Related papers: Optimized Amplitude Amplification for Quantum Stat…
The initialization of quantum states or Quantum State Preparation (QSP) is a basic subroutine in quantum algorithms. In the worst case, general QSP algorithms are expensive due to the application of multi-controlled gates required to build…
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin…
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$,…
A simple method is proposed to prepare conveniently the effective pure state |00...0><0...00| with any number of qubits in a quantum ensemble. The preparation is based on the temporal averaging (Knill, Chuang, and Laflamme, Phys.Rev.A 57,…
Quantum state preparation involving a uniform superposition over a non-empty subset of $n$-qubit computational basis states is an important and challenging step in many quantum computation algorithms and applications. In this work, we…
The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by…
In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently…
Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical…
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…
In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum…
We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of…
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
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…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Quantum state preparation is a fundamental primitive in quantum algorithms for encoding classical data into quantum amplitudes. We compare the cost of preparing general $n$-qubit states with real amplitudes using two common paradigms:…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
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=…