3 Search Results for "Grewal, Sabee"

Document
DOI: 10.4230/LIPIcs.TQC.2023.12
Efficient Tomography of Non-Interacting-Fermion States

Authors: Scott Aaronson and Sabee Grewal

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)

Abstract
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/δ)/ ε⁴) time are sufficient to learn the state to trace distance at most ε with probability at least 1 - δ. Our algorithm empirically estimates one-mode correlations in O(m) different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.
Cite as

Scott Aaronson and Sabee Grewal. Efficient Tomography of Non-Interacting-Fermion States. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 12:1-12:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{aaronson_et_al:LIPIcs.TQC.2023.12,
  author =	{Aaronson, Scott and Grewal, Sabee},
  title =	{{Efficient Tomography of Non-Interacting-Fermion States}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.12},
  URN =		{urn:nbn:de:0030-drops-183222},
  doi =		{10.4230/LIPIcs.TQC.2023.12},
  annote =	{Keywords: free-fermions, Gaussian fermions, non-interacting fermions, quantum state tomography, efficient tomography}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.64
Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom

Authors: Sabee Grewal, Vishnu Iyer, William Kretschmer, and Daniel Liang

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random. Specifically, given an n-qubit pure state |ψ⟩, we give an efficient algorithm that distinguishes whether |ψ⟩ is (i) Haar-random or (ii) a state with stabilizer fidelity at least 1/k (i.e., has fidelity at least 1/k with some stabilizer state), promised that one of these is the case. With black-box access to |ψ⟩, our algorithm uses O(k^{12} log(1/δ)) copies of |ψ⟩ and O(n k^{12} log(1/δ)) time to succeed with probability at least 1-δ, and, with access to a state preparation unitary for |ψ⟩ (and its inverse), O(k³ log(1/δ)) queries and O(n k³ log(1/δ)) time suffice. As a corollary, we prove that ω(log(n)) T-gates are necessary for any Clifford+T circuit to prepare computationally pseudorandom quantum states, a first-of-its-kind lower bound.
Cite as

Sabee Grewal, Vishnu Iyer, William Kretschmer, and Daniel Liang. Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 64:1-64:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{grewal_et_al:LIPIcs.ITCS.2023.64,
  author =	{Grewal, Sabee and Iyer, Vishnu and Kretschmer, William and Liang, Daniel},
  title =	{{Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{64:1--64:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.64},
  URN =		{urn:nbn:de:0030-drops-175670},
  doi =		{10.4230/LIPIcs.ITCS.2023.64},
  annote =	{Keywords: Pseudorandom quantum states, Clifford + T, Haar random, Bell sampling, stabilizer formalism, stabilizer extent, stabilizer fidelity, learning theory, complexity theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.13
The Quantum Supremacy Tsirelson Inequality

Authors: William Kretschmer

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
A leading proposal for verifying near-term quantum supremacy experiments on noisy random quantum circuits is linear cross-entropy benchmarking. For a quantum circuit C on n qubits and a sample z ∈ {0,1}ⁿ, the benchmark involves computing |⟨z|C|0ⁿ⟩|², i.e. the probability of measuring z from the output distribution of C on the all zeros input. Under a strong conjecture about the classical hardness of estimating output probabilities of quantum circuits, no polynomial-time classical algorithm given C can output a string z such that |⟨z|C|0ⁿ⟩|² is substantially larger than 1/(2ⁿ) (Aaronson and Gunn, 2019). On the other hand, for a random quantum circuit C, sampling z from the output distribution of C achieves |⟨z|C|0ⁿ⟩|² ≈ 2/(2ⁿ) on average (Arute et al., 2019). In analogy with the Tsirelson inequality from quantum nonlocal correlations, we ask: can a polynomial-time quantum algorithm do substantially better than 2/(2ⁿ)? We study this question in the query (or black box) model, where the quantum algorithm is given oracle access to C. We show that, for any ε ≥ 1/poly(n), outputting a sample z such that |⟨z|C|0ⁿ⟩|² ≥ (2 + ε)/2ⁿ on average requires at least Ω((2^{n/4})/poly(n)) queries to C, but not more than O (2^{n/3}) queries to C, if C is either a Haar-random n-qubit unitary, or a canonical state preparation oracle for a Haar-random n-qubit state. We also show that when C samples from the Fourier distribution of a random Boolean function, the naive algorithm that samples from C is the optimal 1-query algorithm for maximizing |⟨z|C|0ⁿ⟩|² on average.
Cite as

William Kretschmer. The Quantum Supremacy Tsirelson Inequality. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 13:1-13:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kretschmer:LIPIcs.ITCS.2021.13,
  author =	{Kretschmer, William},
  title =	{{The Quantum Supremacy Tsirelson Inequality}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.13},
  URN =		{urn:nbn:de:0030-drops-135524},
  doi =		{10.4230/LIPIcs.ITCS.2021.13},
  annote =	{Keywords: quantum supremacy, quantum query complexity, random circuit sampling}
}
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