Universal protection of unitary evolution from slow noise: dynamical control pushed to the extreme

Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems

Non-Hermitian degeneracies are classified as defective and nondefective exceptional points~(EP). While in defective EPs, both eigenvalues and eigenenergies coalesce, nondefective EPs are characterized merely by the occurrence of degeneracies in their eigenvalues. It is also known that all degeneracies are either symmetry-protected or accidental. In this paper, I prove that anti-unitary symmetries protect all nondefective twofold EPs. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries are composite of various symmetry operations such as discrete or s…

Faster Digital Quantum Simulation by Symmetry Protection

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular,…

Rydberg铷同位素中量子Zeno效应和非完整控制的相干保护

Coherence protection by the quantum Zeno effect and non-holonomic control in a Rydberg Rubidium isotope

保护开放量子系统的相干性不受其环境的影响是一个非常热门的问题。本文提出了一种方案，它保护一般量子系统不受任意不受控制的幺正演化的作用。该方法的灵感来自于标准纠错（附加、编码和解码）和量子芝诺效应的思想。我们的方法在一个简单的原子系统，即铷同位素的教学示范，提出。

Non-Abelian Berry phase for open quantum systems: Topological protection vs geometric dephasing

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space. For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths. We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator. This operator plays a key role in all experimental protoco…

Protection of quantum systems by nested dynamical decoupling

Based on a theorem we establish on dynamical decoupling of time-dependent systems, we present a scheme of nested Uhrig dynamical decoupling (NUDD) to protect multi-qubit systems in generic quantum baths to arbitrary decoupling orders, using only single-qubit operations. The number of control pulses in NUDD increases polynomially with the decoupling order. For general multi-level systems, this scheme can preserve a set of unitary Hermitian system operators which mutually either commute or anti-commute, and hence all operators in the Lie algebra generated from this set of operators, generating a…

两味施温格模型变分量子模拟中可表达性、对称性保护与硬件噪声的分离

Disentangling Expressibility, Symmetry Protection, and Hardware Noise in Variational Quantum Simulation of the Two-Flavor Schwinger Model

该研究将两味施温格模型的变分量子模拟从N=2扩展到6个格点，发现硬件噪声是主要限制，并确定N=3为可行扩展；同时给出可表达性条件，并揭示电荷守恒对可训练性的保护及噪声模型对跃迁退化的决定性作用。