99 research outputs found
Energy-Consumption Advantage of Quantum Computation
Energy consumption in solving computational problems has been gaining growing
attention as a part of the performance measures of computers. Quantum
computation is known to offer advantages over classical computation in terms of
various computational resources; however, its advantage in energy consumption
has been challenging to analyze due to the lack of a theoretical foundation to
relate the physical notion of energy and the computer-scientific notion of
complexity for quantum computation with finite computational resources. To
bridge this gap, we introduce a general framework for studying energy
consumption of quantum and classical computation based on a computational model
with a black-box oracle, as conventionally used for studying query complexity
in computational complexity theory. With this framework, we derive an upper
bound of energy consumption of quantum computation with covering all costs,
including those of initialization, control, and quantum error correction; in
particular, our analysis shows an energy-consumption bound for a finite-step
Landauer-erasure protocol, progressing beyond the existing asymptotic bound. We
also develop techniques for proving a lower bound of energy consumption of
classical computation based on the energy-conservation law and the
Landauer-erasure bound; significantly, our lower bound can be gapped away from
zero no matter how energy-efficiently we implement the computation and is free
from the computational hardness assumptions. Based on these general bounds, we
rigorously prove that quantum computation achieves an exponential
energy-consumption advantage over classical computation for Simon's problem.
These results provide a fundamental framework and techniques to explore the
physical meaning of quantum advantage in the query-complexity setting based on
energy consumption, opening an alternative way to study the advantages of
quantum computation.Comment: 36 pages, 3 figure
On the Probabilistic Query Complexity of Transitively Symmetric Problems
We obtain optimal lower bounds on the nonadaptive probabilistic query complexity of a class of problems defined by a rather weak symmetry condition. In fact, for each problem in this class, given a number T of queries we compute exactly the performance (i.e., the probability of success on the worst instance) of the best nonadaptive probabilistic algorithm that makes T queries. We show that this optimal performance is given by a minimax formula involving certain probability distributions. Moreover, we identify two classes of problems for which adaptivity does not help. We illustrate these results on a few natural examples, including unordered search, Simon's problem, distinguishing one-to-one functions from two-to-one functions, and hidden translation. For these last three examples, which are of particular interest in quantum computing, the recent theorems of Aaronson, of Laplante and Magniez, and of Bar-Yossef, Kumar and Sivakumar on the probabilistic complexity of black-box problems do not yield any nonconstant lower bound
Quantum Algorithms for Attacking Hardness Assumptions in Classical and Post‐Quantum Cryptography
In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post-quantum secure cryptosystems. The authors provide details on the cost of the quantum algorithms presented in this survey. The authors furthermore discuss ongoing research directions that can impact quantum cryptanalysis in the future
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