arXiv subjects

Chengsi Mao

Publications and source records attributed to Chengsi Mao.

3 recordsLinked to original sources

arXiv2026

A reduction scheme for general-order Ising-like Hamiltonians in quantum heuristic solvers

The Ising model is ubiquitous in various optimization problems but notoriously difficult to solve due to combinatorial explosion. In view of this, Hamiltonian reduction is a useful preprocessing technique for reducing the effective problem size before applying heuristic solvers. However, existing reduction techniques mainly target second-order Ising models, whereas many pseudo-Boolean formulations naturally contain higher-order interactions. In this work, we generalize the concept of non-separable groups to arbitrary-order Ising-like models and develop a Hamiltonian reduction framework that iteratively detects and merges constrained spin groups into single variables. We benchmark the reduction on synthetic hypergraphs and higher-order network datasets, and evaluate its integration with downstream order-reduction and solver workflows. Our results establish a foundation for Hamiltonian reduction in higher-order Ising-like optimization problems.

quant-ph↗

arXiv2024

Third moments of qudit Clifford orbits and 3-designs based on magic orbits

When the local dimension $d$ is an odd prime, the qudit Clifford group is only a 2-design, but not a 3-design, unlike the qubit counterpart. This distinction and its extension to Clifford orbits have profound implications for many applications in quantum information processing. In this work we systematically delve into general qudit Clifford orbits with a focus on the third moments and potential applications in shadow estimation. First, we introduce the shadow norm to quantify the deviations of Clifford orbits from 3-designs and clarify its properties. Then, we show that the third normalized frame potential and shadow norm are both $\mathcal{O}(d)$ for any Clifford orbit, including the orbit of stabilizer states, although the operator norm of the third normalized moment operator may increase exponentially with the number $n$ of qudits when $d\neq 2\mod 3$. Moreover, we prove that the shadow norm of any magic orbit is upper bounded by the constant $15/2$, so a single magic gate can already eliminate the $\mathcal{O}(d)$ overhead in qudit shadow estimation and bridge the gap between qudit systems and qubit systems. Furthermore, we propose simple recipes for constructing approximate and exact 3-designs (with respect to three figures of merit simultaneously) from one or a few Clifford orbits. Notably, accurate approximate 3-designs can be constructed from only two Clifford orbits. For an infinite family of local dimensions, exact 3-designs can be constructed from two or four Clifford orbits. In the course of study, we clarify the key properties of the commutant of the third Clifford tensor power and the underlying mathematical structures.

quant-ph↗

arXiv2024

Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate

Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here we clarify the sample complexity of qudit shadow estimation based on the Clifford group, where the local dimension $d$ is an odd prime. Notably, we show that the overhead of qudit shadow estimation over the qubit counterpart is only $\mathcal{O}(d)$, independent of the qudit number $n$, although the set of stabilizer states may deviate exponentially from a 3-design with respect to the third moment operator. Furthermore, by adding one layer of magic gates, we propose a simple circuit that can significantly boost the efficiency. Actually, a single magic gate can already eliminate the $\mathcal{O}(d)$ overhead in qudit shadow estimation and bridge the gap from the qubit setting.

quant-ph↗