Fedor Herbut
It is pointed out that the question of a purely unitary quantum dynamics amounts to the question if von Neumann entropy of a dynamically closed quantum system is preserved in evolution.
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A purely Quantum Generative Modeling through Unitary Scrambling and Collapse
针对现有量子生成模型受经典组件限制的问题，提出纯量子范式QGen，通过置乱与坍缩过程实现生成，结合基于测量的训练缓解贫瘠高原，在匹配参数预算下性能优于经典和混合基线，适配近期量子硬件。
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by time-dependent external fields. The S-matrix of the cycle is obtained in analytic form. The total number of quanta contained in the system is a conserved quantity. As a consequence the spectrum of the S-matrix is purely discrete and the evolution of the system is quasi-periodic.
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological an…
Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories
本文提出由量子记忆相互作用驱动的酉演化框架，通过非局域非线性方程实现系统自我引导，并分类了丰富的相图与相变行为。
We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: The target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set o…
Experimental Approaches to Distinguishing Quantum Collapse from Unitary Evolution: A Weak Measurement Perspective
本文提出利用弱测量和无意识观察者概念，通过干涉图样区分量子坍缩与幺正演化解释的实验方法。
Shallow Unitary Circuits for Kramers-Wannier Dualities
构建对数深度非局域幺正电路，精确实现一维和二维Z_2及Z_n Kramers-Wannier对偶，将短程纠缠态映射为长程纠缠态，为量子平台研究相变和拓扑对偶提供高效相干路径。
This report continues the discussion of unitary error bases and quantum codes begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases are characterized in terms of the existence of certain characters in a group. A general construction for error bases which are non-abelian over the center is given. The method for obtaining codes due to Calderbank et al. is generalized and expressed purely in representation theoretic terms. The significance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated.
Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dim…
It is generally believed that unconditionally secure quantum bit commitment (QBC) is proven impossible by a "no-go theorem". We point out that the theorem only establishes the existence of a cheating unitary transformation in any QBC scheme secure against the receiver, but this fact alone is not sufficient to rule out unconditionally secure QBC as a matter of principle, because there exists no proof that the cheating unitary transformation must be known to the cheater in all possible cases. In this work, we show how to circumvent the "no-go theorem" and prove that unconditionally secure QBC is…
Implementation of CU gates and its application in a remote-controlled quantum operation
本文提出并实验演示了利用单光子偏振和时间箱自由度实现任意酉门对之间的受控酉（CU）门方案，并以此实现高保真度的远程控制单量子比特酉门，为安全高效的量子信息处理铺平道路。
Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth
该研究证明浅深度下通过共享经典随机性可实现量子生成模型中幺正与信道模型的严格可扩展表征分离，MBQC可自然实现所需随机性，数值实验验证了分析结果。
The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brach…
Granthi: Higher-Order Quantum Programming via Unitary Wiring
本文提出纯酉高阶量子编程语言Granthi，基于三项设计承诺实现量子程序的高阶特性，可将良型项编译为量子电路，支持量子开关等功能。
Over the last decade, Quantum Computing hardware has rapidly developed and become a very intriguing, promising, and active research field among scientists worldwide. To achieve the desired quantum functionalities, quantum algorithms require translation from a high-level description to a machine-specific physical operation sequence. In contrast to classical compilers, state-of-the-art quantum compilers are in their infancy. We believe there is a research need for a quantum compiler that can deal with generic unitary operators and generate basic unitary operations according to quantum machines' …
We introduce a method for analyzing ground state properties of quantum many body systems, based on the characterization of separability and entanglement by single subsystem unitary operations. We apply the method to the study of the ground state structure of several interacting spin-1/2 models, described by Hamiltonians with different degrees of symmetry. We show that the approach based on single qubit unitary operations allows to introduce {\it ``entanglement excitation energies''}, a set of observables that can characterize ground state properties, including the quantification of single-site…
We consider an open bipartite quantum system with dissipative Lindblad type dynamics. In order to study the entanglement of the stationary states, we develop a perturbative approach and apply it to the physically significant case when a purely dissipative perturbation is added to the unperturbed generator which by itself would produce reversible unitary dynamics.
A purely imaginary potential can provide a phenomenological description of creation and absorption of quantum mechanical particles. PT-invariance of such a potential ensures that the non-unitary phenomena occur in a balanced manner. In spite of wells and sinks which locally violate the conservation of quantum probability, there is no net get loss or gain of particles. This, in turn, is intuitively consistent with real energy eigenvalues.
