In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg's uncertainty principle ...limits the intrinsic precision of a state. Although theoretical work has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a 'single quadrature' measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification, adaptive measurement, measurement-based state steering and continuous quantum error correction. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way to study how notions of contemporary quantum foundations arise in such settings.
Quantum-gas microscope for fermionic atoms Cheuk, Lawrence W; Nichols, Matthew A; Okan, Melih ...
Physical review letters,
2015-May-15, Letnik:
114, Številka:
19
Journal Article
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We realize a quantum-gas microscope for fermionic ^{40}K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman ...sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.
The performance of local Møller-Plesset second-order perturbation theory (LMP2) and the impact of domain choice upon accuracy for a series of correlation consistent basis sets have been examined. MP2 ...correlation energies were calculated for 31 molecules ranging from 4 to 26 atoms, and containing up to 10 non-hydrogen atoms. The correlation energies were extrapolated to the complete basis set (CBS) limit using various schemes for comparison. The percent CPU savings for the local MP2 calculations as compared with conventional MP2 calculations are provided.
In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg's uncertainty principle ...limits the intrinsic precision of a state. Although theoretical work1 has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently2,3 has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a 'single quadrature' measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification4, adaptive measurement5,6, measurement-based state steering and continuous quantum error correction7. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way8,9 to study how notions of contemporary quantum foundations10-14 arise in such settings.
The performance of local Moeller-Plesset second-order perturbation theory (LMP2) and the impact of domain choice upon accuracy for a series of correlation consistent basis sets have been examined. ...MP2 correlation energies were calculated for 31 molecules ranging from 4 to 26 atoms, and containing up to 10 non-hydrogen atoms. The correlation energies were extrapolated to the complete basis set (CBS) limit using various schemes for comparison. The percent CPU savings for the local MP2 calculations as compared with conventional MP2 calculations are provided.
Encoder-decoder networks with attention have proven to be a powerful way to solve many sequence-to-sequence tasks. In these networks, attention aligns encoder and decoder states and is often used for ...visualizing network behavior. However, the mechanisms used by networks to generate appropriate attention matrices are still mysterious. Moreover, how these mechanisms vary depending on the particular architecture used for the encoder and decoder (recurrent, feed-forward, etc.) are also not well understood. In this work, we investigate how encoder-decoder networks solve different sequence-to-sequence tasks. We introduce a way of decomposing hidden states over a sequence into temporal (independent of input) and input-driven (independent of sequence position) components. This reveals how attention matrices are formed: depending on the task requirements, networks rely more heavily on either the temporal or input-driven components. These findings hold across both recurrent and feed-forward architectures despite their differences in forming the temporal components. Overall, our results provide new insight into the inner workings of attention-based encoder-decoder networks.
Despite the widespread application of recurrent neural networks (RNNs) across a variety of tasks, a unified understanding of how RNNs solve these tasks remains elusive. In particular, it is unclear ...what dynamical patterns arise in trained RNNs, and how those patterns depend on the training dataset or task. This work addresses these questions in the context of a specific natural language processing task: text classification. Using tools from dynamical systems analysis, we study recurrent networks trained on a battery of both natural and synthetic text classification tasks. We find the dynamics of these trained RNNs to be both interpretable and low-dimensional. Specifically, across architectures and datasets, RNNs accumulate evidence for each class as they process the text, using a low-dimensional attractor manifold as the underlying mechanism. Moreover, the dimensionality and geometry of the attractor manifold are determined by the structure of the training dataset; in particular, we describe how simple word-count statistics computed on the training dataset can be used to predict these properties. Our observations span multiple architectures and datasets, reflecting a common mechanism RNNs employ to perform text classification. To the degree that integration of evidence towards a decision is a common computational primitive, this work lays the foundation for using dynamical systems techniques to study the inner workings of RNNs.
A central challenge in developing versatile machine learning systems is catastrophic forgetting: a model trained on tasks in sequence will suffer significant performance drops on earlier tasks. ...Despite the ubiquity of catastrophic forgetting, there is limited understanding of the underlying process and its causes. In this paper, we address this important knowledge gap, investigating how forgetting affects representations in neural network models. Through representational analysis techniques, we find that deeper layers are disproportionately the source of forgetting. Supporting this, a study of methods to mitigate forgetting illustrates that they act to stabilize deeper layers. These insights enable the development of an analytic argument and empirical picture relating the degree of forgetting to representational similarity between tasks. Consistent with this picture, we observe maximal forgetting occurs for task sequences with intermediate similarity. We perform empirical studies on the standard split CIFAR-10 setup and also introduce a novel CIFAR-100 based task approximating realistic input distribution shift.
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 73-75).
This thesis reports the achievement ...of a two-species apparatus for use in an upcoming experiment with fermionic ultracold atomic gases. First, we describe the construction of a laser system capable of cooling and trapping gaseous lithium-6 atoms in a 3D Magneto-Optical Trap. Second, we discuss the realization of a 2D Magneto-Optical Trap which, in our experiment, acts as a high-flux source of cold potassium-40 atoms. These two systems are critical first steps in cooling the lithium and potassium atoms to quantum degeneracy.
by Vinay Ramasesh.
S.B.
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references ...(pages 83-85).
This thesis reports the construction of a novel apparatus for experiments with ultracold atoms in optical lattices: the Fermi gas microscope. Improving upon similar designs for bosonic atoms, our Fermi gas microscope has the novel feature of being able to achieve single-site resolved imaging of fermionic atoms in an optical lattice; specifically, we use fermionic potassium-40, sympathetically cooled by bosonic sodium-23. In this thesis, several milestones on the way to achieving single-site resolution are described and documented. First, we have tested and mounted in place the imaging optics necessary for achieving single-site resolution. We set up separate 3D magnetooptical traps for capturing and cooling both ²³Na and ⁴⁰K. These species are then trapped simultaneously in a plugged quadrupole magnetic trap and evaporated to degeneracy; we obtain a sodium Bose-Einstein condensate with about a million atoms and a degenerate potassium cloud cooled to colder than 1 muK. Using magnetic transport over a distance of 1 cm, we move the cold cloud of atoms into place under the high-resolution imaging system and capture it in a hybrid magnetic and optical-dipole trap. Further evaporation in this hybrid trap performed by lowering the optical trap depth, and the cooled atoms are immersed in an optical lattice, the setup and calibration of which is also described here. Finally, we cool the atoms with optical molasses beams while in the lattice, with the imaging optics collecting the fluoresence light for high-resolution imaging. With molasses cooling set up, single-site fluoresence imaging of bosons and fermions in the same experimental apparatus is within reach.
by Vinay Venkatesh Ramasesh.
M. Eng.
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