Related papers: BQP and the Polynomial Hierarchy
We present a new method for solving the hidden polynomial graph problem (HPGP) which is a special case of the hidden polynomial problem (HPP). The new approach yields an efficient quantum algorithm for the bivariate HPGP even when the input…
The idea of the quantum computation is based on paradoxical principles of quantum physics, superposition and entanglement of quantum states. This idea looks well-founded on the microscopic level in spite of the absence of an universally…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the…
We consider the problems arising from the presence of Byzantine servers in a quantum private information retrieval (QPIR) setting. This is the first work to precisely define what the capabilities of Byzantine servers could be in a QPIR…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to…
Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here,…
The computational abilities of theories within the generalised probabilistic theory framework has been the subject of much recent study. Such investigations aim to gain an understanding of the possible connections between physical…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer.…
We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that…
The set equality problem is to tell whether two sets $A$ and $B$ are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any $\omega(1)$…