Related papers: Complexity-Theoretic Limitations on Quantum Algori…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
We introduce a new methodology to characterize properties of quantum spacetime in a strongly quantum-fluctuating regime, using tools from topological data analysis. Starting from a microscopic quantum geometry, generated nonperturbatively…
Quantum algorithms for topological data analysis provide significant advantage over the best classical algorithm. Different from the previous simplical complex on points cloud, the GLMY homology introduced by Alexander Grigor'yan, Yong Lin,…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
Since Harrow, Hassidim, and Lloyd (2009) showed that a system of linear equations with $N$ variables and condition number $\kappa$ can be solved on a quantum computer in $\operatorname{poly}(\log(N), \kappa)$ time, exponentially faster than…
Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…
We looked into the algorithm for calculating Betti numbers presented by Lloyd, Garnerone, and Zanardi (LGZ). We present a new algorithm in the same spirit as LGZ with the intent of clarifying quantum algorithms for computing Betti numbers.…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their…
It has been shown that the apparent advantage of some quantum machine learning algorithms may be efficiently replicated using classical algorithms with suitable data access -- a process known as dequantization. Existing works on…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Given a large dataset of many tuples, it is hard for users to pick out their preferred tuples. Thus, the preference query problem, which is to find the most preferred tuples from a dataset, is widely discussed in the database area. In this…
Topological data analysis (TDA) delivers invaluable and complementary information on the intrinsic properties of data inaccessible to conventional methods. However, high computational costs remain the primary roadblock hindering the…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…