50 citations · 140 across the 23 of their papers we have counts for
29 papers
Exponential Correlation Bounds for Polynomials
Eshan Chattopadhyay, Pooya Hatami, Chin Ho Lee +3
We prove that the XOR of majorities on disjoint blocks of bits has correlation at most with every Boolean-valued degree- polynomial over an arbit…
Does Not Relativize
Adam Bouland, Andrew Huang, Anand Natarajan +2
We construct an oracle relative to which , resolving a long-standing open question in quantum complexity theory. Together with recent work d…
Unconditional Certified Randomness without Structure
Andrea Coladangelo, Dakshita Khurana, Saachi Mutreja +3
We obtain a certified randomness protocol in the quantum random oracle model. The protocol is non-interactive and publicly verifiable with a classical verifier, and is based on Yam…
Certified Randomness without Structure Against Shallow-Query Adversaries
Dakshita Khurana, Bhaskar Roberts, Avishay Tal
In a recent breakthrough, Yamakawa and Zhandry (J. ACM 2024) constructed a proof of quantumness in the quantum random oracle model (QROM) in which the quantum prover samples a code…
Quantum Advantage in Tolerant Junta Testing
Avishay Tal, Weiqiang Yuan
We establish the first super-polynomial quantum advantage for the tolerant junta testing problem in the adaptive setting. Specifically, we show that within a certain parameter regi…
A Relativizing MIP for BQP
Scott Aaronson, Anand Natarajan, Avishay Tal +1
Complexity class containments involving interactive proof classes are famously nonrelativizing: although , Fortnow and Sipser showed that that there…
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…
Quantum-Computable One-Way Functions without One-Way Functions
William Kretschmer, Luowen Qian, Avishay Tal
We construct a classical oracle relative to which but quantum-computable quantum-secure trapdoor one-way functions exist. This is a substantial strengthe…
The Power of Adaptivity in Quantum Query Algorithms
Uma Girish, Makrand Sinha, Avishay Tal +1
Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where the depth corresponds to the number of adapti…
Tight Time-Space Lower Bounds for Constant-Pass Learning
Xin Lyu, Avishay Tal, Hongxun Wu +1
In his breakthrough paper, Raz showed that any parity learning algorithm requires either quadratic memory or an exponential number of samples [FOCS'16, JACM'19]. A line of work tha…
Fourier Growth of Communication Protocols for XOR Functions
Uma Girish, Makrand Sinha, Avishay Tal +1
The level- -Fourier weight of a Boolean function refers to the sum of absolute values of its level- Fourier coefficients. Fourier growth refers to the growth of these…
Quantum Cryptography in Algorithmica
William Kretschmer, Luowen Qian, Makrand Sinha +1
We construct a classical oracle relative to which yet single-copy secure pseudorandom quantum states exist. In the language of Impagliazzo's five worlds,…
On Certified Randomness from Fourier Sampling or Random Circuit Sampling
Roozbeh Bassirian, Adam Bouland, Bill Fefferman +2
Certified randomness has a long history in quantum information, with many potential applications. Recently Aaronson (2018, 2020) proposed a novel public certified randomness protoc…
Junta Distance Approximation with Sub-Exponential Queries
Vishnu Iyer, Avishay Tal, Michael Whitmeyer
Leveraging tools of De, Mossel, and Neeman [FOCS, 2019], we show two different results pertaining to the \emph{tolerant testing} of juntas. Given black-box access to a Boolean func…
Fourier Growth of Parity Decision Trees
Uma Girish, Avishay Tal, Kewen Wu
We prove that for every parity decision tree of depth on variables, the sum of absolute values of Fourier coefficients at level is at most $d^{\ell/2} \cdot O(\ell \…
Shrinkage under Random Projections, and Cubic Formula Lower Bounds for
Yuval Filmus, Or Meir, Avishay Tal
Håstad showed that any De Morgan formula (composed of AND, OR and NOT gates) shrinks by a factor of under a random restriction…
Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem
Scott Aaronson, Shalev Ben-David, Robin Kothari +2
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function , : The degree of…
Rigid Matrices From Rectangular PCPs
Amey Bhangale, Prahladh Harsha, Orr Paradise +1
We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned…
Quantum Implications of Huang's Sensitivity Theorem
Scott Aaronson, Shalev Ben-David, Robin Kothari +1
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function , the deterministic query complexity, , is at most quartic in the quantum que…
Towards Optimal Separations between Quantum and Randomized Query Complexities
Avishay Tal
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and oth…
Quantum versus Randomized Communication Complexity, with Efficient Players
Uma Girish, Ran Raz, Avishay Tal
We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense tha…
Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits
Adam Bene Watts, Robin Kothari, Luke Schaeffer +1
Recently, Bravyi, Gosset, and König (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth…
Pseudorandom Generators for Width-3 Branching Programs
Raghu Meka, Omer Reingold, Avishay Tal
We construct pseudorandom generators of seed length that -fool ordered read-once branching programs (ROBPs) of width and length . For…
Extractor-Based Time-Space Lower Bounds for Learning
Sumegha Garg, Ran Raz, Avishay Tal
A matrix corresponds to the following learning problem: An unknown element is chosen uniformly at random. A learner tries to learn $x…