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Scholarship at Harvard
WHAT IS DASH?
DASH is the central, open-access institutional repository of research by members of the Harvard community. Harvard Library Open Scholarship and Research Data Services (OSRDS) operates DASH to provide the broadest possible access to Harvard's scholarship. This repository hosts a wide range of Harvard-affiliated scholarly works, including pre- and post-refereed journal articles, conference proceedings, theses and dissertations, working papers, and reports.
[More about DASH](https://harvardwiki.atlassian.net/wiki/external/ZDU2MTE5YjllNGRkNGQwMmEyYzRjZTBkYWE1MDk0Mzg)
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Publication
[American Jewish Physicians and a Biological basis for Jewishness from the 19th to the 21st Century](/entities/publication/272b3a49-111c-4f44-aa55-29fd33324eb1)
(2025-02-20) Satin, David; Alon, Leigh
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[On the Computational Power of QAC0 with Barely Superlinear Ancillae](/entities/publication/35b9ee21-213d-4864-b062-9247f01ddbfc)
(2024-10-09) Anshu, Anurag; Dong, Yangjing; Ou, Fenging; Yao, Penghui
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QAC0 is the family of constant-depth polynomial-size quantum circuits consisting of arbitrary single qubit unitaries and multi-qubit Toffoli gates. It was introduced by Moore \[arXiv: 9903046\] as a quantum counterpart of AC0, along with the conjecture that QAC0 circuits can not compute PARITY. In this work we make progress on this longstanding conjecture: we show that any depth-d QAC0 circuit requires n1+3−d ancillae to compute a function with approximate degree Θ(n), which includes PARITY, MAJORITY and MODk. We further establish superlinear lower bounds on quantum state synthesis and quantum channel synthesis. This is the first superlinear lower bound on the super-linear sized QAC0. Regarding PARITY, we show that any further improvement on the size of ancillae to n1+exp(−o(d)) would imply that PARITY ∉ QAC0. These lower bounds are derived by giving low-degree approximations to QAC0 circuits. We show that a depth-d QAC0 circuit with a ancillae, when applied to low-degree operators, has a degree (n+a)1−3−d polynomial approximation in the spectral norm. This implies that the class QLC0, corresponding to linear size QAC0 circuits, has approximate degree o(n). This is a quantum generalization of the result that LC0 circuits have approximate degree o(n) by Bun, Robin, and Thaler \[SODA 2019\]. Our result also implies that QLC0≠NC1.
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Publication
[UniqueQMA vs QMA: oracle separation and eigenstate thermalization hypothesis](/entities/publication/411cfdcd-8b27-495c-93dc-af2e7baae406)
(2024-10-31) Anshu, Anurag; Haferkamp, Jonas; Hwang, Yeongwoo; Nguyen, Quynh T.
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We study the long-standing open question of the power of unique witness in quantum protocols, which asks if UniqueQMA, a variant of QMA whose accepting witness space is 1-dimensional, is equal to QMA. We show a quantum oracle separation between UniqueQMA and QMA via an extension of the Aaronson-Kuperberg's QCMA vs QMA oracle separation. In particular, we show that any UniqueQMA protocol must make Ω(D−−√) queries to a subspace phase oracle of unknown dimension ≤D to "find" the subspace. This presents an obstacle to relativizing techniques in resolving this question (unlike its classical analogue - the Valiant-Vazirani theorem - which is essentially a black-box reduction) and suggests the need to study the structure of the ground space of local Hamiltonians in distilling a potential unique witness. Our techniques also yield a quantum oracle separation between QXC, the class characterizing quantum approximate counting, and QMA. Very few structural properties are known that place the complexity of local Hamiltonians in UniqueQMA. We expand this set of properties by showing that the ground energy of local Hamiltonians that satisfy the eigenstate thermalization hypothesis (ETH) can be estimated through a UniqueQMA protocol. Specifically, our protocol can be viewed as a quantum expander test in a low energy subspace of the Hamiltonian and verifies a unique entangled state in two copies of the subspace. This allows us to conclude that if UniqueQMA ≠ QMA, then QMA-hard Hamiltonians must violate ETH under adversarial perturbations (more accurately, under the quantum PCP conjecture if ETH only applies to extensive energy subspaces). Our results serve as evidence that chaotic local Hamiltonians, such as the SYK model, contain polynomial verifiable quantum states in their low energy regime and may be simpler than general local Hamiltonians if UniqueQMA ≠ QMA.
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Publication
[Learning Shallow Quantum Circuits](/entities/publication/033297fb-060a-4cce-916f-6dc844bb3235)
(Association for Computing Machinery, 2024-06-11) Huang, Hsin-Yuan; Anshu, Anurag; Liu, Yunchao; Broughton, Michael; Kim, Isaac; Landau, Zeph; McClean, Jarrod R.
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Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions that are classically hard to sample from, existing learning algorithms do not apply. In this work, we present a polynomial-time classical algorithm for learning the description of any unknown n-qubit shallow quantum circuit U (with arbitrary unknown architecture) within a small diamond distance using single-qubit measurement data on the output states of U. We also provide a polynomial-time classical algorithm for learning the description of any unknown n-qubit state | ψ ⟩ = U | 0n ⟩ prepared by a shallow quantum circuit U (on a 2D lattice) within a small trace distance using single-qubit measurements on copies of | ψ ⟩. Our approach uses a quantum circuit representation based on local inversions and a technique to combine these inversions. This circuit representation yields an optimization landscape that can be efficiently navigated and enables efficient learning of quantum circuits that are classically hard to simulate.
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Publication
[Stimulating Clean Hydrogen Demand: The Current Landscape](/entities/publication/53a4dadc-ccda-4ec5-aedf-87bbb90d197c)
(Belfer Center for Science and International Affairs, 2025-02) Mural, Rachel; Floyd, Matt; Berns, Sebastian; Takahashi, Ai
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Hydrogen is expected to play an important role in the global energy transition as a chemical feedstock and fuel; when produced with renewable energy, hydrogen offers a means of decarbonizing hard-to-abate industrial processes and the heavy transportation sector.1 To support market growth, current hydrogen programs aim to expand clean2 (also called “green”) hydrogen production by providing substantial subsidies in the form of supply-side funding and tax incentives. In 2023, global public investments in clean hydrogen reached $308 billion, with the vast bulk of funding allocated to production-side support.3 While worldwide clean hydrogen production targets4 reached 27-35 megatons (Mt) in 2023, demand targets have stalled at just 14 Mt.5 This trend reflects regional asymmetries in production and demand uptake. Under current projections, demand for renewable hydrogen in Europe is expected to hit 8.5 Mt by 2030, far behind the region’s planned 20 Mt of supply.6 Similarly, although the passage of the United States’ (U.S.) Inflation Reduction Act (IRA) in 2022 spurred an explosion of announced clean hydrogen projects, project offtake has lagged behind policy ambition. Supply-side incentives alone are insufficient to build robust markets for clean hydrogen; therefore, stakeholders must investigate additional demand-side innovation policies to facilitate market growth and development. In the remainder of this brief, we summarize the hydrogen policy landscape in the United States and European Union (EU), concluding with an examination of the causes of demand-side stagnation in the clean hydrogen market.
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