Experimental Hamiltonian Learning of an 11-Qubit Solid-State Quantum Spin Register

Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates.However,it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size.Here,we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond.We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment.Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms,and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.     

串型耦合双量子点处于自旋阻塞区时磁输运性质的研究

使用双杂质安德森模型的哈密顿量,从理论上研究了串型耦合双量子点系统处于自旋阻塞区时的磁输运性质,并用主方程近似方法求解了哈密顿量.结果表明,自旋轨道耦合作用导致的双量子点间的自旋反转隧穿能够解除系统的自旋阻塞.同时也研究了超精细相互作用导致的在量子点内自旋反转和双量子点之间的自旋关联对系统的磁输运性质的影响,取得了一些有价值的结果,并对相关的物理问题进行了讨论.     

AB效应对自旋多端输运的影响

利用紧束缚近似和格林函数方法,研究了AB效应和AB环对电子自旋输运的影响.计算表明,当在AB环的不同位置上连接相同或不同属性的输出端时,在一些能量范围内,由不同的输出端所输出的自旋流的方向是相反的;当固定入射电子的能量时,在同一磁通范围,从两个输出端输出的自旋流属性也是相反的.从而,可以通过控制AB环的结构和环内的磁通在输出端得到不同属性的自旋流. 关键词： 自旋极化输运 量子点 极化率 自旋流     

Spin-polarized quantum transport through an Aharonov--Bohm quantum-dot-ring

In this paper the quantum transport through an Aharonov--Bohm (AB) quantum-dot-ring with two dot-array arms described by a single-band tight-binding Hamiltonian is investigated in the presence of additional magnetic fields applied to the dot-array arms to produce spin flip of electrons. A far richer interference pattern than that in the charge transport alone is found. Besides the usual AB oscillation the tunable spin polarization of the current by the magnetic flux is a new observation and is seen to be particularly useful in technical applications. The spectrum of transmission probability is modulated by the quantum dot numbers on the up-arc and down-arc of the ring, which, however, does not affect the period of the AB oscillation.     

Spin-Polarized Transport through the T-Shaped Double Quantum Dots with Fano-Kondo Interaction

We theoretically investigate the spin-polarized transport properties of the T-shaped double quantum dots coupled to two ferromagnetic leads by the Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. We calculate the density of states and the liner conductance in this system with both parallel and antiparallel lead-polarization alignments, and our results show that the transport properties of this system depend on both the tunnelling strength between the two dots and the spin-polarized strength p. This system is a possible candidate for spin valve transistors in the spintronics.     

Robust quantum state transfer in random unpolarized spin chains

We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling-strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over an arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between nitrogen-vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed.     

Effective spin dephasing mechanism in confined two-dimensional topological insulators

A Kramers pair of helical edge states in quantum spin Hall effect (QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles of two-dimensional (2D) QSHE, which is simulated as quantum dots modeled by 2D massive Dirac Hamiltonian. We demonstrate that the spin dephasing effect can originate from the combination of the Rashba spin-orbit coupling and electron-phonon interaction, which gives rise to inelastic backscattering in edge states within the topological insulator quantum dots, although the time-reversal symmetry is preserved throughout. Finally, we discuss the tunneling between extended helical edge states and local edge states in the QSH quantum dots, which leads to backscattering in the extended edge states. These results can explain the more robust edge transport in InAs/GaSb QSH systems.     

Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki’s proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain (Prosen, in Phys Rev Lett 106:217206, 2011).     

Quantum simulation of classical thermal states

We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum state such that the reduced density operator behaves as the thermal state of the classical system. We show that all these quantum states are unique ground states of a universal 5-body local quantum Hamiltonian acting on a (polynomially enlarged) qubit system on a 2D lattice. The only free parameters of the quantum Hamiltonian are coupling strengths of two-body interactions, which allow one to choose the type and dimension of the classical model as well as the interaction strength and temperature. This opens the possibility to study and simulate classical spin models in arbitrary dimension using a 2D quantum system.     

可控磁性量子点杂质引起的单电子自旋过滤器

本文提出一种基于电子-电子自旋交换相互作用获得自旋极化电流的模型.该方案中,需要两个距离相近的量子点.其中一个是开放系统,另一个是封闭系统.开放系统能完成单电子输运,封闭系统产生比较强的局域磁场,两个系统之间有电子-电子自旋交换相互作用.该相互作用会影响电子输运,从而可以对电子输运产生自旋过滤效应.我们用量子主方程描述开放系统的演化,在有效哈密顿量的基础上,可以得到解析结果.结果显示,在低温条件下,交换相互作用足够强的时候,系统给出的自旋过滤效率接近1.     

Spin-polarization-dependent transport in a quantum dot array coupled with an Aharonov-Bohm ring

In this paper the quantum transport in a dot-array coupled with an Aharonov–Bohm (AB) ring is investigated via single-band tight-binding Hamiltonian. It is shown that the output spin current is a periodic function of the magnetic flux in the quantum unit Φ₀. The resonance positions of the total transmission probability do not depend on the size of the AB ring but the electronic spectrum. Moreover, the persistent currents in the AB ring is also spin-polarization dependent and different from the isolated AB ring where the persistent current is independent of spin polarization.     

Quantum mechanical hamiltonian models of turing machines

Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.     

Essential Self-Adjointness of¶Translation-Invariant Quantum Field Models¶for Arbitrary Coupling Constants

The Hamiltonian of a system of quantum particles minimally coupled to a quantum field is considered for arbitrary coupling constants. The Hamiltonian has a translation invariant part. By means of functional integral representations the existence of an invariant domain under the action of the heat semigroup generated by a self-adjoint extension of the translation invariant part is shown. With a non-perturbative approach it is proved that the Hamiltonian is essentially self-adjoint on a domain. A typical example is the Pauli–Fierz model with spin 1/2 in nonrelativistic quantum electrodynamics for arbitrary coupling constants. Received: 26 May 1999 / Accepted: 9 November 1999     

Quantum decoration transformation for spin models

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.     

Sublattice addressing and spin-dependent motion of atoms in a double-well lattice

We load atoms into every site of an optical lattice and selectively spin flip atoms in a sublattice consisting of every other site. These selected atoms are separated from their unselected neighbors by less than an optical wavelength. We also show spin-dependent transport, where atomic wave packets are coherently separated into adjacent sites according to their internal state. These tools should be useful for quantum information processing and quantum simulation of lattice models with neutral atoms.     

A generalized Laplace formula

Asymptotic expansions have long found utility in quantum field theoretical studies of statistical mechanics. In this context a generalized Laplace formula is discussed and the technique is illustrated by applying it to a simple quantum Hamiltonian spin system.     

An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains

The quantum evolution equation of Loop Quantum Cosmology (LQC)—the quantum Hamiltonian constraint—is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schrödinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.     

Continuous weak measurement and nonlinear dynamics in a cold spin ensemble

A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a nonperturbing measurement on the much longer time scale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.     

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter J a = J b, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase.