Related papers: Generalized Quantum Singular Value Transformation
We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete/continuous-variable (qubit/qumode) hardware. To illustrate the oracle's representation-theoretic power and near-term…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
We present an efficient quantum circuit for block encoding pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle complex position, momentum and energy along a complex trajectory. On the basis of…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
We use one photon to simulate an n-qubit quantum system for the first time. We propose a new scheme to realize universal quantum computation in polynomial time O(n^5). A generating set of gates can be realized with high accuracy in the lab.…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
By encoding a qudit in a harmonic oscillator and investigating the d --> infinity limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject…
We report an experiment to demonstrate a quantum permutation determining algorithm with linear optical system. By employing photon polarization and spatial modes, we realize the quantum ququart states and all the essential permutation…
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that…