相关论文: Fast quantum algorithm for numerical gradient esti…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…
We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Quantum computing is fast evolving as a technology due to recent advances in hardware, software, as well as the development of promising applications. To use this technology for solving specific problems, a suitable quantum algorithm has to…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Gradient-based numerical methods are ubiquitous in optimization techniques frequently applied in industry to solve practical problems. Often times, evaluating the objective function is a complicated process, so estimating the gradient of a…
The $k$'th frequency moment of a sequence of integers is defined as $F_k = \sum_j n_j^k$, where $n_j$ is the number of times that $j$ occurs in the sequence. Here we study the quantum complexity of approximately computing the frequency…
Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…