Related papers: On Arbitrary Phases in Quantum Amplitude Amplifica…
Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success…
This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle $U_\varphi$ on an eigenstate $|x\rangle$ is to apply a state-dependent…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…
Consider a Boolean function $\chi: X \to \{0,1\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A |0\rangle=…
We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase…
Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…
Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search…
Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1 - 5]. However, this fundamental noise penalty in amplification can be…
We present a general phase matching condition for the quantum search algorithm with arbitrary unitary transformation and arbitrary phase rotations. We show by an explicit expression that the phase matching condition depends both on the…
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which…
Amplitude filtering is concerned with identifying basis-states in a superposition whose amplitudes are greater than a specified threshold; probability filtering is defined analogously for probabilities. Given the scarcity of qubits, the…
Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still possible. When the…
Each iteration in Grover's original quantum search algorithm contains 4 steps: two Hadamard-Walsh transformations and two amplitudes inversions. When the inversion of the marked state is replaced by arbitrary phase rotation \theta and the…
For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the…
A deterministic quantum amplifier inevitably adds noise to an amplified signal due to the uncertainty principle in quantum physics. We here investigate how a quantum-noise-limited amplifier can be improved by additionally employing the…
We present two new quantum algorithms. Our first algorithm is a generalization of amplitude amplification to the case when parts of the quantum algorithm that is being amplified stop at different times. Our second algorithm uses the first…
We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more…
We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization)…
We combine lossless, phase-only transformations with fully-transmitting linear-optical scatterers to define the principle of linear-optical phase amplification. This enables a physical phase shift $\phi$ to be nonlinearly mapped to a new…
We propose novel coherent-state phase concentration by probabilistic measurement-induced ampli- fication. The amplification scheme uses novel architecture, thermal noise addition (instead of single photon addition) followed by feasible…