5 papers · 1 filter
Improved Lower Bounds for QAC0
Malvika Raj Joshi, Avishay Tal, Francisca Vasconcelos +1
In this work, we prove the strongest known lower bounds for QAC, allowing polynomially many gates and ancillae. Our main results show that: (1) Depth-3 QAC circuits cannot…
Mixed state tomography reduces to pure state tomography
Angelos Pelecanos, Jack Spilecki, Ewin Tang +1
A longstanding belief in quantum tomography is that estimating a mixed state is far harder than estimating a pure state. This is borne out in the mathematics, where mixed state alg…
The debiased Keyl's algorithm: a new unbiased estimator for full state tomography
Angelos Pelecanos, Jack Spilecki, John Wright
In the problem of quantum state tomography, one is given copies of an unknown rank- mixed state and asked to produce an estimator of . In t…
Optimal lower bounds for quantum state tomography
Thilo Scharnhorst, Jack Spilecki, John Wright
We show that copies are necessary to learn a rank mixed state up to error in trace distance. This matches…
Haar random codes attain the quantum Hamming bound, approximately
Fermi Ma, Xinyu Tan, John Wright
We study the error correcting properties of Haar random codes, in which a -dimensional code space is chosen at random from the Haar distr…