Volume
LIPIcs, Volume 266
18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)
Event
TQC 2023, July 24-28, 2023, Aveiro, PortugalEditors
Publication Details
- published at: 2023-07-18
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-283-9
- DBLP: db/conf/tqc/tqc2023
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Complete Volume
LIPIcs, Volume 266, TQC 2023, Complete Volume
Abstract
LIPIcs, Volume 266, TQC 2023, Complete Volume
Cite as
18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 1-314, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@Proceedings{fawzi_et_al:LIPIcs.TQC.2023,
title = {{LIPIcs, Volume 266, TQC 2023, Complete Volume}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {1--314},
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},
URN = {urn:nbn:de:0030-drops-183099},
doi = {10.4230/LIPIcs.TQC.2023},
annote = {Keywords: LIPIcs, Volume 266, TQC 2023, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{fawzi_et_al:LIPIcs.TQC.2023.0,
author = {Fawzi, Omar and Walter, Michael},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {0:i--0:xii},
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.2023.0},
URN = {urn:nbn:de:0030-drops-183102},
doi = {10.4230/LIPIcs.TQC.2023.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Approximate Degree Lower Bounds for Oracle Identification Problems
Abstract
The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically lifts to a quantum communication lower bound for a related function.
We introduce a framework for proving approximate degree lower bounds for certain oracle identification problems, where the goal is to recover a hidden binary string x ∈ {0, 1}ⁿ given possibly non-standard oracle access to it. Our lower bounds apply to decision versions of these problems, where the goal is to compute the parity of x. We apply our framework to the ordered search and hidden string problems, proving nearly tight approximate degree lower bounds of Ω(n/log² n) for each. These lower bounds generalize to the weakly unbounded error setting, giving a new quantum query lower bound for the hidden string problem in this regime. Our lower bounds are driven by randomized communication upper bounds for the greater-than and equality functions.
Cite as
Mark Bun and Nadezhda Voronova. Approximate Degree Lower Bounds for Oracle Identification Problems. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bun_et_al:LIPIcs.TQC.2023.1,
author = {Bun, Mark and Voronova, Nadezhda},
title = {{Approximate Degree Lower Bounds for Oracle Identification Problems}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {1:1--1:24},
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.2023.1},
URN = {urn:nbn:de:0030-drops-183113},
doi = {10.4230/LIPIcs.TQC.2023.1},
annote = {Keywords: Approximate degree, quantum query complexity, communication complexity, ordered search, polynomial approximations, polynomial method}
}
Document
On the Necessity of Collapsing for Post-Quantum and Quantum Commitments
Abstract
Collapse binding and collapsing were proposed by Unruh (Eurocrypt '16) as post-quantum strengthenings of computational binding and collision resistance, respectively. These notions have been very successful in facilitating the "lifting" of classical security proofs to the quantum setting. A basic and natural question remains unanswered, however: are they the weakest notions that suffice for such lifting?
In this work we answer this question in the affirmative by giving a classical commit-and-open protocol which is post-quantum secure if and only if the commitment scheme (resp. hash function) used is collapse binding (resp. collapsing). We also generalise the definition of collapse binding to quantum commitment schemes, and prove that the equivalence carries over when the sender in this commit-and-open protocol communicates quantum information.
As a consequence, we establish that a variety of "weak" binding notions (sum binding, CDMS binding and unequivocality) are in fact equivalent to collapse binding, both for post-quantum and quantum commitments.
Finally, we prove a "win-win" result, showing that a post-quantum computationally binding commitment scheme that is not collapse binding can be used to build an equivocal commitment scheme (which can, in turn, be used to build one-shot signatures and other useful quantum primitives). This strengthens a result due to Zhandry (Eurocrypt '19) showing that the same object yields quantum lightning.
Cite as
Marcel Dall'Agnol and Nicholas Spooner. On the Necessity of Collapsing for Post-Quantum and Quantum Commitments. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{dallagnol_et_al:LIPIcs.TQC.2023.2,
author = {Dall'Agnol, Marcel and Spooner, Nicholas},
title = {{On the Necessity of Collapsing for Post-Quantum and Quantum Commitments}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {2:1--2:23},
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.2023.2},
URN = {urn:nbn:de:0030-drops-183127},
doi = {10.4230/LIPIcs.TQC.2023.2},
annote = {Keywords: Quantum cryptography, Commitment schemes, Hash functions, Quantum rewinding}
}
Document
Optimal Algorithms for Learning Quantum Phase States
Abstract
We analyze the complexity of learning n-qubit quantum phase states. A degree-d phase state is defined as a superposition of all 2ⁿ basis vectors x with amplitudes proportional to (-1)^{f(x)}, where f is a degree-d Boolean polynomial over n variables. We show that the sample complexity of learning an unknown degree-d phase state is Θ(n^d) if we allow separable measurements and Θ(n^{d-1}) if we allow entangled measurements. Our learning algorithm based on separable measurements has runtime poly(n) (for constant d) and is well-suited for near-term demonstrations as it requires only single-qubit measurements in the Pauli X and Z bases. We show similar bounds on the sample complexity for learning generalized phase states with complex-valued amplitudes. We further consider learning phase states when f has sparsity-s, degree-d in its 𝔽₂ representation (with sample complexity O(2^d sn)), f has Fourier-degree-t (with sample complexity O(2^{2t})), and learning quadratic phase states with ε-global depolarizing noise (with sample complexity O(n^{1+ε})). These learning algorithms give us a procedure to learn the diagonal unitaries of the Clifford hierarchy and IQP circuits.
