With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged as popular approaches to obtain possible quantum advantage in the relatively near future. In particular, how to effectively incorporate the common symmetries in physical systems as hard constraints in VQAs remains a critical and open question. In this paper, we revisit the Hamming Weight (HW) preserving ansatz and establish the links from ansatz to various symmetries and constraints, which both enlarges the usage of HW preserving ansatz and provides a coherent solution for constrained VQAs. Meanwhile, we utilize the quantum optimal control theory and quantum overparameterization theory to analyze the capability and expressivity of HW preserving ansatz and verify these theoretical results on unitary approximation problem. We conduct detailed numerical experiments on two well-studied symmetry-preserving problems, namely ground state energy estimation and feature selection in machine learning. The superior performance demonstrates the efficiency and supremacy of the proposed HW preserving ansatz on constrained VQAs.

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question. In this paper, we manage to combine the Hamming Weight Preserving ansatz with a topological-aware parity check on physical qubits to enforce error mitigation and further hard constraints. We demonstrate the combination significantly outperforms peer VQA methods on both quantum chemistry problems and constrained combinatorial optimization problems e.g. Quadratic Assignment Problem. Intensive experimental results on both simulators and superconducting quantum processors are provided to verify that the combination of HWP ansatz with parity check is among the most promising candidates to demonstrate quantum advantages in the NISQ era to solve more realistic problems.

Automatic quantum architecture search (QAS) has been widely studied across disciplines with different implications. In this paper, beyond a particular domain, we formulate the QAS problem into two basic (and relatively even ideal) tasks: i) arbitrary quantum circuit (QC) regeneration given a target QC; ii) approximating an arbitrary unitary (oracle). The latter can be connected to the setting of various quantum machine learning tasks and other QAS applications. Based on these two tasks, we generate a public QAS benchmark including 900 random QCs and 400 random unitary matrices which is still missing in the literature. We evaluate six baseline algorithms including brute force search, simulated annealing, genetic algorithm, reinforcement learning, hybrid algorithm, and differentiable algorithm as part of our benchmark. One characteristic of our proposed evaluation protocol on the basic tasks is that it deprives the domain-specific designs and techniques as used in existing QAS literature, making a unified evaluation possible and focusing on the vanilla search methods themselves without coupling with domain prior. In fact, the unitary approximation task could be algorithmically more difficult than the specific problems as it needs to explore the whole matrix space to fit the unitary. While specific tasks often only need to fit a partial observation of the unitary as the objective for search. Data and code are available at https://github.com/Lucky-Lance/QAS-Bench.

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era and the fast development of machine learning, variational quantum algorithms (VQA) including Variational Quantum Eigensolver (VQE) and quantum neural network (QNN) have received increasing attention with wide potential applications in foreseeable near future. We study the problem of quantum architecture search (QAS) for VQA to automatically design parameterized quantum circuits (PQC). We devise a differentiable searching algorithm based on Gumbel-Softmax in contrast to peer methods that often require numerous circuit sampling and evaluation. Two versions of our algorithm are provided, namely macro search and micro search, where macro search directly searches for the whole circuit like other literature while the innovative micro search is able to infer the sub-circuit structure from a small-scale and then transfer that to a large-scale problem. We conduct intensive experiments on unweighted Max-Cut, ground state energy estimation, and image classification. The superior performance shows the efficiency and capability of macro search, which requires little prior knowledge. Moreover, the experiments on micro search show the potential of our algorithm for large-scale QAS problems.