We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in [E. Farhi, et al., arXiv:quant-ph/0208135]. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H(τ) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2.
We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H(τ) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield the same fidelity as their adiabatic counterparts, but on fast timescales. In particular, we consider a charged particle in a system of three tunnel-coupled quantum wells, where the presence of a magnetic field can induce a geometric phase during the tunnelling processes. We show that this leads to the appearance of complex tunnelling amplitudes and allows for…
The hydrogen bond is usually described within the clamped nucleus approximation in which electronic and vibrational motions are considered separately. This approach leads to a double-well potential which facilitates proton tunnelling. In this work, the hydrogen bond is described by a formalism based on the non-adiabatic Hamiltonian in which electronic and vibrational motions are coupled. Quasi-degeneracy associated with the hydrogen bond supports this approach which is shown to afford an alternative picture of proton tunnelling.
We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double-well. Assuming fixed inter-well tunnelling rate and intra-well interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunnelling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings (CALC), we extend the realm of full controllability to a…
Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunnelling splitting of energy levels is reduced to constructing the perturbatio n series with degeneracy, the order of degeneracy being proportional to a spin value. Partial summation of this series taking into account ''dangerous terms'' with small denominators is performed and the value of tunnelling splitting is calculated with allowance for the first correction with respect to a magnetic field.
We discuss dynamics of approximate adiabatic invariants in several nonlinear models being related to physics of Bose-Einstein condensates (BEC). We show that nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunnelling, and BEC tunnelling oscillations in a double-well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive ex…
We investigate the dynamics following a global parameter quench for two 1D models with variable-range power-law interactions: a long-range transverse Ising model, which has recently been realised in chains of trapped ions, and a long-range lattice model for spinless fermions with long-range tunnelling. For the transverse Ising model, the spreading of correlations and growth of entanglement are computed using numerical matrix product state techniques, and are compared with exact solutions for the fermionic tunnelling model. We identify transitions between regimes with and without an apparent li…
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective…
Silicon spin qubits are promising candidates for realising large scale quantum processors, benefitting from a magnetically quiet host material and the prospects of leveraging the mature silicon device fabrication industry. We report the measurement of an electron spin in a singly-occupied gate-defined quantum dot, fabricated using CMOS compatible processes at the 300 mm wafer scale. For readout, we employ spin-dependent tunneling combined with a low-footprint single-lead quantum dot charge sensor, measured using radiofrequency gate reflectometry. We demonstrate spin readout in two devices usin…
Efficient quantum-state transfer is achieved in a uniformly coupled spin-1/2 chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective \textit{barriers} induce appearance of two eigenstates, bi-localized at the edges of the chain, which allow a high quality transfer also at relatively long distances. The same mechanism may be used to send an entire e-bit (e.g., an entangled qubit pair) from one to the other end of the chain.
A nano-rod under compression, which is capacitively coupled to a Cooper-pair box, can be modeled in terms of a quartic oscillator linearly interacting with a tunnelling pseudo-spin. We have integrated numerically the quantum dynamics of this system in the partial Wigner representation and calculated the pseudo-spin population difference. Depending on the coupling, we have verified that the quantum tunnelling of the oscillator can lead to a more effective reduction of the Rabi oscillation amplitude of the pseudo-spin. Such findings suggests an experimental set-up that might be able to discrimin…
Adiabatic processes in the quantum Ising model and the anisotropic Heisenberg model are discussed. The adiabatic processes are assumed to consist in the slow variation of the strength of the magnetic field that environs the spin-systems. These processes are of current interest in the treatment of cold atoms in optical lattices and in Adiabatic Quantum Computation. We determine the probability that, during an adiabatic passage starting from the ground state, states with higher energy are excited.
We discussed a method to accelerate an adiabatic quantum dynamics of XY spin model by using the fast-forward method proposed by Masuda and Nakamura. The Accelerated scheme is constructed by adding the driving Hamiltonian to the original Hamiltonian and speeding it up with a large time-scaling factor and an adiabatic parameter that realizes adiabatic quantum dynamics in a shortened time. Accelerated adiabatic dynamics start by assuming the candidate of driving Hamiltonian consists of the pair-wise exchange interaction and magnetic field. The driving Hamiltonian terms multiplied by the velocity …
We report the existence of a sizeable quantum tunnelling splitting between the two lowest electronic spin levels of mononuclear Ni complexes. The level anti-crossing, or magnetic clock transition, associated with this gap has been directly monitored by heat capacity experiments. The comparison of these results with those obtained for a Co derivative, for which tunnelling is forbidden by symmetry, shows that the clock transition leads to an effective suppression of intermolecular spin-spin interactions. In addition, we show that the quantum tunnelling splitting admits a chemical tuning via the …
The problem of spin precession in a time-dependent magnetic field is considered in the adiabatic approximation where the field direction or the angular velocity of its rotation is changing slowly. The precession angles are given by integrals in a way similar to the semi-classical approximation for the Schrödinger equation.
