Compilation by stochastic Hamiltonian sparsification

@article{Ouyang2019CompilationBS,
  title={Compilation by stochastic Hamiltonian sparsification},
  author={Yingkai Ouyang and David R. White and Earl T. Campbell},
  journal={Quantum},
  year={2019},
  volume={4},
  pages={235}
}
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme… 

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References

SHOWING 1-10 OF 49 REFERENCES

Random Compiler for Fast Hamiltonian Simulation.

A randomized compiler for Hamiltonian simulation where gate probabilities are proportional to the strength of a corresponding term in the Hamiltonian, especially suited to electronic structure Hamiltonians relevant to quantum chemistry.

Optimal Hamiltonian Simulation by Quantum Signal Processing.

It is argued that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation.

Phase estimation with randomized Hamiltonians

Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an

Time-dependent Hamiltonian simulation with $L^1$-norm scaling

Two new techniques are introduced: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrodinger equation that is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation.

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H.

Exponential improvement in precision for simulating sparse Hamiltonians

The algorithm is based on a significantly improved simulation of the continuous- and fractional- query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error.

Simulation of electronic structure Hamiltonians using quantum computers

Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However,

On the Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation

It is argued that chemical properties, such as the maximum nuclear charge in a molecule and the filling fraction of orbitals, can be decisive for determining the cost of a quantum simulation.

Faster quantum simulation by randomization

By simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation for product formulas of any given order, and thereby give more efficient simulations of Hamiltonian dynamics.

Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers

This work presents a measurement strategy based on a low-rank factorization of the two-electron integral tensor that provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems.