Related papers: A New Quantum Lower Bound Method, with Application…
We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product…
A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We…
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants…
The polynomial and the adversary methods are the two main tools for proving lower bounds on query complexity of quantum algorithms. Both methods have found a large number of applications, some problems more suitable for one method, some for…
The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the…
We show that quantum query complexity satisfies a strong direct product theorem. This means that computing $k$ copies of a function with less than $k$ times the quantum queries needed to compute one copy of the function implies that the…
Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discrete-time model of quantum computation, it also holds for continuous-time (or…
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and…
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…
In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target…
The quantum adversary method is a versatile method for proving lower bounds on quantum algorithms. It yields tight bounds for many computational problems, is robust in having many equivalent formulations, and has natural connections to…
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
This note complements the paper "One-Way Ticket to Las Vegas and the Quantum Adversary" (arxiv:2301.02003). I develop the ideas behind the adversary bound - universal algorithm duality therein in a different form, using the same perspective…
A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…
The direct product problem is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of k independent inputs scales with k. We prove the following direct product theorem…
We present general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Our results are based on the adversary method of Ambainis.
The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…