23 research outputs found
Simulating Large Quantum Circuits on a Small Quantum Computer
Limited quantum memory is one of the most important constraints for near-term
quantum devices. Understanding whether a small quantum computer can simulate a
larger quantum system, or execute an algorithm requiring more qubits than
available, is both of theoretical and practical importance. In this Letter, we
introduce cluster parameters and of a quantum circuit. The tensor
network of such a circuit can be decomposed into clusters of size at most
with at most qubits of inter-cluster quantum communication. We propose a
cluster simulation scheme that can simulate any -clustered quantum
circuit on a -qubit machine in time roughly , with further
speedups possible when taking more fine-grained circuit structure into account.
We show how our scheme can be used to simulate clustered quantum systems --
such as large molecules -- that can be partitioned into multiple significantly
smaller clusters with weak interactions among them. By using a suitable
clustered ansatz, we also experimentally demonstrate that a quantum variational
eigensolver can still achieve the desired performance for estimating the energy
of the BeH molecule while running on a physical quantum device with half
the number of required qubits.Comment: Codes are available at https://github.com/TianyiPeng/Partiton_VQ
Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
Lie-Trotter-Suzuki decompositions are an efficient way to approximate
operator exponentials when is a sum of (non-commuting)
terms which, individually, can be exponentiated easily. They are employed in
time-evolution algorithms for tensor network states, digital quantum simulation
protocols, path integral methods like quantum Monte Carlo, and splitting
methods for symplectic integrators in classical Hamiltonian systems. We provide
optimized decompositions up to order . The leading error term is expanded
in nested commutators (Hall bases) and we minimize the 1-norm of the
coefficients. For terms, several of the optima we find are close to those
in McLachlan, SlAM J. Sci. Comput. 16, 151 (1995). Generally, our results
substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida,
and Suzuki. We explain why these decompositions are sufficient to efficiently
simulate any one- or two-dimensional lattice model with finite-range
interactions. This follows by solving a partitioning problem for the
interaction graph.Comment: 30 pages, 8 figures, 8 tables; added results, figures, and
references, extended discussio