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We present a quantum algorithm for adiabatic state preparation on agate-based quantum computer, with complexity polylogarithmic in the inverseerror. Our algorithm digitally simulates the adiabatic evolution between twoself-adjoint operators $H_0$ and $H_1$, exponentially suppressing the diabaticerror by harnessing the theoretical concept of quasi-adiabatic continuation asan algorithmic tool. Given an upper bound $\alpha$ on $\|H_0\|$ and $\|H_1\|$along with the promise that the $k$th eigenstate $|\psi_k(s)\rangle$ of $H(s)\equiv (1-s)H_0 + sH_1$ is separated from the rest of the spectrum by a gap ofat least $\gamma > 0$ for all $s \in [0,1]$, this algorithm implements anoperator $\widetilde{U}$ such that $\||\psi_k(1)\rangle -\widetilde{U}|\psi_k(s)\rangle\| \leq \epsilon$ using$O(\alpha^2/\gamma^2)\text{polylog}(\alpha/\gamma\epsilon)$ queries toblock-encodings of $H_0$ and $H_1$. In addition, we develop an algorithm thatis applicable only to ground states and requires multiple queries to an oraclethat prepares $|\psi_0(0)\rangle$, but has slightly better scaling in allparameters. We also show that the costs of both algorithms can be furtherreduced under certain reasonable conditions, such as when $\|H_1 - H_0\|$ issmall compared to $\alpha$, or when more information about the gap of $H(s)$ isavailable. For certain problems, the scaling can even be improved to linear in$\|H_1 - H_0\|/\gamma$ up to polylogarithmic factors.

Fast digital methods for adiabatic state preparation