4 Search Results for "Deshpande, Abhinav"

Document
DOI: 10.4230/LIPIcs.CCC.2026.38
Non-Clifford Gates Are Required for Long-Term Memory

Authors: Jon Nelson, Joel Rajakumar, and Michael J. Gullans

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
We show that all Clifford circuits under interspersed depolarizing noise lose memory of their input exponentially quickly in the depth of the circuit, even when given access to a supply of fresh qubits initialized in arbitrary states. This result applies only in the absence of intermediate measurements, i.e. without intervention by a noiseless external observer such as a classical computer. Nonetheless, this result is surprising given that non-Clifford circuits with access to a supply of fresh qubits can preserve quantum states for arbitrary lengths of time, and even perform fault tolerant quantum computation on them, without requiring any intermediate measurements (Aharonov et al., STOC 1997). Our result shows that such fault tolerance protocols are impossible using only Clifford gates, demonstrating that non-Clifford gates are fundamentally required to store quantum or classical information for long periods of time.
Cite as

Jon Nelson, Joel Rajakumar, and Michael J. Gullans. Non-Clifford Gates Are Required for Long-Term Memory. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{nelson_et_al:LIPIcs.CCC.2026.38,
  author =	{Nelson, Jon and Rajakumar, Joel and Gullans, Michael J.},
  title =	{{Non-Clifford Gates Are Required for Long-Term Memory}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{38:1--38:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.38},
  URN =		{urn:nbn:de:0030-drops-270800},
  doi =		{10.4230/LIPIcs.CCC.2026.38},
  annote =	{Keywords: Fault Tolerance, Quantum Error Correction}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.56
The Hardness of Learning Quantum Circuits and Its Cryptographic Applications

Authors: Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure one-way state generators (OWSGs), digital signature schemes, quantum bit commitments, and private key encryption schemes. We also discuss evidence for these hardness assumptions by analyzing the best-known quantum learning algorithms, as well as proving black-box lower bounds for cloning and learning given state preparation oracles. Our random circuit-based constructions provide concrete instantiations of quantum cryptographic primitives whose security do not depend on the existence of one-way functions. The use of random circuits in our constructions also opens the door to {NISQ-friendly quantum cryptography}. We discuss noise tolerant versions of our OWSG and digital signature constructions which can potentially be implementable on noisy quantum computers connected by a quantum network. On the other hand, they are still secure against {noiseless} quantum adversaries, raising the intriguing possibility of a useful implementation of an end-to-end cryptographic protocol on near-term quantum computers. Finally, our explorations suggest that the rich interconnections between learning theory and cryptography in classical theoretical computer science also extend to the quantum setting.
Cite as

Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen. The Hardness of Learning Quantum Circuits and Its Cryptographic Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 56:1-56:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fefferman_et_al:LIPIcs.ITCS.2026.56,
  author =	{Fefferman, Bill and Ghosh, Soumik and Sinha, Makrand and Yuen, Henry},
  title =	{{The Hardness of Learning Quantum Circuits and Its Cryptographic Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{56:1--56:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.56},
  URN =		{urn:nbn:de:0030-drops-253431},
  doi =		{10.4230/LIPIcs.ITCS.2026.56},
  annote =	{Keywords: quantum learning, quantum circuits, cryptographic hardness, one-way state generators}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.10
On the Complexity of Unique Quantum Witnesses and Quantum Approximate Counting

