We propose a simple method for simulating a general class of nonunitary dynamics as a
linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on …

We introduce a family of identities that express general linear non-unitary evolution
operators as a linear combination of unitary evolution operators, each solving a Hamiltonian …

We develop three new methods to implement any Linear Combination of Unitaries (LCU), a
powerful quantum algorithmic tool with diverse applications. While the standard LCU …

A number of exciting recent results have been seen in the field of quantum error correction.
These include initial demonstrations of error correction on current quantum hardware and …

The well-conditioned multi-product formula (MPF), proposed by [Low, Kliuchnikov, and
Wiebe, 2019], is a simple high-order time-independent Hamiltonian simulation algorithm that …

A major thrust in quantum algorithm development over the past decade has been the search
for the quantum algorithms that will deliver practical quantum advantage first. Today's …

Estimating the eigenstate properties of quantum many-body systems is a long-standing,
challenging problem for both classical and quantum computing. For the task of eigenstate …

Eigenvalue transformations, which include solving time-dependent differential equations as
a special case, have a wide range of applications in scientific and engineering computation …

Many promising quantum applications depend on the efficient quantum simulation of an
exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation …

We present a hybrid quantum-classical framework for simulating generic matrix functions
more amenable to early fault-tolerant quantum hardware than standard quantum singular …