We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of $N$ spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, non-uniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor $1.502(1+1/N)$ of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.
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…
We introduce a ${\mathbb Z}_2$-index for time reversal invariant Hamiltonians with unique gapped ground state on quantum spin chains. We show this is an invariant of a $C^1$-classification of gapped Hamiltonians.
Simulation of materials by using quantum processors is envisioned to be a major direction of development in quantum information science. Here we exploit the mathematical analogies between a triangular spin lattice with Dzyaloshinskii-Moriya coupling on one edge and a three-level system driven by three fields in a loop configuation to emulate spin-transport effects. We show that the spin transport efficiency, seen in the three-level system as population transfer, is enhanced when the conditions for superadiabaticity are satisfied. We demonstrate experimentally that phenomena characteristic to s…
A method for high-fidelity quantum state transfer in a quantum network coupled to a continuum, based on time reversal in the continuum after decay, is theoretically suggested. Provided that the energy spectrum of the network is symmetric around a reference energy and symmetric energy states are coupled the same way to the common continuum, ideal perfect state transfer can be obtained after time reversal. In particular, it is shown that in a linear tight-binding chain a quantum state can be transformed into its mirror image with respect to the center of the chain after a controllable time. As c…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly non-invariant with respect to time reversal. We discuss, in particular, the high-energy behavior of such systems and the limiting situations when one of the edges in the elementary cell of such a graph shrinks to zero. The spectrum depends on the topology and geometry of the graph. The probability that an energy belongs to the spectrum takes three different values r…
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths with fixed, different magnetization. We take graded versions of the model, i.e., asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectificatio…
Explicit solution for the 2-point correlation function in a non-equilibrium steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in the Lindblad formulation is provided. A non-equilibrium quantum phase transition from exponentially decaying correlations to long-range order is discussed analytically. In the regime of long-range order a new phenomenon of correlation resonances is reported, where the correlation response of the system is unusually high for certain discrete values of the external bulk parameter, e.g. the magnetic field.
We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. Exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of groundstates occur, associating with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist for the open c…
We investigate the entanglement properties of a one dimensional chain of spin qubits coupled via nearest neighbor interactions. The entanglement measure used is the n-concurrence, which is distinct from other measures on spin chains such as bipartite entanglement in that it can quantify "global" entanglement across the spin chain. Specifically, it computes the overlap of a quantum state with its time-reversed state. As such this measure is well suited to study ground states of spin chain Hamiltonians that are intrinsically time reversal symmetric. We study the robustness of n-concurrence of gr…
We systematically study the non-Hermitian version of the one-dimensional anisotropic XY model, which in its original form, is a unique exactly solvable quantum spin model for understanding the quantum phase transition. The distinguishing features of this model are that it has full real spectrum if all the eigenvectors are intrinsic rotation-time reversal (RT) symmetric rather than parity-time reversal (PT) symmetric, and that its Hermitian counterpart is shown approximately to be an experimentally accessible system, an isotropic XY spin chain with nearest neighbor coupling. Based on the exact …
Commercial quantum annealers from D-Wave Systems make it possible to obtain approximate solutions of high quality for certain NP-hard problems in nearly constant time. Before solving a problem on D-Wave, several pre-processing methods can be applied, one of them being the so-called spin reversal or gauge transform. The spin reversal transform flips the sign of selected variables and coefficients of the Ising or QUBO (quadratic unconstrained binary optimization) representation of the problem that D-Wave minimizes. The spin reversal transform leaves the ground state of the Ising model invariant,…
Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors, and are therefore a major target of research in modern physics. Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation. Of these, platforms with universal quantum control can experimentally access a wide range of physical properties. However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high fide…
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.…