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. By far, there is no experimental realization of adiabatic quantum computation on a single solid spin system under ambient conditions, which has been proved to be a compatible candidate for scalable quantum computation. In this letter, we report on the first experimental realization of an adiab…
The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins aro…
Many schemes to realize quantum state transfer in spin chains are not robust to random fluctuations in the spin-spin coupling strength. In efforts to achieve robust quantum state transfer, an adiabatic quantum population transfer scheme is proposed in this study. The proposed scheme makes use of a slowly moving external parabolic potential and is qualitatively explained in terms of the adiabatic following of a quantum state with a moving separatrix structure in the classical phase space of a pendulum analogy. Detailed aspects of our adiabatic population transfer scheme, including its robustnes…
We study the entanglement emergence in a dipolar-coupled nuclear spin-1/2 system cooled using the adiabatic demagnetization technique. The unexpected behavior of entanglement for the next- and next-next-neighbor spins is revealed: entangled states of a spin system appear in two distinct temperature and magnetic field regions separated by a zero-concurrence area. The magnetic field dependence of the concurrence can have two maximums which positions are determined by the initial conditions and number of spins in a chain.
We study a single two-level system coupled resonantly to an oscillator mode or a large spin. By adiabatically turning on a linear driving term on the oscillator or the spin, the eigenstates of the system change character and its ground state evolves into squeezed states of the oscillator or the spin. The robust generation of such states is of interest in many experimental systems with applications for sensing and quantum information processing.
We show that the optical absorbance detection of nuclear spin echo gives direct access to the spin concentration, unlike most coherent signal detection techniques where the signal intensity/amplitude is difficult to connect experimentally with the spin concentration. This way we measure the spin refocusing efficiency in a crystal of Tm$^{3+}$:YAG. Given the large inhomogeneous broadening of the spin transition in this material, rephasing the spins with the usual hard pulse procedure would require excessively high radiofrequency power. Instead we resort to an adiabatic pulse sequence that perfe…
In previous implementations of adiabatic quantum algorithms using spin systems, the average Hamiltonian method with Trotter's formula was conventionally adopted to generate an effective instantaneous Hamiltonian that simulates an adiabatic passage. However, this approach had issues with the precision of the effective Hamiltonian and with the adiabaticity of the evolution. In order to address these, we here propose and experimentally demonstrate a novel scheme for adiabatic quantum computation by using the intrinsic Hamiltonian of a realistic spin system to represent the problem Hamiltonian whi…
We propose a method for quantum state transfer in spin chains using an adiabatic passage technique. Modifying even and odd nearest-neighbour couplings in time allows to achieve transfer fidelities arbitrarily close to one, without the need for a precise control of coupling strengths and timing. We study in detail transfer by adiabatic passage in a spin-1 chain governed by a generalized Heisenberg Hamiltonian. We consider optimization of the transfer process applying optimal control techniques. We discuss a realistic experimental implementation using cold atomic gases confined in deep optical l…
We consider transformation from a closed to an open spin chain and vice versa produced by changing single link strength in a pair of neighboring spins. We show that in the non-adiabatic time domain fidelity of such a process can be increased by proper choosing of the control function for spin-spin exchange coupling. We obtain this function for an antiferromagnetic quantum Ising chain and present heuristic reasons restricting possible time-dependences of Hamiltonians applied for a high-fidelity control.
We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into Ising spin chains. To illustrate the method, and as a simple proof of principle, we use a (hybrid) quantum annealer to recover the correct profile of the thin-wall tunnelling solution. This method is applicable to many nonperturbative problems.
We study the simple Hamiltonian, $H=-K(S_{1z}^2 +S_{2z}^2)+ λ\vec S_1\cdot\vec S_2$, of two, large, coupled spins which are taken equal, each of total spin $s$ with $λ$ the exchange coupling constant. The exact ground state of this simple Hamiltonian is not known for an antiferromagnetic coupling corresponding to the $λ>0$. In the absence of the exchange interaction, the ground state is four fold degenerate, corresponding to the states where the individual spins are in their highest weight or lowest weight states, $|\hskip-1 mm\uparrow, \uparrow\rangle, |\hskip-1 mm\downarrow, \downarrow\rangl…
Adiabatic passage techniques, used to drive a system from one quantum state into another, find widespread application in physics and chemistry. We focus on techniques to spatially transport a quantum amplitude over a strongly coupled system, such as STImulated Raman Adiabatic Passage (STIRAP) and Coherent Tunnelling by Adiabatic Passage (CTAP). Previous results were shown to work on certain graphs, such as linear chains, square and triangular lattices, and branched chains. We prove that similar protocols work much more generally, in a large class of (semi-)bipartite graphs. In particular, unde…
We consider a finite-time quantum Otto cycle with single and two-spin-$1/2$ systems as its working medium. In order to mimic adiabatic dynamics at a finite-time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and non-adiabatic performances of the same cycle. Our findings clearly indicate that the use of shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and non-adiabatic counterparts for differe…
We report theoretical studies of adiabatic population transfer using dressed spin states. Quantum optimal control using the algorithm of Chopped Random Basis (CRAB) has been implemented in a negatively charged diamond nitrogen vacancy center that is coupled to a strong and resonant microwave field. We show that the dressed spin states are highly effective in suppressing effects of spin dephasing on adiabatic population transfer. The numerical simulation also demonstrates that CRAB-based quantum optimal control can enable an efficient and robust adiabatic population transfer.
