Quantum computing: A taxonomy, systematic review and future directions

Quantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model in the conventional quantum computing architecture. However, the data reuploading tends to require a large amount of quantum resources, which motivates us to find an alternative strategy for realizing the expressive quantum machine learning efficiently. In this paper, we propose quantum machine learning with Kerr-nonlinear parametric oscillators (KPOs), as another promising quantum computing device. We use not only the ground state and first excited state but also higher excited states, which allows us to use a large Hilbert space even if we have a single KPO. Our numerical simulations show that the expressibility of our method with only one mode of the KPO is much higher than that of the conventional method with six qubits. Our results pave the way towards resource-efficient quantum machine learning, which is essential for the practical applications in the NISQ era.

The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.

Quantum Random Access Memory (QRAM) plays a pivotal role in accelerating quantum algorithms, especially in quantum machine learning. However, its implementation on noisy intermediate-scale quantum (NISQ) computers faces major challenges due to high qubit requirements and large circuit depth. These factors amplify quantum noise, limiting QRAM performance and scalability. In this work, we introduce a gate-pruning strategy that mitigates noise while preserving QRAM functionality. Our approach reduces circuit depth by eliminating small-angle rotation gates which are particularly noise-sensitive on NISQ hardware. This pruning significantly improves QRAM resilience without compromising data-loading efficiency or superposition-based querying. We further show that the pruned QRAM supports a variational quantum classifier capable of parallel training with logarithmic qubit scaling. Experiments on benchmark datasets confirm that our approach enhances noise resilience and classification accuracy, underscoring its potential for practical quantum machine learning in the NISQ era.

We are in the noisy intermediate-scale quantum (NISQ) devices' era, in which quantum hardware has become available for application in real-world problems. However, demonstrations of the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the train dispatching consequences of the arrival of an already delayed train to a given network segment. This problem is computationally hard and needs to be solved almost in real time. We introduce a quadratic unconstrained binary optimization (QUBO) model of this problem, which is compatible with the emerging quantum annealing technology. The model's instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including the conventional solution of a linear integer version of the model as well as the solution of the QUBO model using a tensor network-based algorithm. Our preliminary results illustrate the degree of difficulty of real-life railway instances for the current quantum annealing technology. Moreover, our analysis shows that the new generation of quantum annealers (the advantage system) does not perform well on those instances, either.

TensorCircuit is an open source quantum circuit simulator based on tensor network contraction, designed for speed, flexibility and code efficiency. Written purely in Python, and built on top of industry-standard machine learning frameworks, TensorCircuit supports automatic differentiation, just-in-time compilation, vectorized parallelism and hardware acceleration. These features allow TensorCircuit to simulate larger and more complex quantum circuits than existing simulators, and are especially suited to variational algorithms based on parameterized quantum circuits. TensorCircuit enables orders of magnitude speedup for various quantum simulation tasks compared to other common quantum software, and can simulate up to 600 qubits with moderate circuit depth and low-dimensional connectivity. With its time and space efficiency, flexible and extensible architecture and compact, user-friendly API, TensorCircuit has been built to facilitate the design, simulation and analysis of quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era.

Noisy Intermediate-Scale Quantum (NISQ) hardware has unavoidable noises, and crosstalk error is a significant error source. When multiple quantum operations are executed simultaneously, the quantum state can be corrupted due to the crosstalk between gates during simultaneous operations, decreasing the circuit fidelity. In this work, we first report on several protocols for characterizing crosstalk. Then, we discuss different crosstalk mitigation methods from the hardware and software perspectives. Finally, we perform crosstalk injection experiments on the IBM quantum device and demonstrate the fidelity improvement with the crosstalk mitigation method.