We review recent progress on constructing non-equilibrium steady state density operators of boundary driven locally interacting quantum chains, where driving is implemented via Markovian dissipation channels attached to the chain's ends. We discuss explicit solutions in three different classes of quantum chains, specifically, the paradigmatic (anisotropic) Heisenberg spin-1/2 chain, the Fermi-Hubbard chain, and the Lai-Sutherland spin-1 chain, and discuss universal concepts which characterize these solutions, such as matrix product ansatz and a more structured walking graph state ansatz. The c…
The partial transpose of density matrices in many-body quantum systems, in which one takes the transpose only for a subsystem of the full Hilbert space, has been recognized as a useful tool to diagnose quantum entanglement. It can be used, for example, to define the (logarithmic) negativity. For fermionic systems, it has been known that the partial transpose of Gaussian fermionic density matrices is not Gaussian. In this work, we propose to use partial time-reversal transformation to define (an analog of) the entanglement negativity and related quantities. We demonstrate that for the symmetry-…
We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, and possesses time-reversal symmetry or ${\mathbb Z}_2 \times {\mathbb Z}_2$ symmetry (i.e., the symmetry with respect to the $π$ rotations of spins about the three orthogonal axes). The proof is based on the deep analogy between the matrix product state formulation and the representation of the Cuntz algebra in the von Neumann algebra $π({\mathcal A}_{R})''$ constructed from the ground state restricted to the right h…
We explore an alternative way of finding the link between a PT non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of the scattering problem for an imaginary potential and its time reversal process, it is shown that any real-energy eigenstate of a PT tight-binding lattice with on-site imaginary potentials shares the same wave function with a resonant transmission state of the corresponding Hermitian lattice embedded in a chain. It indicates that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the resonance transmission state of the extended Hermitian Hami…
Symmetry as a route to generalized bosonic Kitaev chains
Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普里茨克分子工程学院）；Université Côte d’Azur, CNRS, Centrale Med, Institut de Physique de Nice（蔚蓝海岸大学、法国国家科学研究中心、中央理工-地中海学院、尼斯物理研究所）
The occurrence of parity-time reversal ($\mathcal{PT}$) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full real spectrum, which occurs if and only if all the eigenvectors are $\mathcal{PT}$ symmetric, can appear only in presence of dimerization, i.e. only if the hopping amplitudes between nearest-neighbor spins assume alternate values along the chain. In order to make a connection between such system and the Hermitian world, we study the critical magnetic properties…
Topological phases are enriched in non-equilibrium open systems effectively described by non-Hermitian Hamiltonians. While several properties unique to non-Hermitian topological systems were uncovered, the fundamental role of symmetry in non-Hermitian physics has yet to be fully understood, and it has remained unclear how symmetry protects non-Hermitian topological phases. Here we show that two fundamental anti-unitary symmetries, time-reversal and particle-hole symmetries, are topologically equivalent in the complex energy plane and hence unified in non-Hermitian physics. A striking consequen…
Spin chains with two Ising symmetries are the Jordan-Wigner duals of one-dimensional interacting fermions with particle-hole and time-reversal symmetry. From earlier works on Majorana chains, it is known that this class of models has 10 distinct topological phases. In this paper, we analyze the physical properties of the correspondent 10 phases of the spin model. In particular, thanks to a set of two non-commuting dualities, we determine the local and non-local order parameters of the phases. We find that 4 phases are topologically protected by the Ising symmetries, while the other 6 break at …
We have developed an efficient computational method to treat long, one-dimensional systems of strongly-interacting atoms forming self-assembled spin chains. Such systems can be used to realize many spin chain model Hamiltonians tunable by the external confining potential. As a concrete demonstration, we consider quantum state transfer in a Heisenberg spin chain and we show how to determine the confining potential in order to obtain nearly-perfect state transfer.
The simplest Tree-Tensor-States (TTS) respecting the Parity and the Time-Reversal symmetries are studied in order to describe the ground states of Long-Ranged Quantum Spin Chains with or without disorder. Explicit formulas are given for the one-point and two-point reduced density matrices that allow to compute any one-spin and two-spin observable. For Hamiltonians containing only one-body and two-body contributions, the energy of the TTS can be then evaluated and minimized in order to obtain the optimal parameters of the TTS. This variational optimization of the TTS parameters is compared with…
Generation of pure spin currents via nonadiabatic quantum pumping in an antiferromagnetic chain
Islamic Azad University（伊斯兰阿扎德大学）；Farhangian University（法尔坎吉安大学）；Imam Khomeini International University（伊玛目霍梅尼国际大学）；Indian Statistical Institute（印度统计研究所）