Authors: Anurag Anshu, Jonas Haferkamp, Yeongwoo Hwang, and Quynh T. Nguyen

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study the long-standing open question on the power of unique witnesses in quantum protocols, which asks if UniqueQMA, a variant of QMA whose accepting witness space is 1-dimensional, contains QMA under quantum reductions. This work rules out any black-box reduction from QMA to UniqueQMA by showing a quantum oracle separation between BQP^UniqueQMA and QMA. This provides a contrast to the classical case, where the Valiant-Vazirani theorem shows a black-box randomized reduction from UniqueNP to NP, and suggests the need for studying the structure of the ground space of local Hamiltonians in distilling a potential unique witness. Via similar techniques, we show, relative to a quantum oracle, that QMA^QMA cannot decide quantum approximate counting, ruling out a quantum analogue of Stockmeyer’s algorithm in the black-box setting. Our results employ a subspace reflection oracle, previously considered in [Scott Aaronson and Greg Kuperberg, 2007; Scott Aaronson et al., 2020; She and Yuen, 2023], but we introduce new tools which allow us to exploit the unique witness constraint. We also show a strong "polarization" behavior of QMA circuits, which could be of independent interest in studying quantum polynomial hierarchies. We then ask a natural question; what structural properties of the local Hamiltonian problem can we exploit? We introduce a physically motivated candidate by showing that the ground energy of local Hamiltonians that satisfy a computational variant of the eigenstate thermalization hypothesis (ETH) can be estimated through a UniqueQMA protocol. Our protocol can be viewed as a quantum expander test in a low energy subspace of the Hamiltonian and verifies a unique entangled state across two copies of the subspace. This allows us to conclude that if UniqueQMA is not equivalent to QMA, then QMA-hard Hamiltonians must violate ETH under adversarial perturbations (more accurately, further assuming the quantum PCP conjecture if ETH only applies to extensive energy subspaces). Under the same assumption, this also serves as evidence that chaotic local Hamiltonians, such as the SYK model may be computationally simpler than general local Hamiltonians.
Cite as

Anurag Anshu, Jonas Haferkamp, Yeongwoo Hwang, and Quynh T. Nguyen. On the Complexity of Unique Quantum Witnesses and Quantum Approximate Counting. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{anshu_et_al:LIPIcs.ITCS.2026.10,
  author =	{Anshu, Anurag and Haferkamp, Jonas and Hwang, Yeongwoo and Nguyen, Quynh T.},
  title =	{{On the Complexity of Unique Quantum Witnesses and Quantum Approximate Counting}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.10},
  URN =		{urn:nbn:de:0030-drops-252978},
  doi =		{10.4230/LIPIcs.ITCS.2026.10},
  annote =	{Keywords: Quantum complexity, approximate counting, Valiant-Vazirani, eigenstate thermalization hypothesis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.54
The Importance of the Spectral Gap in Estimating Ground-State Energies

Authors: Abhinav Deshpande, Alexey V. Gorshkov, and Bill Fefferman

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. The main object of study is the Local Hamiltonian problem, which is concerned with estimating the ground-state energy of a local Hamiltonian and is complete for the class QMA, a quantum generalization of the class NP. A major challenge in the field is to understand the complexity of the Local Hamiltonian problem in more physically natural parameter regimes. One crucial parameter in understanding the ground space of any Hamiltonian in many-body physics is the spectral gap, which is the difference between the smallest two eigenvalues. Despite its importance in quantum many-body physics, the role played by the spectral gap in the complexity of the Local Hamiltonian problem is less well-understood. In this work, we make progress on this question by considering the precise regime, in which one estimates the ground-state energy to within inverse exponential precision. Computing ground-state energies precisely is a task that is important for quantum chemistry and quantum many-body physics. In the setting of inverse-exponential precision (promise gap), there is a surprising result that the complexity of Local Hamiltonian is magnified from QMA to PSPACE, the class of problems solvable in polynomial space (but possibly exponential time). We clarify the reason behind this boost in complexity. Specifically, we show that the full complexity of the high precision case only comes about when the spectral gap is exponentially small. As a consequence of the proof techniques developed to show our results, we uncover important implications for the representability and circuit complexity of ground states of local Hamiltonians, the theory of uniqueness of quantum witnesses, and techniques for the amplification of quantum witnesses in the presence of postselection.
Cite as

Abhinav Deshpande, Alexey V. Gorshkov, and Bill Fefferman. The Importance of the Spectral Gap in Estimating Ground-State Energies. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 54:1-54:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{deshpande_et_al:LIPIcs.ITCS.2022.54,
  author =	{Deshpande, Abhinav and Gorshkov, Alexey V. and Fefferman, Bill},
  title =	{{The Importance of the Spectral Gap in Estimating Ground-State Energies}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{54:1--54:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.54},
  URN =		{urn:nbn:de:0030-drops-156501},
  doi =		{10.4230/LIPIcs.ITCS.2022.54},
  annote =	{Keywords: Local Hamiltonian problem, PSPACE, PP, QMA}
}
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