238 research outputs found
Quantum Simulation Logic, Oracles, and the Quantum Advantage
Query complexity is a common tool for comparing quantum and classical
computation, and it has produced many examples of how quantum algorithms differ
from classical ones. Here we investigate in detail the role that oracles play
for the advantage of quantum algorithms. We do so by using a simulation
framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms
that solve some problems with the same success probability and number of
queries as the quantum algorithms. The framework can be simulated using only
classical resources at a constant overhead as compared to the quantum resources
used in quantum computation. Our results clarify the assumptions made and the
conditions needed when using quantum oracles. Using the same assumptions on
oracles within the simulation framework we show that for some specific
algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no
advantage in terms of query complexity. This does not detract from the fact
that quantum query complexity provides examples of how a quantum computer can
be expected to behave, which in turn has proved useful for finding new quantum
algorithms outside of the oracle paradigm, where the most prominent example is
Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
QKD based on symmetric entangled Bernstein-Vazirani
This paper introduces a novel entanglement-based QKD protocol, that makes use
of a modified symmetric version of the Bernstein-Vazirani algorithm, in order
to achieve a secure and efficient key distribution. Two variants of the
protocol, one fully symmetric and one semi-symmetric, are presented. In both
cases, the spatially separated Alice and Bob share multiple EPR pairs, one
qubit of the pair each. The fully symmetric version allows both parties to
input a secret key from the irrespective location and, finally, acquire in the
end a totally new and original key, an idea which was inspired by the
Diffie-Hellman key exchange protocol. In the semi-symmetric version, Alice
sends her chosen secret key to Bob (or vice versa). Furthermore, their
performance against an eavesdropper's attack is analyzed. Finally, in order to
illustrate the operation of the protocols in practice, two small scale but
detailed examples are given.Comment: 16 pages, 8 figure
On non-adaptive quantum chosen-ciphertext attacks and Learning with Errors
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong “quantum access” security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of
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