对于n是偶数个量子比特和v是酉演化，酉群的矩阵分解v=k1 a k2是明确可计算的，并且允许研究并发纠缠单调的动力学。该并发正则分解（CCD）的边因子k1和k2是并发对称的，因此动力学问题归结为对因子a的考虑。在这项工作中，我们提供了一个显式的数值算法计算v=k1 k2为n奇数。此外，在奇数情况下，我们将单调性提升为双参数函数，从而允许奇数量子比特中的并发动力学理论。一般化也可以使用CCD来研究，再次导致大多数酉的最大并发能力。关键的技术是考虑自旋翻转作为一个时间反演对称运营商在维格纳的公理化，原来的CCD推导可以重述完全在这个时间反演。在途中，我们观察到Kramers的非简并性：任何时间反演对称n-量子比特哈密顿量的非简并本征态的存在要求（i）n偶数和（ii）所述本征态的最大并发。我们提供了如何应用这项工作的例子来研究自旋链哈密顿纠缠的运动学和动力学。
英文摘要：
For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers' nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians.
By the standard second law of thermodynamics, heat spontaneously flows from a hotter body to a colder body. However, quantum systems in which quantum correlations play a prominent role can exhibit a non-classical reversal of such heat flow. We propose a quantum system consisting of a chain of qubits, each in local Gibbs states, where only adjacent qubits are allowed to thermally interact. By controlling initial quantum correlations along the chain, we then demonstrate non-classical heat reversal for the special case of a three-qubit chain on a quantum computer. We explore multiple initial cond…
As the number of qubits available on noisy quantum computers grows, it will become necessary to efficiently select a subset of physical qubits to use in a quantum computation. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while r…
Time-Reversal Selection Rules for Quantum Error Correction
Quantum Initiative, Florida State University（佛罗里达州立大学量子倡议）；Department of Mathematics, Florida State University（佛罗里达州立大学数学系）；Department of Mathematics, University of California, San Diego（加州大学圣地亚哥分校数学系）
Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding non-locality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown (Verstraete et.al. {Phys. Rev. A, 64, 010101(R) (2001)) that an arbitrary two-qubit state gets transformed under SLOCC into one of the {\em two} different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other non-diagonal canonical form is obtained for a fam…
Time reversal of complex evolution on a quantum computer
Mindbreeze GmbH（Mindbreeze有限公司）；Basic Research Community for Physics e.V.（基础物理研究社区协会）；Univ Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学、法国国家科学研究中心、理论物理实验室）
Unifying Qubit Routing Across Diverse Quantum ISAs via Canonical Representation
The Hong Kong University of Science and Technology（香港科技大学）；Tsinghua University（清华大学）；Pengcheng Laboratory（鹏城实验室）；The University of Edinburgh（爱丁堡大学）；Leiden University（莱顿大学）；Shenzhen Polytechnic University（深圳职业技术大学）；Fudan University（复旦大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences（上海数学与交叉学科研究院）
In this work, we study quantum many-body teleportation, where a single qubit is teleported through a strongly-interacting quantum system, as a result of a scrambling unitary and local measurements on a few qubits. Usual many-body teleportation protocols require a double copy of the system, and backward time evolution, we demonstrate that teleportation is possible in the 2D spin-$1/2$ XY model, without these constraints. The necessary long-range entanglement for teleportation is generated from the model hosting special eigenstates known as rainbow scars. We outline a specific protocol for prepa…
Complete product-state contact set and optimality of the canonical three-qubit Shifts witness
School of Physics and Electronic Technology, Liaoning Normal University（辽宁师范大学物理与电子科技学院）；Center for Theoretical and Experimental High Energy Physics, Liaoning Normal University（辽宁师范大学理论与实验高能物理中心）
We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length $n$, we show that there exists a constant $ε\approx 0.034$ such that the quantum routing time is at most $(1-ε)n$, whereas any swap-based protocol needs at least time $n-1$. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. …
In condensed matter systems, coherent backscattering and quantum interference in the presence of time-reversal symmetry lead to well-known phenomena such as weak localization (WL) and universal conductance fluctuations (UCF). Here we use multi-pass Landau-Zener transitions at the avoided crossing of a highly-coherent superconducting qubit to emulate these phenomena. The average and standard deviation of the qubit transition rate exhibit a dip and peak when the driving waveform is time-reversal symmetric, analogous to WL and UCF, respectively. The higher coherence of this qubit enabled the real…
In 2008 Coecke and Duncan proposed the graphical ZX-calculus rewrite system which came to formalize reasoning with quantum circuits, measurements and quantum states. The ZX-calculus is sound for qubit quantum mechanics. Hence, equality of diagrams under ZX-equivalent transformations lifts to an equality of corresponding equations over matrices. Conversely, in 2014 Backens proved completeness, establishing that any derivation done in stabilizer quantum mechanics with matrices can be derived graphically using the ZX-calculus. A graphical rewrite system that is both confluent and also terminates …
