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Register a new userMay a dissipative environment be beneficial for quantum annealing?
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Added by
Gianluca Passarelli
Publication date
2019
fields
Physics
and research's language is
English
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We discuss the quantum annealing of the fully-connected ferromagnetic $ p $-spin model in a dissipative environment at low temperature. This model, in the large $ p $ limit, encodes in its ground state the solution to the Grovers problem of searching in unsorted databases. In the framework of the quantum circuit model, a quantum algorithm is known for this task, providing a quadratic speed-up with respect to its best classical counterpart. This improvement is not recovered in adiabatic quantum computation for an isolated quantum processor. We analyze the same problem in the presence of a low-temperature reservoir, using a Markovian quantum master equation in Lindblad form, and we show that a thermal enhancement is achieved in the presence of a zero temperature environment moderately coupled to the quantum annealer.
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We investigate the quantum annealing of the ferromagnetic $ p $-spin model in a dissipative environment ($ p = 5 $ and $ p = 7 $). This model, in the large $ p $ limit, codifies the Grovers algorithm for searching in an unsorted database. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large $ N $, and $ p $. While at weak system bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or classical limit.
Recent empirical results using quantum annealing hardware have shown that mid anneal pausing has a surprisingly beneficial impact on the probability of finding the ground state for of a variety of problems. A theoretical explanation of this phenomenon has thus far been lacking. Here we provide an analysis of pausing using a master equation framework, and derive conditions for the strategy to result in a success probability enhancement. The conditions, which we identify through numerical simulations and then prove to be sufficient, require that relative to the pause duration the relaxation rate is large and decreasing right after crossing the minimum gap, small and decreasing at the end of the anneal, and is also cumulatively small over this interval, in the sense that the system does not thermally equilibrate. This establishes that the observed success probability enhancement can be attributed to incomplete quantum relaxation, i.e., is a form of beneficial non-equilibrium coupling to the environment.
Quantum metrology pursues high-precision measurements to physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrology error tends to divergent in the long-encoding-time regime due to the Born-Markovian approximate decoherence, which is called no-go theorem of noisy quantum metrology. We here propose a Gaussian quantum metrology scheme using bimodal quantized optical fields as quantum probe. It achieves the precision of sub-Heisenberg limit in the ideal case. However, the Markovian decoherence causes the metrological error contributed from the center-of-mass mode of the probe to be divergent. A mechanism to remove this ostensible no-go theorem is found in the non-Markovian dynamics. Our result gives an efficient way to realize high-precision quantum metrology in practical continuous-variable systems.
Pebble accretion is an emerging paradigm for the fast growth of planetary cores. Pebble flux and pebble sizes are the key parameters used in the pebble accretion models. We aim to derive the pebble sizes and fluxes from state-of-the-art dust coagulation models, understand their dependence on disk parameters and the fragmentation threshold velocity, and the impact of those on the planetary growth by pebble accretion. We use a one-dimensional dust evolution model including dust growth and fragmentation to calculate realistic pebble sizes and mass flux. We use this information to integrate the growth of planetary embryos placed at various locations in the protoplanetary disk. Pebble flux strongly depends on disk properties, such as its size and turbulence level, as well as on the dust aggregates fragmentation threshold. We find that dust fragmentation may be beneficial to planetary growth in multiple ways. First of all, it prevents the solids from growing to very large sizes, for which the efficiency of pebble accretion drops. What is more, small pebbles are depleted at a slower rate, providing a long-lasting pebble flux. As the full coagulation models are computationally expensive, we provide a simple method of estimating pebble sizes and flux in any protoplanetary disk model without substructure and with any fragmentation threshold velocity.
New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systems
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