Ran Raz

We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$

by a single quantum state $|\Psi \rangle$ of size $O(n)$ qubits,

such that:

for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$,

the values of the bits $a_{i_1},...,a_{i_k}$ can be retrieved

from $|\Psi \rangle$ by a one-round Arthur-Merlin interactive ...
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Scott Aaronson

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number of measurements that grows only linearly with n. Besides possible ... more >>>

Scott Aaronson

This mini-course will introduce participants to an exciting frontier for quantum computing theory: namely, questions involving the computational complexity of preparing a certain quantum state or applying a certain unitary transformation. Traditionally, such questions were considered in the context of the Nonabelian Hidden Subgroup Problem and quantum interactive proof systems, ... more >>>

Scott Aaronson

We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within additive error $\varepsilon$, for each of the $M$ measurements. How many copies of $\rho$ are needed to achieve this, ... more >>>

Scott Aaronson

We show that combining two different hypothetical enhancements to quantum computation---namely, quantum advice and non-collapsing measurements---would let a quantum computer solve any decision problem whatsoever in polynomial time, even though neither enhancement yields extravagant power by itself. This complements a related result due to Raz. The proof uses locally decodable ... more >>>

Kai-Min Chung, Siyao Guo, Qipeng Liu, Luowen Qian

In function inversion, we are given a function $f: [N] \mapsto [N]$, and want to prepare some advice of size $S$, such that we can efficiently invert any image in time $T$. This is a well studied problem with profound connections to cryptography, data structures, communication complexity, and circuit lower ... more >>>