Search results for "Quantum physic"
showing 10 items of 1596 documents
Neural Teleportation
2023
In this paper, we explore a process called neural teleportation, a mathematical consequence of applying quiver representation theory to neural networks. Neural teleportation "teleports" a network to a new position in the weight space and preserves its function. This phenomenon comes directly from the definitions of representation theory applied to neural networks and it turns out to be a very simple operation that has remarkable properties. We shed light on surprising and counter-intuitive consequences neural teleportation has on the loss landscape. In particular, we show that teleportation can be used to explore loss level curves, that it changes the local loss landscape, sharpens global m…
On the Complexity of Solving Subtraction Games
2018
We study algorithms for solving Subtraction games, which sometimes are referred to as one-heap Nim games. We describe a quantum algorithm which is applicable to any game on DAG, and show that its query compexity for solving an arbitrary Subtraction game of $n$ stones is $O(n^{3/2}\log n)$. The best known deterministic algorithms for solving such games are based on the dynamic programming approach. We show that this approach is asymptotically optimal and that classical query complexity for solving a Subtraction game is generally $\Theta(n^2)$. This paper perhaps is the first explicit "quantum" contribution to algorithmic game theory.
Quantum autoencoders via quantum adders with genetic algorithms
2017
The quantum autoencoder is a recent paradigm in the field of quantum machine learning, which may enable an enhanced use of resources in quantum technologies. To this end, quantum neural networks with less nodes in the inner than in the outer layers were considered. Here, we propose a useful connection between quantum autoencoders and quantum adders, which approximately add two unknown quantum states supported in different quantum systems. Specifically, this link allows us to employ optimized approximate quantum adders, obtained with genetic algorithms, for the implementation of quantum autoencoders for a variety of initial states. Furthermore, we can also directly optimize the quantum autoe…
Upperbounds on the probability of finding marked connected components using quantum walks
2019
Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked vertices, that if only one of them is marked. In this paper, we analyze the probability of finding any of marked vertices in such scenarios and prove upper bounds for various sets of marked vertices. We apply the upper bounds to large collection of graphs and show that the quantum search may be slow even when taking real-world networks.
Optimal one-shot quantum algorithm for EQUALITY and AND
2017
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box. Quantum algorithms are inherently probabilistic; we are interested in the lowest possible probability that the algorithm outputs incorrect answer (the error probability) for a fixed number of queries. We show that the lowest possible error probability for $AND_n$ and $EQUALITY_{n+1}$ is $1/2-n/(n^2+1)$.
The quantum query complexity of certification
2009
We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for 1-certificates. In particular, this shows that the zero-error quantum query complexity of evaluating such formulas is O(d^{(k+1)/2}) (again neglecting a logarithmic factor). Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem.
On the Power of Non-adaptive Learning Graphs
2012
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates in the input string, not the precise values therein. Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for all certificate structures. By this, we mean that there exists a function possessing the certificate structure and such that a learning graph gives an optimal quantum query algorithm for it. For a special case of certificate structures generated by cer…
Adversary Lower Bound for the k-sum Problem
2013
We prove a tight quantum query lower bound $\Omega(n^{k/(k+1)})$ for the problem of deciding whether there exist $k$ numbers among $n$ that sum up to a prescribed number, provided that the alphabet size is sufficiently large. This is an extended and simplified version of an earlier preprint of one of the authors arXiv:1204.5074.
Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities
2016
One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parity-oblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity oblivious random access codes and obtain bounds on the success probabilities of performing such task…
Quantum, stochastic, and pseudo stochastic languages with few states
2014
Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all th…