-core Bose-Hubbard (HCBH) lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the centre of the spectrum and a crossover to the onset of area-law scaling near its edges.

Qubit Efficient Quantum Algorithms for the Vehicle Routing Problem on Noisy Intermediate‐Scale Quantum Processors

AbstractThe vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, the use of a previously‐introduced qubit encoding scheme is explored to reduce the number of qubits, to evaluate the effectiveness of Noisy Intermediate‐Scale Quantum (NISQ) devices when applied to industry relevant optimization problems. A quantum variational approach is applied to a testbed of multiple VRPTW instances ranging from 11 to 3964 routes. These intances are formulated as quadratic unconstrained binary optimization (QUBO) problems based on realistic shipping scenarios. The results are compared with standard binary‐to‐qubit mappings after executing on simulators as well as various quantum hardware platforms, including IBMQ, AWS (Rigetti), and IonQ. These results are benchmarked against the classical solver, Gurobi. The approach can find approximate solutions to the VRPTW comparable to those obtained from quantum algorithms using the full encoding, despite the reduction in qubits required. These results suggest that using the encoding scheme to fit larger problem sizes into fewer qubits is a promising step in using NISQ devices to find approximate solutions for industry‐based optimization problems, although additional resources are still required to eke out the performance from larger problem sizes.

Hybrid Classical-Quantum Branch-and-Bound Algorithm for Solving Integer Linear Problems.

Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. In order to deal with this issue, we propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits. We analyze the performance of this method on two problems, the knapsack problem and the traveling salesman problem. Our results show the advantages of this method, that balances the number of steps that the algorithm has to make with the amount of error in the solution found by the quantum hardware that the user is willing to risk. The results are obtained using the commercially available quantum hardware D-Wave Advantage, and they outline the strategy for a practical application of the quantum annealers.

Improved Quantum Approximate Optimization Algorithm for Low‐Density Parity‐Check Channel Decoding

AbstractQuantum computing shows promise for 6G networks due to its parallel computing capabilities. In the context of the Noisy Intermediate‐Scale Quantum era, the introduction of hybrid quantum‐classical algorithms like Quantum Approximate Optimization Algorithm (QAOA) offer powerful solutions to many combinatorial optimization problems in 6G. This paper focuses on Low‐Density Parity‐Check (LDPC) channel decoding and proposes an improved QAOA algorithm assisted by the learning‐to‐learn strategy. We also investigate the parameter concentration phenomenon in QAOA‐based LDPC decoding to assess the rationality. To evaluate effectiveness, a comprehensive numerical expression for the energy expectation of single‐layer QAOA and propose indicators for transfer performance evaluation is provided. Based on simulation results, the similarity in parameter distribution across specific LDPC configurations is investigated. This similarity facilitates the transfer of training outcomes from smaller to larger‐scale problems for optimization initialization, thereby avoiding the need for retraining. This approach offers insights and potential solutions for rapid, large‐scale channel decoding in 6G networks, despite the current limitations of quantum hardware.

Hybrid Approaches for Efficient Simulations of 3-Qubit Quantum Fourier Transform (QFT) Circuit Using Quick Quantum Circuit Simulation (QQCS)

The research devised efficient methods for simulating 3-qubit Quantum Fourier Transform (QFT) circuits using Quick Quantum Circuit Simulation (QQCS). The hybrid methodologies suggested as a solution for efficiently simulating the circuit involve the combination of decision diagrams and property exploitation techniques. This paper incorporated two methods based on decision diagrams: the reordering trick and decision diagram approximations, template-based optimization, and linear reversible circuit synthesis for property exploitation. The proposed approaches significantly improved and optimized quantum algorithms and hardware by aiming to simulate quantum circuits accurately and quickly. Simulations using QQCS proved the effectiveness of these strategies, which were then compared to the original circuit. The results yielded valuable insights into enhancing simulation efficiency while upholding circuit accuracy.

Quantum homogenization as a quantum steady-state protocol on noisy intermediate-scale quantum hardware

Quantum homogenization as a quantum steady-state protocol on noisy intermediate-scale quantum hardware

Quantum Computing in Machine Learning - The Future of Quantum Computing

In order to solve challenging optimization issues, analyze data effectively, and improve the capabilities of current machine learning algorithms, quantum computing has the potential to revolutionize the area of machine learning. The proposed work examines the fundamental ideas and methods of quantum computing—including quantum gates, quantum circuits, and quantum algorithms—as they relate to machine learning in this abstract. Various quantum computing applications in machine learning, including quantum neural networks, quantum support vector machines, and conventional methods influenced by quantum mechanics are also discussed. A review of state-of-the-art in quantum computing for machine learning, including recent advancements in quantum hardware and software has been done and the future prospects of this fascinating area has been examined.

Experimental advances with the QICK (Quantum Instrumentation Control Kit) for superconducting quantum hardware

Experimental advances with the QICK (Quantum Instrumentation Control Kit) for superconducting quantum hardware