Efficient Quantum State Synthesis with One Query
Abstract
We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially close approximation of $|\psi\rangle$. Previous algorithms for this problem either used a linear number of queries and polynomial time, or a constant number of queries and polynomially many ancillae but no nontrivial bound on the runtime. As corollaries we do the following: - We simplify the proof that statePSPACE $\subseteq$ stateQIP (a quantum state analogue of PSPACE $\subseteq$ IP) and show that a constant number of rounds of interaction suffices. - We show that QAC$\mathsf{_f^0}$ lower bounds for constructing explicit states would imply breakthrough circuit lower bounds for computing explicit boolean functions. - We prove that every $n$-qubit state can be constructed to within 0.01 error by an $O(2^n/n)$-size circuit over an appropriate finite gate set. More generally we give a size-error tradeoff which, by a counting argument, is optimal for any finite gate set.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- 10.48550/arXiv.2306.01723
- arXiv:
- arXiv:2306.01723
- Bibcode:
- 2023arXiv230601723R
- Keywords:
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- Quantum Physics;
- Computer Science - Computational Complexity
- E-Print:
- 40 pages, 2 figures