Scott Aaronson
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View article: Wide Neural Networks as a Baseline for the Computational No-Coincidence Conjecture
Wide Neural Networks as a Baseline for the Computational No-Coincidence Conjecture Open
We establish that randomly initialized neural networks, with large width and a natural choice of hyperparameters, have nearly independent outputs exactly when their activation function is nonlinear with zero mean under the Gaussian measure…
View article: Demonstrating an unconditional separation between quantum and classical information resources
Demonstrating an unconditional separation between quantum and classical information resources Open
A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum system…
View article: Future of Quantum Computing
Future of Quantum Computing Open
On Tuesday 26th November 2024, four discussants participated in a moderated virtual panel titled Future of Quantum Computing as one session of the 8th International Conference on Quantum Techniques in Machine Learning hosted by the Univers…
View article: Certified randomness using a trapped-ion quantum processor
Certified randomness using a trapped-ion quantum processor Open
View article: Generalised Linial-Nisan Conjecture Is False for DNFs
Generalised Linial-Nisan Conjecture Is False for DNFs Open
Aaronson (STOC 2010) conjectured that almost k-wise independence fools constant-depth circuits; he called this the generalised Linial-Nisan conjecture. Aaronson himself later found a counterexample for depth-3 circuits. We give here an imp…
View article: The profile of symptom change with Transcranial Magnetic Stimulation for Major Depressive Disorder
The profile of symptom change with Transcranial Magnetic Stimulation for Major Depressive Disorder Open
View article: The impact of treatment gaps on effectiveness of Transcranial Magnetic Stimulation in Major Depressive Disorder
The impact of treatment gaps on effectiveness of Transcranial Magnetic Stimulation in Major Depressive Disorder Open
View article: How much to give and when to give again: Dosing the acute TMS course and retreatment following relapse
How much to give and when to give again: Dosing the acute TMS course and retreatment following relapse Open
View article: Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries
Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries Open
In this paper we study a quantum version of the multiparty simultaneous message-passing (SMP) model, and we show that in some cases, quantum communication can replace public randomness, even with no entanglement between the parties. This w…
View article: Comparison of the PHQ-9 and QIDS-SR in assessing the antidepressant effects of Transcranial Magnetic Stimulation: sensitivity to change
Comparison of the PHQ-9 and QIDS-SR in assessing the antidepressant effects of Transcranial Magnetic Stimulation: sensitivity to change Open
View article: The impact of TMS on symptomatology in Major Depressive Disorder: What is being changed?
The impact of TMS on symptomatology in Major Depressive Disorder: What is being changed? Open
View article: Improved separation between quantum and classical computers for sampling and functional tasks
Improved separation between quantum and classical computers for sampling and functional tasks Open
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with po…
View article: On verifiable quantum advantage with peaked circuit sampling
On verifiable quantum advantage with peaked circuit sampling Open
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical computati…
View article: PDQMA = DQMA = NEXP: QMA With Hidden Variables and Non-collapsing Measurements
PDQMA = DQMA = NEXP: QMA With Hidden Variables and Non-collapsing Measurements Open
We define and study a variant of QMA (Quantum Merlin Arthur) in which Arthur can make multiple non-collapsing measurements to Merlin's witness state, in addition to ordinary collapsing measurements. By analogy to the class PDQP defined by …
View article: A Qubit, a Coin, and an Advice String Walk into a Relational Problem
A Qubit, a Coin, and an Advice String Walk into a Relational Problem Open
Relational problems (those with many possible valid outputs) are different from decision problems, but it is easy to forget just how different. This paper initiates the study of FBQP/qpoly, the class of relational problems solvable in quan…
View article: Testing GPT-4 with Wolfram Alpha and Code Interpreter plug-ins on math and science problems
Testing GPT-4 with Wolfram Alpha and Code Interpreter plug-ins on math and science problems Open
This report describes a test of the large language model GPT-4 with the Wolfram Alpha and the Code Interpreter plug-ins on 105 original problems in science and math, at the high school and college levels, carried out in June-August 2023. O…
View article: Certified Randomness from Quantum Supremacy
Certified Randomness from Quantum Supremacy Open
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experime…
View article: An Automated Approach to the Collatz Conjecture
An Automated Approach to the Collatz Conjecture Open
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed binar…
View article: Discrete bulk reconstruction
Discrete bulk reconstruction Open
A bstract According to the AdS/CFT correspondence , the geometries of certain spacetimes are fully determined by quantum states that live on their boundaries — indeed, by the von Neumann entropies of portions of those boundary states. This…
View article: Certified Randomness from Quantum Supremacy
Certified Randomness from Quantum Supremacy Open
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experime…
View article: A Prospective, Multi-center Randomized, Controlled, Blinded Trial of Vagus Verve Stimulation for Difficult to Treat Depression: the RECOVER Trial
A Prospective, Multi-center Randomized, Controlled, Blinded Trial of Vagus Verve Stimulation for Difficult to Treat Depression: the RECOVER Trial Open
Introduction: Therapeutic Vagus Nerve Stimulation (VNS) has been FDA-approved for treatment-resistant depression (TRD). In 2007, the US Centers for Medicare and Medicaid Services (CMS) issued a non-coverage decision, making access difficul…
View article: Dosing Transcranial Magnetic Stimulation: Efficacy in Major Depressive Disorder as a function of number of treatment sessions
Dosing Transcranial Magnetic Stimulation: Efficacy in Major Depressive Disorder as a function of number of treatment sessions Open
View article: Efficient Tomography of Non-Interacting-Fermion States
Efficient Tomography of Non-Interacting-Fermion States Open
We give an efficient algorithm that learns a non-interacting-fermion state, given copies of the state. For a system of n non-interacting fermions and m modes, we show that O(m³ n² log(1/δ) / ε⁴) copies of the input state and O(m⁴ n² log(1/…
View article: Discrete Bulk Reconstruction
Discrete Bulk Reconstruction Open
According to the AdS/CFT correspondence, the geometries of certain spacetimes are fully determined by quantum states that live on their boundaries -- indeed, by the von Neumann entropies of portions of those boundary states. This work inve…
View article: How Much Structure Is Needed for Huge Quantum Speedups?
How Much Structure Is Needed for Huge Quantum Speedups? Open
I survey, for a general scientific audience, three decades of research into which sorts of problems admit exponential speedups via quantum computers -- from the classics (like the algorithms of Simon and Shor), to the breakthrough of Yamak…
View article: Learning Distributions over Quantum Measurement Outcomes
Learning Distributions over Quantum Measurement Outcomes Open
Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography proc…
View article: A very preliminary analysis of DALL-E 2
A very preliminary analysis of DALL-E 2 Open
The DALL-E 2 system generates original synthetic images corresponding to an input text as caption. We report here on the outcome of fourteen tests of this system designed to assess its common sense, reasoning and ability to understand comp…
View article: Open Problems Related to Quantum Query Complexity
Open Problems Related to Quantum Query Complexity Open
I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA and BQP versus IP , to time/space tradeoffs for collision and element distinctness, to polynomial degre…
View article: The Acrobatics of BQP
The Acrobatics of BQP Open
One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the behavi…
View article: Degree vs. approximate degree and Quantum implications of Huang’s sensitivity theorem
Degree vs. approximate degree and Quantum implications of Huang’s sensitivity theorem Open
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, $\bullet \quad \mathrm{deg}(f) = O(\widetilde{\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$.…