Quantum computing is expected to play an important role in solving the problem of huge computational costs in various applications by utilizing the collective properties of quantum states, including superposition, interference, and entanglement, to perform computations. Quantum mechanical (QM) methods are candidates for various applications and can provide accurate absolute energy calculations in structure-based methods. QM methods are powerful tools for describing reaction pathways and their potential energy surfaces (PES). In this study, we applied quantum computing to describe the PES of the bimolecular nucleophilic substitution (SN2) reaction between chloromethane and chloride ions. We performed noiseless and noise simulations using quantum algorithms and compared the accuracy and noise effects of the ansatzes. In noiseless simulations, the results from UCCSD and k-UpCCGSD are similar to those of full configurational interaction (FCI) with the same active space, which indicates that quantum algorithms can describe the PES of the SN2 reaction. In noise simulations, UCCSD is more susceptible to quantum noise than k-UpCCGSD. Therefore, k-UpCCGSD can serve as an alternative to UCCSD to reduce quantum noisy effects in the noisy intermediate-scale quantum era, and k-UpCCGSD is sufficient to describe the PES of the SN2 reaction in this work. The results showed the applicability of quantum computing to the SN2 reaction pathway and provided valuable information for structure-based molecular simulations with quantum computing.

Stabilizing quantum states in physical qubits quantum computers has been a widely explored topic in the Noisy Intermediate-Scale Quantum era. However, much of this work has focused on simulation rather than practical implementation. In this study, an experimental advancement in Bell state stabilization is presented, which utilizes surface codes for quantum error correction across three quantum computers: ibm_fez, ibm_torino, and ibm_brisbane. Our findings indicate that error correction produces an improvement of approximately 3% in accuracy for 127-qubit systems while demonstrating a more significant enhancement of around 20% for 156-qubit systems in stabilizing the Bell state with fidelity up to 0.6 in all the experiments. This paper outlines the methodology for implementing this strategy in other applications, offering a pathway to improve results (≈20%) when experimenting with superconducting quantum computers.

The current state of Quantum computing (QC) is extremely optimistic, and we are at a point where researchers have produced highly sophisticated quantum algorithms to address far reaching problems. However, it is equally apparent that the noisy quantum environment is a larger threat than many may realize. The noisy intermediate scale quantum era can be viewed as an inflection point for the enterprise of QC where decoherence could stagnate progress if left unaddressed. One tactic for handling decoherence is to address the problem from a hardware level by implementing topological materials into the design. In this work, we model several Josephson junctions that are modified by the presence of topological superconducting nanowires in between the host superconductors. Our primary result is a numerical calculation of the energy-phase relationship for topological nanowire junctions which is a key parameter of interest for the dynamics of qubit circuits. In addition to this, we report on the qualitative physical behavior of the bound states as a function of superconducting phase. These results can be used to further develop and inform the construction of more complicated systems, and it is hopeful that these types of designs could manifest as a fault tolerant qubit.

Quantum computing is a promising and emerging field of computer science with the potential to improve artificial intelligence techniques, particularly those related to optimization. However, current quantum devices operate in the Noisy Intermediate-Scale Quantum era, in which quantum noise can significantly compromise computational reliability. Evolutionary algorithms are inherently stochastic and may therefore be less sensitive to such noise, or even benefit from it. This study evaluates the performance of a hybrid quantum genetic algorithm on a set of combinatorial and continuous optimization problems under various realistic noise models. The findings demonstrate that quantum noise does not hinder the algorithm's performance and can even enhance its exploratory capabilities in some cases. This suggests that noise-aware quantum evolutionary strategies have the potential to be effective even with today's imperfect quantum hardware.

NISQ (Noisy Intermediate-Scale Quantum) era constraints, high sensitivity to noise and limited qubit count, impose significant barriers on the usability of QPUs (Quantum Process Units) capabilities. To overcome these challenges, researchers are exploring methods to maximize the utility of existing QPUs despite their limitations. Building upon the idea that the execution of a quantum circuit’s shots does not need to be treated as a singular monolithic unit, we propose a methodological framework, termed shot-wise, which enables the distribution of shots for a single circuit across multiple QPUs. Our framework features customizable policies to adapt to various scenarios. Additionally, it introduces a calibration method to pre-evaluate the accuracy and reliability of each QPU’s output before the actual distribution process and an incremental execution mechanism for dynamically managing the shot allocation and policy updates. Such an approach enables flexible and fine-grained management of the distribution process, taking into account various user-defined constraints and (contrasting) objectives. Demonstration results show that shot-wise distribution consistently and significantly improves the execution performance, with no significant drawbacks and additional qualitative advantages. Overall, the shot-wise methodology improves result stability and often outperforms single QPU runs, offering a robust and flexible approach to managing variability in quantum computing.

