Related papers: Stabilizer Approximation II: From H$_2$O To C$_6$H…
Quantum computers attract much attention as they promise to outperform their classical counterparts in solving certain type of problems. One of them with practical applications in quantum chemistry is simulation of complex quantum systems.…
We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random. Specifically, given an $n$-qubit pure state $|\psi\rangle$, we give an efficient algorithm that distinguishes whether…
The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to…
Reservoir engineering is a powerful technique to autonomously stabilize a quantum state. Traditional schemes involving multi-body states typically function for discrete entangled states. In this work, we enhance the stabilization capability…
How many $\mathrm{H_{2}O}$ molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic…
Estimating the fidelity of state preparation in multi-qubit systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the…
In this work, we use the Born-Oppenheimer approximation where the potential between atoms can be approximated as a function of distance between the two nuclei to study the four-quark bound states. By the approximation, Heitler and London…
Mixtures of quantum fluids, that is gases or liquids, are considered with the emphasis on the conditions characterizing the stability of the mixtures. The mixtures, that can be formed by cold atoms or molecules, are assumed to be quantum…
A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…
Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit…
Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…
We present a simple proof of the stability of the hydrogen molecule $(M^+M^+m^-m^-)$. It does not rely on the proton-to-electron mass ratio $M/m$ being very large, and actually holds for arbitrary values of $M/m$. Some asymmetric molecules…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
Water is essential for life and technological applications, mainly for its unique thermodynamic and dynamic properties, often anomalous or counterintuitive. These anomalies result from the hydrogen-bonds fluctuations, as evidenced by…
Bell sampling is a simple yet powerful tool based on measuring two copies of a quantum state in the Bell basis, and has found applications in a plethora of problems related to stabiliser states and measures of magic. However, it was not…
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that…
Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a high-Q microwave resonator in the ultra-strong dispersive…
This paper builds on the idea of simulating stabiliser circuits through transformations of quadratic form expansions. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing…