Related papers: Superlinear Amplitude Amplification
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we…
In recent years, quantum-enhanced machine learning has emerged as a particularly fruitful application of quantum algorithms, covering aspects of supervised, unsupervised and reinforcement learning. Reinforcement learning offers numerous…
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with…
Linear quantum amplifiers are indispensable tools for quantum technologies, yet their performance is fundamentally limited by quantum noise, precluding any signal-to-noise ratio (SNR) enhancement unless supplemented by post-selection or…
Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires…
A universal deterministic noiseless quantum amplifier has been shown to be impossible. However, probabilistic noiseless amplification of a certain set of states is physically permissible. Regarding quantum state amplification as quantum…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation…
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory…
We introduce the Real Quantum Amplitude Estimation (RQAE) algorithm, an extension of Quantum Amplitude Estimation (QAE) which is sensitive to the sign of the amplitude. RQAE is an iterative algorithm which offers explicit control over the…
Quantum amplitude amplification and quantum phase estimation are two fundamental quantum algorithms. All known quantum algorithms are derived from these two algorithms. Even the adiabatic quantum algorithms can also be efficiently simulated…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
Amplitude amplification provides a quadratic speed-up for an array of quantum algorithms when run on a quantum machine perfectly isolated from its environment. However, the advantage is substantially diminished as the NISQ-era quantum…
It is a fundamental principle of quantum theory that an unknown state cannot be copied or, as a consequence, an unknown optical signal cannot be amplified deterministically and perfectly. Here we describe a protocol that provides…
The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the…
Principal component analysis is a multivariate statistical method frequently used in science and engineering to reduce the dimension of a problem or extract the most significant features from a dataset. In this paper, using a similar notion…