Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific com...
Thomas Joachim Friese, Özgün Kum, A. Harrow et al.· 0 citations
In the quantum linear systems problem (QLSP), we are given query access to a $d$-sparse $N\times N$ matrix $A$ with condition number $\kappa$, and the ability to prepare a quantum state proportional to a vector $\vec b$. The goal is to output an $\epsilon$-approximation to the quantum state proportional to the solution...
Carlos Bravo-Prieto, A. Harrow, Robin Kothari· 2 citations· ⚡1
This work suggests that for many physical systems, gate count must scale polynomially in $1/\epsilon$, contrary to the complexity suggested by counting coherent oracle queries such as those in the block-encoding model.
Alexander Zlokapa, Richard R. Allen, A. Harrow· 3 citations
We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the...
Anurag Anshu, Shankar Balasubramanian, Jonas Haferkamp et al.· 2 citations· ⚡1
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