In this paper, we generalize the concept of strong quantum nonlocality from two aspects. First, in a tripartite quantum system, we present a construction of strongly nonlocal quantum states containing $6{(d-1)}^2$ orthogonal product states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$ and build $6d^2-8d+4$ product states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^{d+1}$, which have been proved to be strongly nonlocal. Obviously, both results turn out to be one order of magnitude smaller than the number of basis states $d^3$ for $d\ge 3$. Second, we give explicit forms of strongly nonlocal orthogonal product basis in ${\mathbb{C}}^3\otimes {\mathbb{C}}^3\otimes {\mathbb{C}}^3\otimes {\mathbb{C}}^3$ and ${\mathbb{C}}^4\otimes {\mathbb{C}}^4\otimes {\mathbb{C}}^4\otimes {\mathbb{C}}^4$ quantum systems, where four is the largest known number of subsystems in which there exists strong quantum nonlocality without entanglement up to now. All the results positively answer the open problems raised by Halder et al. [ Phys. Rev. Lett. 122, 040403 (2019)]; that is, there do exist a small number of quantum states that can demonstrate strong quantum nonlocality without entanglement.

A controlled-not (cnot) circuit is the key gadget for entangling qubits in quantum computing systems. However, the qubit connectivity of noisy intermediate-scale quantum (NISQ) devices is constrained by their limited-connectivity architecture. To improve the performance of cnot circuits on NISQ devices, we investigate the optimization of the size/depth of cnot circuits under the limited-connectivity architecture. We present a method that can optimize the size of any $n$-qubit cnot circuit $O\left(\frac{n^2}{log\delta }\right)$ on any connected graph with minimum degree $\delta$, and prove this bound is optimal for the regular graph. For the near-term sparsely connected structure, we additionally present a method that can optimize the size of any $n$-qubit cnot circuit to below $2n^2$. The numerical experiment shows that our method performs better than state-of-the-art results. Specifically, we present an example to illustrate the applicability of our algorithm. For the grid structure, which is commonly used in current quantum devices, we demonstrate that the depth of any $n$-qubit cnot circuit can be optimized to be linear in $n$ with certain ancillary qubits (ancillas). Experimental results indicate that this method has significant improvements compared with all of the existing methods. We additionally test our algorithms on the five-qubit IBMQ devices, and the experiments show that the measurement results of the optimized circuit with our algorithm are more robust to noise compared with the IBM mapping method.

We present a necessary condition for two sets of maximally entangled states to be locally equivalent in terms of local invariants. With the help of these invariants, first, we are able to completely classify all the distinguishable and indistinguishable sets of four generalized Bell states in the $4\otimes 4$ quantum system: there are ten inequivalent classes including three locally indistinguishable and seven locally distinguishable quadruples. All distinguishable quadruples in this case can be distinguished by using only one-way classical communication, implying that the two-way classical communication has no advantage over one-way classical communication, similar to the case of qubit lattice states. Second, we are able to completely classify all the triplets of generalized Bell states in the quantum systems of all prime dimensions as well as in some composite dimensions.

In quantum chemistry, the variational quantum eigensolver (VQE) is a promising algorithm for molecular simulations on near-term quantum computers. However, VQEs using hardware-efficient circuits face scaling challenges due to the barren plateau problem. This raises the question of whether chemically inspired circuits from unitary coupled cluster (UCC) methods can avoid this issue. Here we provide theoretical evidence indicating they may not. By examining alternated dUCC ansätzes and relaxed Trotterized UCC ansätzes, we find that in the infinite depth limit, a separation occurs between particle-hole one- and two-body unitary operators. While one-body terms yield a polynomially concentrated energy landscape, adding two-body terms leads to exponential concentration. Numerical simulations support these findings, suggesting that popular 1-step Trotterized unitary coupled-cluster with singles and doubles (UCCSD) ansätze may not scale. Our results emphasize the link between trainability and circuit expressiveness, raising doubts about VQEs’ ability to surpass classical methods.