Variational Quantum Algorithms (VQAs) have emerged as a powerful class of algorithms that is highly suitable for noisy quantum devices. Therefore, investigating their design has become key in quantum computing research. Previous works have shown that choosing an effective parameterized quantum circuit (PQC) or ansatz for a VQA is crucial to its overall performance, especially on near-term devices. In this paper, we utilize pulse-level access to quantum machines, our understanding of their two-qubit interactions, and, more importantly, our knowledge of VQAs, to customize the design of two-qubit entanglers. Our analysis shows that utilizing customized pulse gates for ansatze reduces state preparation times by more than half, maintains expressibility relative to standard ansatze, and produces PQCs that are more trainable through local cost function analysis. Our algorithm performance results show that in three cases, our PQC configuration outperforms the base implementation. Experiments using IBM Quantum hardware demonstrate that our pulse-based PQC configurations are more capable of solving MaxCut and Chemistry problems compared to a standard configuration.
Variational Quantum Algorithms (VQAs) have emerged as a powerful class of algorithms that is highly suitable for noisy quantum devices. Therefore, investigating their design has become key in quantum computing research. Previous works have shown that choosing an effective parameterized quantum circuit (PQC) or ansatz for a VQA is crucial to its overall performance, especially on near-term devices. In this paper, we utilize pulse-level access to quantum machines, our understanding of their two-qubit interactions, and, more importantly, our knowledge of VQAs, to customize the design of two-qubit entanglers. Our analysis shows that utilizing customized pulse gates for ansatze reduces state preparation times by more than half, maintains expressibility relative to standard ansatze, and produces PQCs that are more trainable through local cost function analysis. Our algorithm performance results show that in three cases, our PQC configuration outperforms the base implementation. Experiments using IBM Quantum hardware demonstrate that our pulse-based PQC configurations are more capable of solving MaxCut and Chemistry problems compared to a standard configuration.
In this paper, we propose an ansatz approximation approach for variational quantum algorithms (VQAs) that uses one of the hardware's main attributes, its crosstalk behavior, as its main approximation driver. By utilizing crosstalk-adaptive scheduling, we are able to apply a circuit-level approximation/optimization to our ansatz. Our design procedure involves first characterizing the hardware's crosstalk and then approximating the circuit by a desired level of crosstalk mitigation, all while effectively reducing its duration and gate counts. We demonstrate the effect of crosstalk mitigation on expressibility, trainability, and entanglement: key components that drive the utility of parameterized circuits. We tested our approach on real quantum hardware against a base configuration, and our results showed superior performance for the circuit-level optimized ansatz over a base ansatz for two quantum chemistry benchmarks. We take into consideration that applications vary in their response to crosstalk, and we believe that this approximation strategy can be used to create ansatze that are expressive, trainable, and with crosstalk mitigation levels tailored for specific workloads.
Quantum computers promise a great computational advantage over classical computers, which might help solve various computational challenges such as the simulation of complicated quantum systems, finding optimum in large optimization problems, and solving large-scale linear algebra problems. Current available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved accurately with those devices. Variational quantum algorithms (VQAs) have emerged as a leading strategy to address these limitations by optimizing cost function based on measurement results of shallow depth circuits. Recently, various pulse engineering methods were suggested in order to improve VQA results, including optimizing pulse parameters instead of gate angles as part of the VQA optimization process. In this paper, we suggest a novel pulse-based ansatz, which is parameterized mainly by pulses’ duration of pre-defined pulse structures. This ansatz structure provides relatively low amounts of optimization parameters while maintaining high expressibility, allowing fast convergence. In addition, the ansatz has structured adaptivity to the entanglement level required by the problem, allowing low noise and accurate results. We tested this ansatz against quantum chemistry problems. Specifically, finding the ground-state energy associated with the electron configuration problem, using the variational quantum eigensolver (VQE) algorithm for several different molecules. We manage to achieve chemical accuracy both in simulation for several molecules and on one of IBM’s NISQ devices for the H2 molecule in the STO-3G basis, without the need for extensive error mitigation. Our results are compared to a common gate-based ansatz and show better accuracy and significant latency reduction—up to 7× shorter ansatz schedules.
