17 research outputs found
Parameter Sharing in Coagent Networks
In this paper, we aim to prove the theorem that generalizes the Coagent
Network Policy Gradient Theorem (Kostas et. al., 2019) to the context where
parameters are shared among the function approximators involved. This provides
the theoretical foundation to use any pattern of parameter sharing and leverage
the freedom in the graph structure of the network to possibility exploit
relational bias in a given task. As another application, we will apply our
result to give a more intuitive proof for the Hierarchical Option Critic Policy
Gradient Theorem, first shown in (Riemer et. al., 2019)
The Smallest Interacting Universe
The co-emergence of locality between the Hamiltonian and initial state of the
universe is studied in a simple toy model. We hypothesize a fundamental loss
functional for the combined Hamiltonian and quantum state and minimize it by
gradient descent. This minimization yields a tensor product structure
simultaneously respected by both the Hamiltonian and the state, suggesting that
locality can emerge by a process analogous to spontaneous symmetry breaking. We
discuss the relevance of this program to the arrow of time problem.
In our toy model, we interpret the emergence of a tensor factorization as the
appearance of individual degrees of freedom within a previously
undifferentiated (raw) Hilbert space. Earlier work [5, 6] looked at the
emergence of locality in Hamiltonians only, and found strong numerical
confirmation of that raw Hilbert spaces of are unstable and prefer
to settle on tensor factorization when is not prime, and in [6] even
primes were seen to "factor" after first shedding a small summand, e.g.
. This was found in the context of a rather general potential
functional on the space of metrics on , the
Lie algebra of symmetries. This emergence of qunits through operator-level
spontaneous symmetry breaking (SSB) may help us understand why the world seems
to consist of myriad interacting degrees of freedom. But understanding why the
universe has an initial Hamiltonian with a many-body structure is of
limited conceptual value unless the initial state, , is also
structured by this tensor decomposition. Here we adapt to become a
functional on , and find SSB now produces a conspiracy between and
, where they simultaneously attain low entropy by settling on
the same qubit decomposition
Quantum computing with Octonions
There are two schools of "measurement-only quantum computation". The first
([11]) using prepared entanglement (cluster states) and the second ([4]) using
collections of anyons, which according to how they were produced, also have an
entanglement pattern. We abstract the common principle behind both approaches
and find the notion of a graph or even continuous family of equiangular
projections. This notion is the leading character in the paper. The largest
continuous family, in a sense made precise in Corollary 4.2, is associated with
the octonions and this example leads to a universal computational scheme.
Adiabatic quantum computation also fits into this rubric as a limiting case:
nearby projections are nearly equiangular, so as a gapped ground state space is
slowly varied the corrections to unitarity are small.Comment: Added some new results in section
Improved Bayesian Regret Bounds for Thompson Sampling in Reinforcement Learning
In this paper, we prove the first Bayesian regret bounds for Thompson
Sampling in reinforcement learning in a multitude of settings. We simplify the
learning problem using a discrete set of surrogate environments, and present a
refined analysis of the information ratio using posterior consistency. This
leads to an upper bound of order in the time
inhomogeneous reinforcement learning problem where is the episode length
and is the Kolmogorov dimension of the space of environments.
We then find concrete bounds of in a variety of settings, such as
tabular, linear and finite mixtures, and discuss how how our results are either
the first of their kind or improve the state-of-the-art.Comment: 37th Conference on Neural Information Processing Systems (NeurIPS
2023
Quantum simulation of battery materials using ionic pseudopotentials
Ionic pseudopotentials are widely used in classical simulations of materials
to model the effective potential due to the nucleus and the core electrons.
Modeling fewer electrons explicitly results in a reduction in the number of
plane waves needed to accurately represent the states of a system. In this
work, we introduce a quantum algorithm that uses pseudopotentials to reduce the
cost of simulating periodic materials on a quantum computer. We use a
qubitization-based quantum phase estimation algorithm that employs a
first-quantization representation of the Hamiltonian in a plane-wave basis. We
address the challenge of incorporating the complexity of pseudopotentials into
quantum simulations by developing highly-optimized compilation strategies for
the qubitization of the Hamiltonian. This includes a linear combination of
unitaries decomposition that leverages the form of separable pseudopotentials.
Our strategies make use of quantum read-only memory subroutines as a more
efficient alternative to quantum arithmetic. We estimate the computational cost
of applying our algorithm to simulating lithium-excess cathode materials for
batteries, where more accurate simulations are needed to inform strategies for
gaining reversible access to the excess capacity they offer. We estimate the
number of qubits and Toffoli gates required to perform sufficiently accurate
simulations with our algorithm for three materials: lithium manganese oxide,
lithium nickel-manganese oxide, and lithium manganese oxyfluoride. Our
optimized compilation strategies result in a pseudopotential-based quantum
algorithm with a total runtime four orders of magnitude lower than the previous
state of the art for a fixed target accuracy