arXiv subjects
Publications and source records attributed to Nikolai A. Sinitsyn.
Connection formulas for the asymptotic solutions of a system of n> 1 coupled Painleve'-II equations with symmetry-breaking parameters are written explicitly. An asymptotically exact WKB approach to these formulas relies on the quantum-mechanical independent crossing approximation for an explicitly time-dependent Schroedinger equation.
Unlike second-order phase transitions, a first-order transition has a stage, in which a system is trapped in a metastable state. The decay of this state leads to abundant excitations over the ground state. We present a field theory for kinetics of defects emerging during quantum annealing computations. This theory predicts several power laws for the error generation rate during quantum annealing either though or near the first-order phase transition. Sharp changes between the power exponents are predicted for continuous parameter changes. Observation of this behavior would be a signature of first-order critical points and could help identify and avoid them for better computations. The driven Lipkin-Meshkov-Glick model (LMGm) serves as the minimal model of interacting Ising spins that demonstrates this behavior.
We predict a gyroscopic effect that can be demonstrated with Rydberg atoms following the dynamics of a Kepler Hamiltonian with an additional uniaxial anisotropy induced by optical ponderomotive force. This effect is analogous to the rotation of the Foucault pendulum in response to the Earth's rotation. We argue that in Rydberg states with a large principal quantum number a similar geometric angle can be generated by mechanical rotations of an atomic-optical setup on time scales between $1~μ$s and $1~$ms.
We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the importance of the mass parameter of a harmonic oscillator, alongside its frequency, in explicitly time-dependent situations.
We discuss the progress on exactly solvable multistate Landau-Zener models from a perspective of their application to competing reactions of particle creation from a false vacuum. Such models generally predict that, even with identical initial conditions, and for nearly the same other particle parameters, a quantum coherent evolution results in a final particle distribution with significant asymmetry. We use an exact solution of the driven bosonic Tavis-Cummings model for two reaction pathways in order to quantify this effect, reveal a corresponding phase transition, and identify its universality class.
We propose and solve a minimal model of dynamic passage through a second-order phase transition in the presence of symmetry breaking interactions and no dissipation. Our model generalizes the Hamiltonian dynamics of the Painleve'-2 equation to the case with many degrees of freedom, while maintaining the integrability property. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking parameter of the Hamiltonian is. This suggests a potential mechanism for strong asymmetry in the production of quasi-particles with nearly identical characteristics. The model's integrability also yields exact exponents for the scaling of the density of the nonadiabatically excited quasi-particles.
Advances in atomic physics have led to the possibility of a coherent transformation between ultra-cold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the constituent atoms and molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these effects, along with scaling laws for the reaction yield in non-adiabatic regimes.
The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although the system is passing slowly very close to it. We show that the leading exponent for the excitation probability then can be obtained by standard arguments of the Dykhne formula but the exponential prefactor is no longer simple, and behaves as a power law on the characteristic transition rate. We derive this prefactor for the nonlinear Landau-Zener (nLZ) model by adjusting the Dykhne's approach. Then, we introduce an exactly solvable model of the transition near a critical point in the Stark ladder. We derive the number of the excitations for it without approximations, and find qualitatively similar results for the excitation scaling.
The Number Partitioning Problem (NPP) is one of the NP-complete computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $\sqrt{N}$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $N$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time-dependence of the physical parameters or the choice of the annealing protocol.
We investigate magnetic fluctuations of a mesoscopic critical region at the interface induced by smooth time-independent spacial changes of a control parameter across its critical value. Near the spatial critical point, the order parameter fluctuations are mesoscopic, i.e., much larger than the lattice constant but decaying away from the critical region. We propose a minimal model to describe this behavior and show that it leads to the integrable Painlevé-II equation for the local order parameter. We argue that known mathematical properties of this equation produce insight into the nonlinear susceptibilities of this region.
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design. Here, we propose a realization of Grover's oracle for a large class of searching problems using a quantum annealing step. The time of this step grows only logarithmically with the size of the database. This suggests an efficient path to application of Grover's algorithm to practically important problems, such as finding the ground state of a Hamiltonian with a spectral gap over its ground state.
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual state is generally mixed, it is described by a Hermitian matrix. In this article, we present a randomized channel-state duality. In other words, a quantum channel is represented by a collection of $N$ pure quantum states that are produced from a random source. The accuracy of this randomized duality relation is given by $1/N$, with regard to an appropriate distance measure. For large systems, $N$ is much smaller than the dimension of the exact dual matrix of the quantum channel. This provides a highly accurate low-rank approximation of any quantum channel, and, as a consequence of the duality relation, an efficient data compression scheme for mixed quantum states. We demonstrate these two immediate applications of the randomized channel-state duality with a chaotic $1$-dimensional spin system.
Information scrambling refers to the rapid spreading of initially localized information over an entire system, via the generation of global entanglement. This effect is usually detected by measuring a temporal decay of the out-of-time order correlators. However, in experiments, decays of these correlators suffer from fake positive signals from various sources, e.g., decoherence due to inevitable couplings to the environment, or errors that cause mismatches between the purported forward and backward evolutions. In this work, we provide a simple and robust approach to single out the effect of genuine scrambling. This allows us to benchmark the scrambling process by quantifying the degree of the scrambling from the noisy backgrounds.
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, $H_I$. Here, we point to the existence of an analytical solution for such a problem for an arbitrary $H_I$ beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time $T$ of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of $H_I$, the solution also shows a considerable quantum speedup in computations.
Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the inter quantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble using a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach maintaining local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the electron g factor on the spin-noise power-spectra. We demonstrate that the quantum dot ensemble can be mapped on an effective two-quantum dot problem and discuss how the characteristic length scale of the inter-dot interaction modifies the low-frequency cross-correlation spectrum. We argue that details on the interaction strength distribution can be extracted from the cross-correlation spectrum when applying a longitudinal or a transversal external magnetic field.
In this work, we study the real-time evolution of periodically driven (Floquet) systems on a quantum computer using IBM quantum devices. We consider a driven Landau-Zener model and compute the transition probability between the Floquet steady states as a function of time. We find that for this simple one-qubit model, Floquet states can develop in real-time, as indicated by the transition probability between Floquet states. Next, we model light-driven spin chains and compute the time-dependent antiferromagnetic order parameter. We consider models arising from light coupling to the underlying electrons as well as those arising from light coupling to phonons. For the two-spin chains, the quantum devices yield time evolutions that match the effective Floquet Hamiltonian evolution for both models once readout error mitigation is included. For three-spin chains, zero-noise extrapolation yields a time dependence that follows the effective Floquet time evolution. Therefore, the current IBM quantum devices can provide information on the dynamics of small Floquet systems arising from light drives once error mitigation procedures are implemented.
We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a nonexponential dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate. We find that the emerging phase can have a thermalized energy distribution with the temperature defined by the rate of the transition. This phase, however, has strong purely quantum correlations.
We explore nonadiabatic quantum phase transitions in an Ising spin chain with a linearly time-dependent transverse field and two different spins per unit cell. Such a spin system passes through critical points with gapless excitations, which support nonadiabatic transitions. Nevertheless, we find that the excitations on one of the chain sub-lattices are suppressed in the nearly-adiabatic regime exponentially. Thus, we reveal a coherent mechanism to induce exponentially large density separation for different quasiparticles.