Related papers: Block encoding of matrix product operators
Efficient block encoding of many-body Hamiltonians is a central requirement for quantum algorithms in scientific computing, particularly in the early fault-tolerant era. In this work, we introduce new explicit constructions for block…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Image processing is one of the most promising applications for quantum machine learning (QML). Quanvolutional Neural Networks with non-trainable parameters are the preferred solution to run on current and near future quantum devices. The…
The information of quantum pathways can be extracted in the framework of the Hamiltonian-encoding and Observable-decoding method. For closed quantum systems, only off-diagonal elements of the Hamiltonian in the Hilbert space is required to…
Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian…
Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical…
Isometry operations encode the quantum information of the input system to a larger output system, while the corresponding decoding operation would be an inverse operation of the encoding isometry operation. Given an encoding operation as a…
We present a protocol for encoding $N$ real numbers stored in $N$ memory registers into the amplitudes of the quantum superposition that describes the state of $\log_2N$ qubits. This task is one of the main steps in quantum machine learning…
With the development of quantum hardware bringing the error-corrected quantum circuits to the near future, the lack of an efficient polynomial-time decoding algorithms for logical circuits presents a critical bottleneck. While quantum…
Exponentiation of Hamiltonians refers to a mathematical operation to a Hamiltonian operator, typically in the form e^(-i.t.H), where H is the Hamiltonian and t is a time parameter. This operation is fundamental in quantum mechanics,…
Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components…
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…
We describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action…
Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state $\rho$, QSP enables the evaluation of nonlinear functions of the form…
As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of $n$-variable Boolean…
In recent years, quantum Boltzmann methods have gained more and more interest as they might provide a viable path towards solving fluid dynamics problems on quantum computers once this emerging compute technology has matured and…
Here, we numerically simulate probabilistic elementary entangling operations between rail-encoded photons for the purpose of scalable universal quantum computation or communication. We propose grouping logical qubits into single-photon…
This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and…
Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a…