Solving optimization problems using variational algorithms stands out as a crucial application for noisy intermediate-scale devices. Instead of constructing gate-based quantum computers, our focus centers on designing variational quantum algorithms within the analog paradigm. This involves optimizing parameters that directly control pulses, driving quantum states toward target states without the necessity to compile a quantum circuit. In this work, we introduce pulse-based variational quantum optimization (PBVQO) as a hardware-level framework. We illustrate the framework by optimizing external fluxes on superconducting quantum interference devices, effectively driving the wave function of this specific quantum architecture to the ground state of an encoded problem Hamiltonian. Given that the performance of variational algorithms relies heavily on appropriate initial parameters, we introduce a global optimizer as a metalearning technique to tackle a simple problem. The synergy between PBVQO and metalearning provides an advantage over conventional gate-based variational algorithms.
Solving optimization problems using variational algorithms stands out as a crucial application for noisy intermediate-scale devices. Instead of constructing gate-based quantum computers, our focus centers on designing variational quantum algorithms within the analog paradigm. This involves optimizing parameters that directly control pulses, driving quantum states toward target states without the necessity to compile a quantum circuit. In this work, we introduce pulse-based variational quantum optimization (PBVQO) as a hardware-level framework. We illustrate the framework by optimizing external fluxes on superconducting quantum interference devices, effectively driving the wave function of this specific quantum architecture to the ground state of an encoded problem Hamiltonian. Given that the performance of variational algorithms relies heavily on appropriate initial parameters, we introduce a global optimizer as a metalearning technique to tackle a simple problem. The synergy between PBVQO and metalearning provides an advantage over conventional gate-based variational algorithms.
Quantum computing is among the most promising emerging techniques to solve problems that are computationally intractable on classical hardware. A large body of existing works focus on using variational quantum algorithms on the gate level for machine learning tasks, such as the variational quantum circuit (VQC). However, VQC has limited flexibility and expressibility due to limited number of parameters, e.g. only one parameter can be trained in one rotation gate. On the other hand, we observe that quantum pulses are lower than quantum gates in the stack of quantum computing and offers more control parameters. Inspired by the promising performance of VQC, in this paper we propose variational quantum pulses (VQP), a novel paradigm to directly train quantum pulses for learning tasks. The proposed method manipulates variational quantum pulses by pulling and pushing the amplitudes of pulses in an optimization framework. Similar to variational quantum algorithms, our framework to train pulses maintains the robustness to noise on Noisy Intermediate-Scale Quantum (NISQ) computers. In an example task of binary classification, VQP learning achieves up to 11% and 9% higher accuracy compared with VQC learning on the qiskit pulse simulators (with system model from real machine) and ibmq-jarkata, respectively, demonstrating its effectiveness and feasibility. Stability for VQP to obtain reliable results has also been verified in the presence of noise.
Current quantum programs are mostly synthesized and compiled on the gate-level, where quantum circuits are composed of quantum gates. The gate-level workflow, however, introduces significant redundancy when quantum gates are eventually transformed into control signals and applied on quantum devices. For superconducting quantum computers, the control signals are microwave pulses. Therefore, pulse-level optimization has gained more attention from researchers due to their advantages in terms of circuit duration. Recent works, however, are limited by their poor scalability brought by the large parameter space of control signals. In addition, the lack of gate-level "knowledge" also affects the performance of pure pulse-level frameworks. We present a hybrid gate-pulse model that can mitigate these problems. We propose to use gate-level compilation and optimization for "fixed" part of the quantum circuits and to use pulse-level methods for problem-agnostic parts. Experimental results demonstrate the efficiency of the proposed framework in discrete optimization tasks. We achieve a performance boost at most 8% with 60% shorter pulse duration in the problem-agnostic layer.
Variational quantum algorithms (VQAs) are the leading candidates for practical applications of noisy intermediate-scale quantum (NISQ) devices. Recently, pulse-based variational quantum algorithms (p-VQAs) have emerged as a compelling alternative to traditional gate-based VQAs. By optimizing continuous control fields directly on hardware-native Hamiltonians, pulse-based methods are easy to implement and can significantly reduce quantum resource overhead, thereby enhancing the overall performance of quantum algorithms on NISQ devices. In this review, we present a comprehensive survey over recent advances in p-VQAs, covering theory, algorithms, and hardware deployments across various quantum computing platforms. We also review applications of p-VQAs to variational quantum eigensolver in quantum chemistry, quantum approximate optimization algorithm for combinatorial optimization, and quantum machine learning tasks.
