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 nativepulse ansatz. Experiments are conducted on both simulators and quantum devices for Variational Quantum Eigensolver (VQE) tasks to envaluate our methods. When adopted on NISQ machines, NAPA obtained improved the performance with decreased latency by an average of 86%. NAPA is able to achieve 96.482% and 99.336% accuracy for VQE tasks on H2 and HeH+ respectively. An average accuracy of 97.27% is achieved for medium-size quantum chemistry tasks on CO2, H2O, and NaH. NAPA also demonstrates advantages on quantum optimization tasks even with considerable noises in NISQ machines.
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 nativepulse ansatz. Experiments are conducted on both simulators and quantum devices for Variational Quantum Eigensolver (VQE) tasks to envaluate our methods. When adopted on NISQ machines, NAPA obtained improved the performance with decreased latency by an average of 86%. NAPA is able to achieve 96.482% and 99.336% accuracy for VQE tasks on H2 and HeH+ respectively. An average accuracy of 97.27% is achieved for medium-size quantum chemistry tasks on CO2, H2O, and NaH. NAPA also demonstrates advantages on quantum optimization tasks even with considerable noises in NISQ machines.
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.
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) 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.
At present, quantum computing is in the noisy intermediate-scale quantum (NISQ) era, marked by small qubit counts and high levels of noise and errors. Building a quantum computer with sufficient size and low error rates remains a challenge. In many promising quantum hardware architectures, the state of the physical qubits is controlled by pulse signals. In this paper, we will explore pulse-level control of quantum gates. Unlike the usual gate-level control, the pulse-level control provides increased flexibility and reduced latency. One direct application of pulse-level control is Variational Quantum Algorithms (VQA). The inherent properties of VQA allow us to disregard the gate-based evolution process and concentrate on the final target loss function. From the perspective of pulse-level control, we can generate a sequence of pulse-based gates to rotate the quantum state directly to the desired destination. In this study, we demonstrate an application of pulse-level VQA in estimating the ground state energy of molecular hydrogen. Our experiment is conducted using Quanlse which specializes in pulse-level control of quantum gates. The experimental results reveal a rapid convergence rate of optimization iterations, and the control pulses for each pulse-based gate is also displayed. These results highlight the considerable potential of pulse-level control techniques in practical applications.
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.
Variational Quantum Algorithms (VQA) are promising to demonstrate quantum advantages on near-term devices. Designing ansatz, a variational circuit with parameterized gates, is of paramount importance for VQA as it lays the foundation for parameter optimizations. Due to the large noise on Noisy-Intermediate Scale Quantum (NISQ) machines, considering circuit size and real device noise in the ansatz design process is necessary. Unfortunately, recent works on ansatz design either consider no noise impact or only treat the real device as a black box with no specific noise information. In this work, we propose to open the black box by designing specific ansatz tailored for the qubit topology on target machines. Specifically, we propose a bottom-up approach to generate topology-specific ansatz. Firstly, we generate topology-compatible sub-circuits with desirable properties such as high expressibility and entangling capability. Then, the sub-circuits are combined together to form an initial ansatz. We further propose circuits stitching to solve the sparse connectivity issue between sub-circuits, and dynamic circuit growing to improve the accuracy. The ansatz constructed with this method is highly flexible and thus we can explore a much larger design space than previous state-of-the-art method in which all ansatz candidates are strict subsets of a pre-defined large ansatz. We use a popular VQA algorithm - Quantum Neural Networks (QNN) for Machine Learning (ML) task as the benchmarks. Experiments on 14 ML tasks show that under the same performance, the TopGen-searched ansatz can reduce the circuit depth and the number of CNOT gates by up to 2 * and 4 * respectively. Experiments on three real quantum machines demonstrate on average 17% accuracy improvements over baselines.