Adiabatic transport of information is a widely invoked resource in connection with quantum information processing and distribution. The study of adiabatic transport via spin-half chains or clusters is standard in the literature, while in practice the true realisation of a completely isolated two-level quantum system is not achievable. We explore here, theoretically, the extension of spin-half chain models to higher spins. Considering arrangements of three spin-one particles, we show that adiabatic transport, specifically a generalisation of the Dark State Adiabatic Passage procedure, is applic…
Adiabatic methods are potentially important for quantum information protocols because of their robustness against many sources of technical and fundamental noise. They are particularly useful for quantum transport, and in some cases elementary quantum gates. Here we explore the extension of a particular protocol, dark state adiabatic passage, where a spin state is transported across a branched network of initialised spins, comprising one `input' spin, and multiple leaf spins. We find that maximal entanglement is generated in systems of spin-half particles, or where the system is limited to one…
We apply the transitionless quantum driving method to control the electron spin of a two-electron double quantum dot with spin-orbit coupling by time-dependent electric fields. The $x$ and $y$ components of applied electric fields in each dot are designed to achieve fast adiabatic-like passage in the nanosecond timescale. To simplify the setup, we can further transform Hamiltonian by z axis to design an alternative speed-up adiabatic passage, without using the applied electric field in $y$ direction.
We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.
We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin-singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, and discuss possible implementations and identify parameters that can be used to c…
We consider a process to create quasi long-range quantum discord between the non-interacting end spins of a quantum spin chain, with the end spins weakly coupled to the bulk of the chain. The process is not only capable of creating long-range quantum correlation but the latter remains frozen, when certain weak end-couplings are adiabatically varied below certain thresholds. We term this phenomenon as adiabatic freezing of quantum correlation. We observe that the freezing is robust to moderate thermal fluctuations and is intrinsically related to the cooperative properties of the quantum spin ch…
The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit gate fidelities for an electron spin qubit bound to a $^{31}$P atom in natural silicon, by applying adiabatic inversion instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled do…
An exact solution is derived for the wave function of an electron in a semiconductor quantum wire with spin-orbit interaction and driven by external time dependent harmonic confining potential. The formalism allows analytical expressions for various quantities to be derived, such as spin and pseudo-spin rotations, energy and occupation probabilities for excited states. It is demonstrated how perfect spin and pseudo-spin flips can be achieved at high frequencies of order ω, the confining potential level spacing. By an appropriately chosen driving term, spin manipulation can be exactly performed…
A unified theoretical treatment is presented to describe the physics of electron dynamics in semiconductor and graphene systems. Electron spin fast alignment with the Zeeman magnetic field (physical or effective) is treated as a form of adiabatic spin evolution which necessarily generates a monopole in magnetic space. One could transform this monopole into the physical and intuitive topological magnetic fields in the useful momentum (K) or real spaces (R). The physics of electron dynamics related to spin Hall, torque, oscillations and other technologically useful spinor effects can be inferred…
We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-co…
Transporting quantum information is an important prerequisite for quantum computers. We study how this can be done in Heisenberg-coupled spin networks using adiabatic control over the coupling strengths. We find that qudits can be transferred and entangled pairs can be created between distant sites of bipartite graphs with a certain balance between the maximum spin of both parts, extending previous results that were limited to linear chains. The transfer fidelity in a small star-shaped network is numerically analysed, and possible experimental implementations are discussed.
We study the adiabatic quantum dynamics of an anisotropic spin-1 XY chain across a second order quantum phase transition. The system is driven out of equilibrium by performing a quench on the uniaxial single-spin anisotropy, that is supposed to vary linearly in time. We show that, for sufficiently large system sizes, the excess energy after the quench admits a non trivial scaling behavior that is not predictable by standard Kibble-Zurek arguments for isolated critical points or extended critical regions. This emerges from a competing effect of many accessible low-lying excited states, inside t…
Tunnelling is one of the most paradigmatic and evocative phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from SQUID magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel, however, has remained controversial since the first attempts to calculate it, which relied on the group delay. It is now well understood that this delay (the arrival time of the transmitted wave packet peak at the far side of the barrier) can be smaller than the barrier thickness divided by the…
The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum com…
Motivated by the $Ω$-spectrum proposal of unique gapped ground states by Kitaev, we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable models in one and two spatial dimensions and discuss how nontrivial adiabatic cycles are detected. For one spatial dimension, we study the adiabatic cycle in detail with the matrix product state and show that the symmetry charge can act on the space of matrices without changing the physical states, which leads to nontrivial loops with symmetry charges. For generic spatial dimensions, based on the Bock…
