52 research outputs found
Entanglement properties of quantum grid states
Grid states form a discrete set of mixed quantum states that can be described
by graphs. We characterize the entanglement properties of these states and
provide methods to evaluate entanglement criteria for grid states in a
graphical way. With these ideas we find bound entangled grid states for
two-particle systems of any dimension and multiparticle grid states that
provide examples for the different aspects of genuine multiparticle
entanglement. Our findings suggest that entanglement theory for grid states,
although being a discrete set, has already a complexity similar to the one for
general states.Comment: 6 pages, 4 figures, v2: small changes, final versio
Combinatorial structures in quantum information
This work is an exploration of how graphs and permutations can be applied in the context of quantum information processing. In Chapter 2 we consider problems about the permutations of the subsystems of a quantum system. Explicitly, we attempt to understand the problem of determining if two quantum states of N qubits are isomorphic: if one can be obtained from the other by permuting its subsystems. We show that the well known graph isomorphism problem is a special case of state isomorphism. We also show that the complement of state isomorphism, the problem of determining if two states are not isomorphic, can be verified by a quantum interactive proof system, and that this proof system can be made statistical zero knowledge. We also consider the complexity of isomorphism problems for stabilizer states, and mixed states. In Chapter 3 we work with a special class of quantum states called grid states, in an effort to develop a toy model for mixed state entanglement. The key idea with grid states is that they can be represented by what we call a grid-labelled graph, literally, a graph forced to have vertices on a two dimensional grid. We show that whether or not a grid state is entangled can sometimes be determined solely from the structural properties of its corresponding grid-labelled graph. We use the grid state framework to build families of bound entangled states, suggesting that even in this restricted setting detecting entanglement is non-trivial and will require more than a single entanglement criterion
The Computational Complexity of Portal and Other 3D Video Games
We classify the computational complexity of the popular video games Portal and Portal 2. We isolate individual mechanics of the game and prove NP-hardness, PSPACE-completeness, or pseudo-polynomiality depending on the specific game mechanics allowed. One of our proofs generalizes to prove NP-hardness of many other video games such as Half-Life 2, Halo, Doom, Elder Scrolls, Fallout, Grand Theft Auto, Left 4 Dead, Mass Effect, Deus Ex, Metal Gear Solid, and Resident Evil. These results build on the established literature on the complexity of video games [Aloupis et al., 2014][Cormode, 2004][Forisek, 2010][Viglietta, 2014]
Towards learning to explain with concept bottleneck models: mitigating information leakage
Concept bottleneck models perform classification by first predicting which of
a list of human provided concepts are true about a datapoint. Then a downstream
model uses these predicted concept labels to predict the target label. The
predicted concepts act as a rationale for the target prediction. Model trust
issues emerge in this paradigm when soft concept labels are used: it has
previously been observed that extra information about the data distribution
leaks into the concept predictions. In this work we show how Monte-Carlo
Dropout can be used to attain soft concept predictions that do not contain
leaked information
Hierarchical quantum classifiers
Quantum circuits with hierarchical structure have been used to perform binary
classification of classical data encoded in a quantum state. We demonstrate
that more expressive circuits in the same family achieve better accuracy and
can be used to classify highly entangled quantum states, for which there is no
known efficient classical method. We compare performance for several different
parameterizations on two classical machine learning datasets, Iris and MNIST,
and on a synthetic dataset of quantum states. Finally, we demonstrate that
performance is robust to noise and deploy an Iris dataset classifier on the
ibmqx4 quantum computer
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