Related papers: Quantum singular value transformation without bloc…
A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of…
Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols…
Quantum computing can be used to speed up the simulation time (more precisely, the number of queries of the algorithm) for physical systems; one such promising approach is the Hamiltonian simulation (HS) algorithm. Recently, it was proven…
Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in…
Quantum measurement is a fundamental yet experimentally challenging ingredient of quantum information processing. Many recent studies on quantum dynamics focus on expectation values of nonlinear observables; however, their experimental…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy.…
We introduce a hybrid oscillator-qubit formulation of linear combination of Hamiltonian simulation (LCHS) for solving linear ordinary differential equations. Instead of representing the quadrature rule with a discrete-variable (DV) ancilla…
Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called…
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…
We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
The characterization of the evolution of a quantum system is one of the main tasks to accomplish to achieve quantum information processing. The standard quantum process tomography (SQPT) has the unique property that it can be applied…
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…
Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from…