Variational quantum algorithms (VQAs) have emerged as the leading strategy for using these noisy devices to achieve an advantage over their classical counterparts.VQAs use a hybrid quantum-classical framework, in which one employs the quantum computer to prepare a parameterized quantum state and outsource the optimization to a classical subroutine. VQAs have been proposed for applications in various fields, including physics, quantum chemistry, machine learning, and optimization. Nevertheless, many challenges must be addressed before we can use them for practical tasks. In this dissertation, we propose strategies to overcome some challenges in implementing VQAs. We first look at the issue of trainability for VQAs and propose three methods for optimizing them.The first method is based on natural evolutionary strategies (NES) and can alleviate the issue of vanishing gradients for randomly initialized parameterized quantum circuits (PQCs). The second method is based on the notion of information flow in PQCs and uses a mutual information-based distance metric to define paths for stochastic optimization of VQAs. Finally, we develop gradient evaluation procedures for optimizing objectives with the unitary coupled-cluster ansatz. Next, we study the issue of expressibility of PQCs used in variational algorithms.First, using the theory of quantum optimal control we define a notion of reachability of general ans\"atze used in VQAs. Next, using a variational autoencoder (VAE) coupled with a regression model, we try to gain a better understanding of the parameterization of PQCs. Finally, we attempt to remedy the inefficient usage of quantum resources for storing quantum data using evolutionary strategies to design quantum circuits for compressing quantum data. We present numerical evidence that the work presented here can increase trainability, efficiency, and understanding of VQAs.We believe our work is of interest to the quantum computing community as we continue to push the limits of NISQ devices for solving practical problems.
Variational quantum algorithms (VQAs) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability of the algorithm to efficiently explore the solution space and converge to more optimal solutions. Quantum architecture search (QAS) is therefore a highly relevant topic, in which the selection of an appropriate circuit topology, gate set, and parameterization scheme is determinant to achieve good performance. In addition, it is not only problem-dependent, but the quantum hardware used also has a significant impact on the results. Therefore, we present BPQCO, a Bayesian optimization-based strategy to search for optimal PQCs adapted to the problem to be solved and to the characteristics and limitations of the chosen quantum hardware. To this end, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems (a synthetic dataset and the well-known Iris dataset), focusing on the design of the circuit ansatz. In addition, we study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers. To mitigate the effect of noise, two alternative optimization strategies based on the characteristics of the quantum system are proposed. The results obtained confirm the relevance of the presented approach and allow its adoption in further work based on the use of PQCs.
In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure circuits, which may not be taylored for specific problems or hardware configurations. A leading strategy to address this issue are Adaptative VQAs, which dynamically modify the circuit structure by adding and removing gates, and optimize their parameters during the training. Several Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement capability and hardware compatibility, have already been proposed in the literature, but there is still lack of a systematic comparison between the different methods. In this paper, we aim to fill this gap by analyzing three Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline. In order to compare these algorithms to traditional VQAs, we also include the Quantum Approximate Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to QUBO problems and study their performance by examining the quality of the solutions found and the computational times required. Additionally, we investigate how the choice of the hyperparameters can impact the overall performance of the algorithms, highlighting the importance of selecting an appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices and provides valuable insights to guide future research in this area.
Parameterized quantum circuits (PQCs) serve as a flexible framework for implementing various quantum algorithms, particularly in quantum machine learning and optimization tasks. However, their training is challenging due to both theoretical constraints and the inherent limitations in current quantum hardware. A judicious choice of PQC architecture is crucial for accurately representing the solution space, and for ensuring convergence in training. Several works introduced measures of expressibility and entangling capability for PQCs, and compared these metrics across different circuit structures, providing insights into how they impact performance and efficiency. However, these investigations often assumed idealized all-to-all qubit connectivity, which is not applicable to most hardware architectures. In practice, additional transpilation steps are performed prior to execution on hardware. The potential impact of better alignment of the PQC structure with the underlying native topology has in fact motivated introduction of hardware-efficient ansatze. In our work, we extend the methodology of measuring PQC efficiency to include more realistic quantum hardware models. We examine several popular hardware topologies, including hexagonal, square, circular, linear, and all-to-all. We evaluate the expressibility and entangling capability of circuits with different connectivity types and various arrangements of rotation gates. We assess the training performance of these PQC types in the context of a variational compiling procedure and identify the preferred gate patterns. This approach provides a more realistic evaluation of PQC performance, thus offering practical insights into their applications on existing quantum devices.