The Space Just Above One Clean Qubit
Dale Jacobs, Saeed Mehraban

TL;DR
This paper introduces the BQP model, a quantum computational framework that generalizes DQC1, demonstrating it can perform many exponential speed-up algorithms but also has limitations similar to DQC1.
Contribution
The paper characterizes the computational power of the BQP model, showing it can simulate several key quantum algorithms and establishing its limitations compared to BQP.
Findings
BQP can simulate IQP, Deutsch-Jozsa, Bernstein-Vazirani, Simon's problem, and period finding.
BQP can solve Order Finding and Factoring outside of oracles.
BQP cannot distinguish unitaries close in trace distance and cannot achieve Grover's quadratic speedup.
Abstract
Consider the model of computation where we start with two halves of a -qubit maximally entangled state. We get to apply a universal quantum computation on one half, measure both halves at the end, and perform classical postprocessing. This model, which we call BQP, was defined in STOC 2017 [ABKM17] to capture the power of permutational computations on special input states. As observed in [ABKM17], this model can be viewed as a natural generalization of the one-clean-qubit model (DQC1) where we learn the content of a high entropy input state only after the computation is completed. An interesting open question is to characterize the power of this model, which seems to sit nontrivially between DQC1 and BQP. In this paper, we show that despite its limitations, this model can carry out many well-known quantum computations that are candidates for exponential speed-up over…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Theories · Relativity and Gravitational Theory