Quantum computer systems require robust software integration to support quantum algorithm development towards addressing practical challenges in many important problem areas including logistics, chemistry, and AI/ML. Researchers predict quantum algorithms will achieve computational advantage over classical algorithms for these specific problem areas in the Noisy Intermediate Scale Quantum (NISQ) era [1]. We consider one such algorithm, the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm for solving combinatorial optimization problems [2]. QAOA promises to be a practical alternative to inefficient classical algorithms for large problem sizes, but quantum hardware capabilities lag behind the requirements for practical application. We show that the Superstaq quantum compiler can support performance improvements for QAOA by exploiting optimization opportunities only revealed at levels lower than logic gates, i.e., at the level of pulses, quantum hardware instructions.
Variational quantum algorithms (VQAs) have demonstrated great potentials in the Noisy Intermediate Scale Quantum (NISQ) era. In the workflow of VQA, the parameters of ansatz are iteratively updated to approximate the desired quantum states. We have seen various efforts to draft better ansatz with less gates. Some works consider the physical meaning of the underlying circuits, while others adopt the ideas of neural architecture search (NAS) for ansatz generator. However, these designs do not exploit the full advantages of VQAs. Because most techniques target gate ansatz, and the parameters are usually rotation angles of the gates. In quantum computers, the gate ansatz will eventually be transformed into control signals such as microwave pulses on superconducting qubits. These control pulses need elaborate calibrations to minimize the errors such as over-rotation and under-rotation. In the case of VQAs, this procedure will introduce redundancy, but the variational properties of VQAs can naturally handle problems of over-rotation and under-rotation by updating the amplitude and frequency parameters. Therefore, we propose NAPA, a native-pulse ansatz generator framework for VQAs. We generate native-pulse ansatz with trainable parameters for amplitudes and frequencies. In our proposed NAPA, we are tuning parametric pulses, which are natively supported on NISQ computers. Given the limited availability of gradient-based optimizers for pulse-level quantum programs, we choose to deploy non-gradient optimizers in our framework. To constrain the number of parameters sent to the optimizer, we adopt a progressive way to generate our native-pulse ansatz. Experiments are conducted on both simulators and quantum devices for Variational Quantum Eigensolver (VQE) tasks to evaluate our methods.
In this work, we first consider standard quantum control problems for superconducting transmon qubits. Such quantum systems have been studied extensively both from an analytical and a numerical perspective [MSG&al11; TMW16]. Analytical pulses usually show dependencies from system parameters that are not easily found in numerical solutions. Therefore, our approach is then to employ neural networks to learn the functional dependence of optimal quantum control solutions from system parameters. We show that we can optimize such solutions analytically for single and two-qubit gates using either very few parameter samples or large numbers of pulse frequencies for large parameter ranges. Afterward, we move to a higher level of optimization. We consider variational gates in trapped-ion quantum computers [MMN&al16]. In this setting, we employ a hybrid scheme that uses both reinforcement learning and continuous optimization to optimize both circuit structure and variational angles concurrently [BDS&al18; SEL&al22]. We show that our reinforcement learning algorithm assisted by a continuous optimizer can construct effective solutions to the gate synthesis problem that matches and surpasses standard circuit compilers. Next, we consider variational optimization of non-linear maps [HCS&al23] acting on quantum states such as entanglement purification protocols. An entanglement purification protocol acts as a highly non-linear map, but it still outputs a faithful representation of a quantum system. Optimizing it for a specific family of states requires reducing the number of operations needed to retrieve the original state. This optimization has the potential to make purification protocols easier to implement on a quantum device. In fact, the exponential scaling of the purification protocol with the number of states [DB07] implies that such protocols may not be applied directly without careful engineering. We also show that the performance of standard purification protocols for arbitrary two-qubit input states leads to poor output values of the concurrence. Our optimized protocols prove instead able to increase the value of the concurrence above the maximum limit of traditional analytical protocols. We also show how the twirling operation becomes an obstacle to the performance of the protocol itself when considering random two-qubit states, although it is a useful tool in the design of entanglement purification protocols. Finally, we study parameter sampling in quantum circuits, focusing in particular on the LCU methods. Such problems are particularly interesting for meta-variational settings [CKA21] where we compute the average over observables evaluated at different points in the parameter space. They are also relevant for optimal quantum control algorithms because the computation of the fidelity with respect to a target operation is the basis of most optimal quantum control routines. In conclusion, we analyze several optimization problems that are relevant for quantum science and technology. We show that machine learning-assisted solutions can be applied successfully to engineer optimal quantum control pulses and compilation strategies based on variational angles. Also in the context of entanglement purification, we show how our optimized protocols can surpass current strategies for multiparametric families of states.