Papers › Hamiltonian Simulation by Qubitization
Hamiltonian Simulation by Qubitization
Guang Hao Low, Isaac L. Chuang
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We present the problem of approximating the time-evolution operator e^(-iĤt) to error ϵ, where the Hamiltonian Ĥ=(⟨G|⊗ℐ̂)Û(|G⟩⊗ℐ̂) is the projection of a unitary oracle Û onto the state |G⟩ created by another unitary oracle. Our algorithm solves this with a query complexity 𝒪(t+log(1/ϵ)) to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are d-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where Ĥ is a density matrix. A key technical result is `qubitization', which uses the controlled version of these oracles to embed any Ĥ in an invariant SU(2) subspace. A large class of operator functions of Ĥ can then be computed with optimal query complexity, of which e^(-iĤt) is a special case.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections