{"paper":{"title":"Power of Uninitialized Qubits in Shallow Quantum Circuits","arxiv_id":"1608.07020","primary_cat":"quant-ph","submitted_at":"2016-08-25T05:48:44+00:00","version_compiled":"v3"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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time.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.24,"quantitative":true,"quantitative_p":0.69,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.95,"id":"s2","own":true,"role":"result","text":"Then, we regard such a circuit as an oracle and show that a polynomial-time classical algorithm with the oracle can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on $n$ qubits.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.6,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.95,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":3,"p":1.0,"id":"s3","own":true,"role":"interpretation","text":"Since it seems unlikely that these tasks can be done with only $O(\\log n)$ initialized ancillary qubits, our results give evidences that adding uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only $O(\\log n)$ initialized ancillary qubits.","hedge":{"p":0.93,"label":"hedged_possibility"},"own_p":0.59,"main_claim_p":0.72,"quantitative":true,"quantitative_p":0.89,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":1.0}},{"i":4,"p":0.6,"id":"s4","own":true,"role":"limitation","text":"Lastly, to understand the limitations of uninitialized ancillary qubits, we focus on near-logarithmic-depth quantum circuits with them and show the impossibility of computing the parity function on $n$ 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