Title: Natural Orbitals: Old Concepts, New Developments
Date/Time: 08-Feb, 03:00PM
Venue: Lecture Theatre 27
Abstract: Since their introduction in 1955, the natural orbitals (NOs) have been employed in numerous approaches to quantum-mechanical description of systems composed of indistinguishable particles, proving to be an indispensable tool in both computation and interpretation of electronic and nuclear wavefunctions. However, despite their importance to quantum chemistry and nuclear physics, the NOs have been the subject of a relatively small number of studies aiming at understanding of their properties. This disappointing state of affairs has been rectified only very recently with the uncovering of high-order off-diagonal cusp conditions for the reduced density matrices of Coulombic species that opened an avenue to an asymptotic formalism for the NOs. This approach has turned out to reveal surprising universalities among the NOs (and their occupation numbers) of diverse systems. It also produced rigorous estimates for the truncation errors in the electronic properties computed with basis sets of finite sizes employed in quantum-chemical calculations. The present talk reviews both the basic properties of the NOs and those afforded by the aforementioned new developments. Joint Colloquium with NUS Physics & NUS Chemistry
Title: Mixing ultracold atoms in external confinements
Date/Time: 07-Feb, 03:00PM
Venue: CQT Level 5 Seminar Room (S15-05-15)
Abstract: Ultracold molecules confined in optical lattices are promising candidates for quantum simulation and quantum computation. However, loading the lattice from a bulk gas presents two problems. First, collisional properties of molecules have recently been revealed more intricate than expected. Second good lattice filling requires low entropy. Here, I will review a protocol for mixing two atomic BECs in an optical lattice which leads to the formation of a low entropy sample of isolated molecules. And I will focus on the interplay between the different forms of confinement and the interplay between the confinement and atomic interactions, which characterize the intermediate steps.
Title: Does qubit connectivity impact quantum circuit complexity?
Date/Time: 08-Feb, 04:00PM
Venue: Via Zoom
Abstract: Some physical implementation schemes of quantum computing -- such as those based on superconducting qubits, quantum dots, and cold atoms -- can apply two-qubit gates only on certain pairs of qubits. Other schemes -- such as those based on trapped ions and photonics -- are not subject to such constraints. These qubit connectivity constraints are commonly viewed as a disadvantage; for example, compiling an unrestricted n-qubit quantum circuit to one with poor qubit connectivity, such as a 1D chain, usually results in a blowup of depth by O(n2) and size by O(n). It is appealing to conjecture that this overhead is unavoidable -- a random circuit on n qubits has Θ(n) 2-qubit gates in each layer and a constant fraction of them act on qubits separated by distance Θ(n).
While it is known that almost all n-qubit unitaries need quantum circuits of Ω(4n/n) depth and Ω(4n) size to realize, in this paper, we show that all n-qubit unitaries can be implemented by circuits of O(4n/n) depth and O(4n) size even under 1D chain qubit connectivity constraints.
We extend this result and investigate qubit connectivity along three directions. First, we consider more general connectivity graphs, and show that the size can always be made O(4n) as long as the graph is connected. For depth, we study d-dimensional grids, complete d-ary trees and expander graphs, and show results similar to the 1D chain. Second, we consider the case when ancillae are available. We show that, with ancillae, the depth can be made polynomial, and the space-depth trade-off is not impaired by the qubit connectivity constraint unless we have exponentially many ancillae. Third, we consider special unitaries, including diagonal unitaries and quantum state preparation, the last being a fundamental task used in many quantum algorithms for machine learning and linear algebra problems.
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Title: Typicality and Strong Prethermalization of Nonequilibrium Steady Currents
Date/Time: 08-Feb, 04:30PM
Venue: CQT Level 5 Seminar Room, S15-05-14
Abstract: We study the steady currents between two finite nonintegrable environments. Each environment is able to thermalize by itself following the so-called eigenstate thermalization hypothesis. With typical initial states for each bath, i.e., random superposition of eigenstates within certain energy shell, we first that the emergent steady currents are also typical, i.e., the vast majority of the current has a value close to steady current obtained from baths with microcanonical initial conditions. We then show that the formation of the steady currents is a manifestation of the prethermalization phenomenon, a quasi-equilibrium dynamical process with weak breaking of conserved quantities. We then study more generalized initial states, i.e., a random product state with fixed and different energy constraints (within the mean energy ensemble). Such an initialization, not being constrained to superpositions or mixtures of many-body eigenstates, opens the door to experimental realization and also significantly simplifies numerical simulations. We again show that such dynamical process is typical as the current variance decreases exponentially with respect to the size of baths. Particularly, we demonstrate that the emerging current is prethermalized in a strong sense, analogously to strong thermalization, meaning that the current values stay close to the microcanonical one most of the time.
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Date/Time: 02-Mar, 04:00PM
Venue: CQT Level 3 Seminar Room, S15-03-15