Related papers: Quantum algorithms for Uhlmann transformation
Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one…
The curvelet transform is a directional wavelet transform over R^n, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I…
While the no-cloning theorem forbids the perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can take…
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…
Quantum information theory is a multidisciplinary field whose objective is to understand what happens when information is stored in the state of a quantum system. Quantum mechanics provides us with a new resource, called quantum…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction…
We propose efficient algorithms with logarithmic step complexities for the generation of entangled $GHZ_N$ and $W_N$ states useful for quantum networks, and we demonstrate an implementation on the IBM quantum computer up to $N=16$. Improved…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
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…