Quantum RNNs and LSTMs Through Entangling and Disentangling Power of Unitary Transformations
本文提出利用幺正变换的纠缠与解纠缠能力构建量子递归神经网络及长短期记忆网络框架，将纠缠解释为信息保留机制，解纠缠解释为遗忘机制，从而提升优化过程的效率。
In quantum zero knowledge, the assumption was made that the verifier is only using unitary operations. Under this assumption, many nice properties have been shown about quantum zero knowledge, including the fact that Honest-Verifier Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier Quantum Statistical Zero Knowledge (QSZK) (see [Wat02,Wat06]). In this paper, we study what happens when we allow an honest verifier to flip some coins in addition to using unitary operations. Flipping a coin is a non-unitary operation but doesn't seem at first to enhance the cheating possibi…
Quantum Dissipative Search via Lindbladians
本文通过 Lindblad 主方程分析纯耗散量子随机游走在无结构搜索空间中的收敛性，证明 OQRW 并不优于经典搜索，并利用低实现成本的耗散基态制备算法揭示相干性对二次加速的关键作用。
We show that a single-mode squeeze operator S(z) being an unitary operator with a purely continuous spectrum gives rise to a family of discrete real generalized eigenvalues. These eigenvalues are closely related to the spectral properties of S(z) and the corresponding generalized eigenvectors may be interpreted as resonant states well known in the scattering theory. It turns out that these states entirely characterize the action of S(z). This result is then generalized to N-mode squeezing.
Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
本文研究幺正动力学对纯耗散开放量子多体系统时间尺度层级的影响，发现强耗散下两体相互作用的谱特征稳健，弱耗散下谱簇对应哈密顿量局域对称性。
Adaptive quantum circuits employ unitary gates assisted by mid-circuit measurement, classical computation on the measurement outcome, and the conditional application of future unitary gates based on the result of the classical computation. In this paper, we experimentally demonstrate that even a noisy adaptive quantum circuit of constant depth can achieve a task that is impossible for any purely unitary quantum circuit of identical depth: the preparation of long-range entangled topological states with high fidelity. We prepare a particular toric code ground state with fidelity of at least $76.…
Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is purely algebraic, in terms of the coefficients of the equation. In a second part, we consider general quantum Langevin equations and we prove that they can always be split into a maximal part driven by classical noises and a purely quantum one.
Starting with unitary quantum dynamics, we investigate how to add quantum measurements. Quantum measurements have four essential components: the furcation, the witness production, an alignment projection, and the actual choice decision. The first two components still lie in the domain of unitary quantum dynamics. The decoherence concept explains the third contribution. It can be based on the requirement that witnesses reaching the end of time on the wave function side and the conjugate one have to be identical. In this way, it also stays within the quantum dynamics domain. The surjection hypot…
To guarantee the normal functioning of quantum devices in different scenarios, appropriate benchmarking tool kits are quite significant. Inspired by the recent progress on quantum state verification, here we establish a general framework of verifying a target unitary gate. In both the non-adversarial and adversarial scenarios, we provide efficient methods to evaluate the performance of verification strategies for any qudit unitary gate. Furthermore, we figure out the optimal strategy and its realization with local operations. Specifically, for the commonly-used quantum gates like single qubit …
Two-particle Hadamard walk on dynamically percolated line and circle
本文研究了双粒子在动态渗流线与圆上的Hadamard行走的渐近动力学，构建了随机酉演化吸引子空间的基并证明其完备性，发现共享渗流图能作为弱相互作用使初始不相关粒子产生关联。
Smearing of dynamical quantum phase transitions in dissipative free-fermion systems
研究耗散二次费米子系统中约化洛施密特回声的李布兰德动力学，探讨非解析性在RLE时间演化中的持续性，揭示在纯增益或纯损耗过程下非解析性可存活，但两者同时存在时会被弥散。
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably normalized vectors belonging to the two-complex-dimensional spaces that occur in local orthogonal decompositions of isomorphic copies of Cartan's space. The corresponding dynamical variables thus show up as bounded pseudo-Hermitian operator restrictions that possess real discrete spectra. Any measurement processes have to be performed locally in orthocronous p…
Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics
本文提出了一种基于Weyl有序KvN生成器和求和-按部分离散化的方案，用于在量子计算机上实现流体和等离子体动力学的精确模拟，通过证明离散幺正性来克服网格分辨率的限制。
Materials Beyond Hamiltonian Limits -- Quantum Measurement as a Resource for Material Design
研究探讨了量子测量作为动力学元素的电子动力学基础，揭示了非递归单电子传输、新型磁性材料及超越卡诺极限的能量转换平台。
Non-unitary enhanced transfer efficiency in quantum walk search on complex networks
本文通过在搜索图中添加陷阱顶点，研究混合经典-量子游走的传输效率，发现非酉动力学可增强或降低传输，取决于拓扑和参数，并关联熵衰减率。
Depth-1 expanders on the unitary group and applications
该研究构造了深度1的量子扩展器及酉群上的对应扩展器，将其应用于无挫折哈密顿量、纠缠态检测协议，改进了Bourgain等人关于酉群带间隙游走的前期工作。
Permissible extensions of classical to quantum games combining three strategies
本文研究在每位参与者的两个经典策略外加入一个幺正策略以构造量子博弈，给出保持同构不变性的条件，并据此将囚徒困境扩展为具有更接近帕累托最优的唯一纳什均衡的量子博弈。
We study a class of (1+1)D symmetric random quantum circuits with two competing types of measurements in addition to random unitary dynamics. The circuit exhibits a rich phase diagram involving robust symmetry-protected topological (SPT), trivial, and volume law entangled phases, where the transitions are hidden to expectation values of operators and can only be accessed through the entanglement entropy averaged over quantum trajectories. In the absence of unitary dynamics, we find a purely measurement-induced critical point with logarithmic scaling of the entanglement entropy, which we map ex…
Geometric Complexity of Quantum Channels via Unitary Dilations
本文提出了一种基于幺正扩张的量子通道几何复杂性度量方法，区分了实现依赖性和内在复杂性，并建立了噪声复杂性度量及多种理论边界。
Derivatives of Quantum Randomness: Separating Pseudorandom Unitaries from Pseudorandom (Function-like) States
本文通过研究候选PRU构造映射的导数低秩性，在量子预言机模型下证明了PRFSG不蕴含PRU，揭示了量子态与酉算子伪随机性的根本区别。
We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform some basic analysis of this black box system and show that it is resistant to black box attacks. In order to instantiate this protocol, one needs to find a cryptographically complicated system of computable, commuting, unitary operators. To fill this need, we propose using Brandt operators acting on the Brandt modules associated to certain quaternion algebras. We explain why we believe this instantiation is likely to…
Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
本文研究了非厄米特量子动力学在量子计算中的可扩展性，证明了非厄米特动力学模型在计算复杂性上的强大能力，但指出其效率受限于后选择概率。
Critical behaviors of magic and participation entropy at measurement induced phase transitions
研究非单位ary量子电路动力学中参与熵和稳定子熵的临界行为，发现其饱和时间与系统规模线性相关，与纯单位ary动力学不同。
We find for the unitary evolution of spin-1/2 systems that the "purely mathematical mixed state holonomy of Uhlmann limitedly agrees, in the case of evolution over geodesic spherical triangles, with the holonomy "in the experimental context of quantum interferometry" recently proposed by Sjoqvist, Pati, Ekert, Anandan, Ericsson, Oi and Vedral (Phys. Rev. Lett. 85 [2000], 2845-2848).
Recent theoretical work has shown that the competition between coherent unitary dynamics and stochastic measurements, performed by the environment, along wavefunction trajectories can give rise to transitions in the entanglement scaling. In this work, complementary to these previous studies, we analyze a situation where the role of Hamiltonian and dissipative dynamics is reversed. We consider an engineered dissipation, which stabilizes an entangled phase of a quantum spin$-1/2$ chain, while competing single-particle or interacting Hamiltonian dynamics induce a disentangled phase. Focusing on t…
Geometric Measures of Complexity for Open and Closed Quantum Systems
针对非幺正量子动力学难以用李群几何刻画的问题，本文扩展 Nielsen 的几何复杂性理论，为一类通用量子信道提出几何复杂性定义并加以分析。
Quantum versus classical $P$-divisibility
针对经典与量子非马尔可夫过程中的$P$-可分性，研究揭示量子生成器的$P$-可分性与经典约化的可分性等价，但动力学映射约化时该等价性失效，还阐释了纯耗散及正交协变量子比特动力学中量子与经典$P$-可分性的关系及信息回流机制。
After stating the measurement problem, physicists usually assume the problem to be coming from the measurement part. Since classical probabilities also collapse when updating information, there is nothing special about quantum state collapse. I believe the problem comes from the unitary evolution part of quantum theory. The question we should be asking is not 'what happens during measurement?' but 'what is time?'. After discussing the problems with time evolution in quantum theory, we propose a new approach to interpret time and argue how it would emerge from the non-commutativity of quantum t…
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