13 papers
Optimal Lower Bound for Ground-State Energy Estimation with a Guiding State
Rolando D. Somma, Ronald de Wolf
The guided Hamiltonian problem is the following: given access to the unitary for some Hamiltonian , and given access to a unitary that prepares a guiding state promi…
Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Sophia Simon, Dominic W. Berry, Rolando D. Somma
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond.…
Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders
Vishnu Iyer, Siddhartha Jain, Stephen Jordan +1
We present efficient quantum circuits that implement high-dimensional unitary irreducible representations (irreps) of , where is constant. For dimension and er…
Efficient Quantum Hermite Transform
Siddhartha Jain, Vishnu Iyer, Rolando D. Somma +2
We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inver…
Optimal quantum simulation of linear non-unitary dynamics
Guang Hao Low, Rolando D. Somma
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator with non-positive logarithmic norm, thereby serving as a nat…
Quantum algorithm for linear matrix equations
Rolando D. Somma, Guang Hao Low, Dominic W. Berry +1
We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B, and C are given complex matrices and X is unknown. This is known as the Sylve…