241 research outputs found
Adiabatic Quantum State Generation and Statistical Zero Knowledge
The design of new quantum algorithms has proven to be an extremely difficult
task. This paper considers a different approach to the problem, by studying the
problem of 'quantum state generation'. This approach provides intriguing links
between many different areas: quantum computation, adiabatic evolution,
analysis of spectral gaps and groundstates of Hamiltonians, rapidly mixing
Markov chains, the complexity class statistical zero knowledge, quantum random
walks, and more.
We first show that many natural candidates for quantum algorithms can be cast
as a state generation problem. We define a paradigm for state generation,
called 'adiabatic state generation' and develop tools for adiabatic state
generation which include methods for implementing very general Hamiltonians and
ways to guarantee non negligible spectral gaps. We use our tools to prove that
adiabatic state generation is equivalent to state generation in the standard
quantum computing model, and finally we show how to apply our techniques to
generate interesting superpositions related to Markov chains.Comment: 35 pages, two figure
Quantum Commuting Circuits and Complexity of Ising Partition Functions
Instantaneous quantum polynomial-time (IQP) computation is a class of quantum
computation consisting only of commuting two-qubit gates and is not universal
in the sense of standard quantum computation. Nevertheless, it has been shown
that if there is a classical algorithm that can simulate IQP efficiently, the
polynomial hierarchy (PH) collapses at the third level, which is highly
implausible. However, the origin of the classical intractability is still less
understood. Here we establish a relationship between IQP and computational
complexity of the partition functions of Ising models. We apply the established
relationship in two opposite directions. One direction is to find subclasses of
IQP that are classically efficiently simulatable in the strong sense, by using
exact solvability of certain types of Ising models. Another direction is
applying quantum computational complexity of IQP to investigate (im)possibility
of efficient classical approximations of Ising models with imaginary coupling
constants. Specifically, we show that there is no fully polynomial randomized
approximation scheme (FPRAS) for Ising models with almost all imaginary
coupling constants even on a planar graph of a bounded degree, unless the PH
collapses at the third level. Furthermore, we also show a multiplicative
approximation of such a class of Ising partition functions is at least as hard
as a multiplicative approximation for the output distribution of an arbitrary
quantum circuit.Comment: 36 pages, 5 figure
Beyond Sparsity: Tree Regularization of Deep Models for Interpretability
The lack of interpretability remains a key barrier to the adoption of deep
models in many applications. In this work, we explicitly regularize deep models
so human users might step through the process behind their predictions in
little time. Specifically, we train deep time-series models so their
class-probability predictions have high accuracy while being closely modeled by
decision trees with few nodes. Using intuitive toy examples as well as medical
tasks for treating sepsis and HIV, we demonstrate that this new tree
regularization yields models that are easier for humans to simulate than
simpler L1 or L2 penalties without sacrificing predictive power.Comment: To appear in AAAI 2018. Contains 9-page main paper and appendix with
supplementary materia
Universally Composable Quantum Multi-Party Computation
The Universal Composability model (UC) by Canetti (FOCS 2001) allows for
secure composition of arbitrary protocols. We present a quantum version of the
UC model which enjoys the same compositionality guarantees. We prove that in
this model statistically secure oblivious transfer protocols can be constructed
from commitments. Furthermore, we show that every statistically classically UC
secure protocol is also statistically quantum UC secure. Such implications are
not known for other quantum security definitions. As a corollary, we get that
quantum UC secure protocols for general multi-party computation can be
constructed from commitments
What Can We Learn Privately?
Learning problems form an important category of computational tasks that
generalizes many of the computations researchers apply to large real-life data
sets. We ask: what concept classes can be learned privately, namely, by an
algorithm whose output does not depend too heavily on any one input or specific
training example? More precisely, we investigate learning algorithms that
satisfy differential privacy, a notion that provides strong confidentiality
guarantees in contexts where aggregate information is released about a database
containing sensitive information about individuals. We demonstrate that,
ignoring computational constraints, it is possible to privately agnostically
learn any concept class using a sample size approximately logarithmic in the
cardinality of the concept class. Therefore, almost anything learnable is
learnable privately: specifically, if a concept class is learnable by a
(non-private) algorithm with polynomial sample complexity and output size, then
it can be learned privately using a polynomial number of samples. We also
present a computationally efficient private PAC learner for the class of parity
functions. Local (or randomized response) algorithms are a practical class of
private algorithms that have received extensive investigation. We provide a
precise characterization of local private learning algorithms. We show that a
concept class is learnable by a local algorithm if and only if it is learnable
in the statistical query (SQ) model. Finally, we present a separation between
the power of interactive and noninteractive local learning algorithms.Comment: 35 pages, 2 figure
Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection
We define rewinding operators that invert quantum measurements. Then, we
define complexity classes , , and as
sets of decision problems solvable by polynomial-size quantum circuits with a
polynomial number of rewinding operators, cloning operators, and adaptive
postselections, respectively. Our main result is that . As a
byproduct of this result, we show that any problem in can be
solved with only postselections of outputs whose probabilities are polynomially
close to one. Under the strongly believed assumption that , or the shortest independent vectors problem cannot be
efficiently solved with quantum computers, we also show that a single rewinding
operator is sufficient to achieve tasks that are intractable for quantum
computation. In addition, we consider rewindable Clifford and instantaneous
quantum polynomial time circuits.Comment: 29 pages, 3 figures, v2: Added Result 3 and improved Result
Efficient Threshold-Optimal ECDSA
This paper proposes a threshold-optimal ECDSA scheme based on the first threshold signature scheme by Gennaro et al. with efficient non-interactive signing for any signers in the group, provided the total group size is more than twice the threshold . The scheme does not require any homomorphic encryption or zero-knowledge proofs and is proven to be robust and unforgeable with identifiable aborts tolerating at most corrupted participants. The security of the scheme is proven in a simulation-based definition, assuming DDH and that ECDSA is existentially unforgeable under chosen message attack. To evaluate the performance of the protocol, it has been implemented in C++ and the results demonstrate the non-interactive signing phase takes 0.12ms on average meaning over 8000 signatures can be created per second. With pre-signing phase, it takes 3.35ms in total, which is over 144 times faster than the current state of the art
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