Pseudo-Deterministic Quantum Algorithms
Hugo Aaronson | University of Cambridge
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions include the following complexity separations, which require new lower bound techniques specifically tailored to pseudo-determinism:
- We exhibit a problem, Avoid One Encrypted String (AOES), whose classical randomized query complexity is O(1) but is maximally hard for pseudo-deterministic quantum algorithms (Ω(N) query complexity).
- We exhibit a problem, Quantum-Locked Estimation (QL-Estimation), for which pseudo-deterministic quantum algorithms admit an exponential speed-up over classical pseudo-deterministic algorithms (O(log(N)) vs. Θ(√N)), while the randomized query complexity is O(1).
Complementing these separations, we show that for any total problem R, pseudo-deterministic quantum algorithms admit at most a quintic advantage over deterministic algorithms, i.e., D(R) = O˜(psQ(R)^5). On the algorithmic side, we identify a class of quantum search problems that can be made pseudo-deterministic with small overhead, including Grover search, element distinctness, triangle finding, k-sum, and graph collision.
Location
- QNC 3206
- Online on Zoom
- Meeting ID: 955 2636 6664
- Passcode: 419811
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