J Ceasar Aguma
Using lie algebra, this brief text provides an upper bound on the universality of QAOA. That is, we prove that the upper bound for the number of alterations of QAOA required to approximate a universal gate set is within O(n)
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Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give univer…
It was shown by M.A. Nielsen and I.L. Chuang 1997, that it is impossible to build strictly universal programmable quantum gate array, that could perform any unitary operation precisely and it was suggested to use probabilistic gate arrays instead. In present work is shown, that if to use more physical and weak condition of universality (suggested already in earliest work by D.Deutsch 1985) and to talk about simulation with arbitrary, but finite precision, then it is possible to build universal programmable gate array. But now the same no-go theorem by Nielsen and Chuang will have new interesti…
The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work [S. Lloyd, arXiv:1812.1…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In order to formalize these other forms of computation, while pointing out the role and the necessity of classical control in measurement-based computation, and for establishing a new upper bound of the minimal resources needed to quantum universality, a formal model is introduced by means of Measurement-based Quantum Turing Machines.
Approximate universality and large measurement gain of Rabi model in a linear potential under strong Doppler broadening
本文利用 SU(2) 李群理论和 Fisher 信息理论，推导线形势中 Rabi 模型的 Riccati 方程，证明强多普勒展宽下相位旋转测量协议具有近似普适性和大测量增益，为高灵敏度抗噪声原子重力仪奠定理论基础。
Can quantum-mechanical particles propagating on a fixed spacetime background be approximated as test bodies satisfying the weak equivalence principle? We ultimately answer the question in the negative but find that, when universality of free-fall is assessed locally, a nontrivial agreement between quantum mechanics and the weak equivalence principle exists. Implications for mass sensing by quantum probes are discussed in some details.
We say that collection of $n$-qudit gates is universal if there exists $N_0\geq n$ such that for every $N\geq N_0$ every $N$-qudit unitary operation can be approximated with arbitrary precision by a circuit built from gates of the collection. Our main result is an upper bound on the smallest $N_0$ with the above property. The bound is roughly $d^8 n$, where $d$ is the number of levels of the base system (the '$d$' in the term qu$d$it.) The proof is based on a recent result on invariants of (finite) linear groups.
Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution
本文探讨了多重体投影集合框架在量子机器学习中的普遍性，证明了其能近似任意纯态分布，并提出改进训练的增量MPE方法，通过实验验证了其在复杂量子数据分布学习中的有效性。
The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics. In particular, we will show that rather the definition of heat has to be modified to account for the thermodynamic cost for maintaining coherence and entanglement. Our theoretical findings are numerically illus…
Isolated quantum system in a pure state may be perceived as thermal if only substantially small fraction of all degrees of freedom is probed. We propose that in a chaotic quantum many-body system all states with sufficiently small energy fluctuations are approximately thermal. We refer to this hypothesis as Canonical Universality (CU). The CU hypothesis complements the Eigenstate Thermalization Hypothesis (ETH) which proposes that for chaotic systems individual energy eigenstates are thermal. Integrable and MBL systems do not satisfy CU. We provide theoretical and numerical evidence supporting…
Polynomial-time certification of fidelity for many-body mixed states and mixed-state universality classes
本文提出一种多项式时间算法，用于高效计算许多体混合态的保真度下界和上界，通过变分优化量子电路并提取临界指数，提升量子系统验证的精度。
We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of programmable quantum processors based on (1) the C-NOT gate, (2) the SWAP operation, and (3) the model of the quantum information distributor - the QID processor. We show under which conditions the measurement assisted QID processor is optimal. We also investigate optimality of the so-called U-processors and we also compare the optimal approximative implementation o…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In order to formalize these other forms of computation, while pointing out the role and the necessity of classical control in measurement-based computation, and for establishing a new upper bound of the minimal resources needed to quantum universality, a formal model is introduced by means of Measurement-based Quantum Turing Machines.
Universality and weak-ergodicity breaking in quantum quenches
针对量子猝灭后孤立多体系统的平衡化与普适性问题，研究人员以大n极限下的量子O(n)模型为对象，通过映射到可积Neumann系统并推导新作用量-角描述，解释了表观异常的起源，明确了热普适类的恢复区域及振荡消失的极限情况。
We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the ``…
We provide two simple universality criteria. Our first criterion states that $\mathcal{S}\subset G_d:=U(d)$ is universal if and only if $\mathcal{S}$ forms a $δ$-approximate $t(d)$-design, where $t(2)=6$ and $t(d)=4$ for $d\geq3$. Our second universality criterion says that $\mathcal{S}\subset G_d$ is universal if and only if the centralizer of $\mathcal{S}^{t(d),t(d)}=\{U^{\otimes t(d)}\otimes \bar{U}^{\otimes t(d)}|U\in \mathcal{S}\}$ is equal to the centralizer of $G_d^{t(d),t(d)}=\{U^{\otimes t(d)}\otimes \bar{U}^{\otimes t(d)}|U\in G_d\}$, where $t(2)=3$, and $t(d)=2$ for $d\geq 3$. The e…
We show that the existence of a minimum measurable length and the related Generalized Uncertainty Principle (GUP), predicted by theories of Quantum Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb Shift, the Landau levels and the tunnelling current in a Scanning Tunnelling Microscope (STM). We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the qu…
Emergent random matrix universality in quantum operator dynamics
本文通过递归方法证明了量子算子动力学中快模式的动力学具有随机矩阵普遍性，揭示了谱函数近似方法与库仑气体优化的联系。
We recently showed [Phys. Rev. Lett. 121, 220602 (2018)] that the average bipartite entanglement entropy of all energy eigenstates of the quantum Ising chain exhibits a universal (for translationally invariant quadratic fermionic models) leading term that scales linearly with the subsystem's volume, while in the thermodynamic limit the first subleading correction does not vanish at the critical field (it only depends on the ratio $f$ between the volume of the subsystem and volume of the system) and vanishes otherwise. Here we show, analytically for bounds and numerically for averages, that the…
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