Quantum field theory in the presence of strong background fields contains interesting problems where quantum computers may someday provide a valuable computational resource. In the noisy intermediate-scale quantum era it is useful to consider simpler benchmark problems in order to develop feasible approaches, identify critical limitations of current hardware, and build new simulation tools. Here we perform quantum simulations of strong-field QED (SFQED) in 3+1 dimensions, using real-time nonlinear Breit-Wheeler pair production as a prototypical process. The strong-field QED Hamiltonian is derived and truncated in the Furry-Volkov mode expansion, and the interactions relevant for Breit-Wheeler are transformed into a quantum circuit. Quantum simulations of a “null double slit” experiment are found to agree well with classical simulations following the application of various error mitigation strategies, including an asymmetric depolarization algorithm which we develop and adapt to the case of Trotterization with a time-dependent Hamiltonian. We also discuss longer-term goals for the quantum simulation of SFQED. Published by the American Physical Society 2024

Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the Noisy Intermediate-Scale Quantum era. Since the inception of the first such algorithm, the Adaptive Derivative-Assembled Problem-Tailored Variational Quantum Eigensolver (ADAPT-VQE), many improvements have appeared in the literature. We combine the key improvements along with a novel operator pool—which we term Coupled Exchange Operator (CEO) pool—to assess the cost of running state-of-the-art ADAPT-VQE on hardware in terms of measurement counts and circuit depth. We show a dramatic reduction of these quantum computational resources compared to the early versions of the algorithm: CNOT count, CNOT depth and measurement costs are reduced by up to 88%, 96% and 99.6%, respectively, for molecules represented by 12 to 14 qubits (LiH, H6 and BeH2). We also find that our state-of-the-art CEO-ADAPT-VQE outperforms the Unitary Coupled Cluster Singles and Doubles ansatz, the most widely used static VQE ansatz, in all relevant metrics, and offers a five order of magnitude decrease in measurement costs as compared to other static ansätze with competitive CNOT counts.

Quantum approximate optimization algorithm (QAOA) is a quantum–classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the noisy intermediate-scale quantum era and has been extensively studied. However, the performance limitations of low-level QAOA have also been demonstrated across various instances. In this work, we first analytically prove the performance limitations of the standard level-1 QAOA in solving the MAX-CUT problem on bipartite graphs. To this end, we derive an upper bound for the approximation ratio based on the average degree of bipartite graphs. Second, we demonstrate that recursive QAOA (RQAOA), which recursively reduces graph size using QAOA as a subroutine, outperforms the standard level-1 QAOA. However, the performance of RQAOA exhibits limitations as the graph size increases. Finally, we show that RQAOA with a restricted parameter regime can fully address these limitations. Surprisingly, this modified RQAOA always finds the exact maximum cut for any bipartite graphs and even for a more general graph with parity-signed weights.

Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus (BPs) phenomenon, where gradients of cost functions vanish exponentially with the number of qubits. In this paper, inspired by transfer learning, where knowledge of pre-solved tasks could be further used in a different but related work with training efficiency improved, we report a parameter initialization method to mitigate BP. In the method, a small-sized task is solved with a VQA. Then the ansatz and its optimum parameters are transferred to tasks with larger sizes. Numerical simulations show that this method could mitigate BP and improve training efficiency. A brief discussion on how this method can work well is also provided. This work provides a reference for mitigating BP, and therefore, VQAs could be applied to more practical problems.