Cite as
Srinivasan Arunachalam, Sergey Bravyi, Arkopal Dutt, and Theodore J. Yoder. Optimal Algorithms for Learning Quantum Phase States. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 3:1-3:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{arunachalam_et_al:LIPIcs.TQC.2023.3,
author = {Arunachalam, Srinivasan and Bravyi, Sergey and Dutt, Arkopal and Yoder, Theodore J.},
title = {{Optimal Algorithms for Learning Quantum Phase States}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {3:1--3:24},
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.2023.3},
URN = {urn:nbn:de:0030-drops-183139},
doi = {10.4230/LIPIcs.TQC.2023.3},
annote = {Keywords: Tomography, binary phase states, generalized phase states, IQP circuits}
}
Document
Computational Quantum Secret Sharing
Abstract
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security.
We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.
Cite as
Alper Çakan, Vipul Goyal, Chen-Da Liu-Zhang, and João Ribeiro. Computational Quantum Secret Sharing. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 4:1-4:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{cakan_et_al:LIPIcs.TQC.2023.4,
author = {\c{C}akan, Alper and Goyal, Vipul and Liu-Zhang, Chen-Da and Ribeiro, Jo\~{a}o},
title = {{Computational Quantum Secret Sharing}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {4:1--4:26},
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.2023.4},
URN = {urn:nbn:de:0030-drops-183144},
doi = {10.4230/LIPIcs.TQC.2023.4},
annote = {Keywords: Quantum secret sharing, quantum cryptography}
}
Document
Quantum Algorithm for Path-Edge Sampling
Abstract
We present a quantum algorithm for sampling an edge on a path between two nodes s and t in an undirected graph given as an adjacency matrix, and show that this can be done in query complexity that is asymptotically the same, up to log factors, as the query complexity of detecting a path between s and t. We use this path sampling algorithm as a subroutine for st-path finding and st-cut-set finding algorithms in some specific cases. Our main technical contribution is an algorithm for generating a quantum state that is proportional to the positive witness vector of a span program.
Cite as
Stacey Jeffery, Shelby Kimmel, and Alvaro Piedrafita. Quantum Algorithm for Path-Edge Sampling. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 5:1-5:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{jeffery_et_al:LIPIcs.TQC.2023.5,
author = {Jeffery, Stacey and Kimmel, Shelby and Piedrafita, Alvaro},
title = {{Quantum Algorithm for Path-Edge Sampling}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {5:1--5:28},
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.2023.5},
URN = {urn:nbn:de:0030-drops-183151},
doi = {10.4230/LIPIcs.TQC.2023.5},
annote = {Keywords: Algorithm design and analysis, Query complexity, Graph algorithms, Span program algorithm, Path finding, Path detection}
}
Document
Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians
Abstract
We give a classical 1/(qk+1)-approximation for the maximum eigenvalue of a k-sparse fermionic Hamiltonian with strictly q-local terms, as well as a 1/(4k+1)-approximation when the Hamiltonian has both 2-local and 4-local terms. More generally we obtain a 1/O(qk²)-approximation for k-sparse fermionic Hamiltonians with terms of locality at most q. Our techniques also yield analogous approximations for k-sparse, q-local qubit Hamiltonians with small hidden constants and improved dependence on q.
Cite as
Daniel Hothem, Ojas Parekh, and Kevin Thompson. Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hothem_et_al:LIPIcs.TQC.2023.6,
author = {Hothem, Daniel and Parekh, Ojas and Thompson, Kevin},
title = {{Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {6:1--6:10},
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.2023.6},
URN = {urn:nbn:de:0030-drops-183163},
doi = {10.4230/LIPIcs.TQC.2023.6},
annote = {Keywords: Approximation algorithms, Extremal eigenvalues, Sparse Hamiltonians, Fermionic Hamiltonians, Qubit Hamiltonians}
}
Document
Improved Algorithm and Lower Bound for Variable Time Quantum Search
Abstract
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity O(√Tlog n) where T = ∑_{i = 1}ⁿ t_i² with t_i denoting the time to check the i^th item. Our second result is a quantum lower bound of Ω(√{Tlog T}). Both the algorithm and the lower bound improve over previously known results by a factor of √{log T} but the algorithm is also substantially simpler than the previously known quantum algorithms.
Cite as
Andris Ambainis, Martins Kokainis, and Jevgēnijs Vihrovs. Improved Algorithm and Lower Bound for Variable Time Quantum Search. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{ambainis_et_al:LIPIcs.TQC.2023.7,
author = {Ambainis, Andris and Kokainis, Martins and Vihrovs, Jevg\={e}nijs},
title = {{Improved Algorithm and Lower Bound for Variable Time Quantum Search}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {7:1--7:18},
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.2023.7},
URN = {urn:nbn:de:0030-drops-183177},
doi = {10.4230/LIPIcs.TQC.2023.7},
annote = {Keywords: quantum search, amplitude amplification}
}
Document
Fully Device-Independent Quantum Key Distribution Using Synchronous Correlations
Abstract
We derive a device-independent quantum key distribution protocol based on synchronous correlations and their Bell inequalities. This protocol offers several advantages over other device-independent schemes including symmetry between the two users and no need for pre-shared randomness. We close a "synchronicity" loophole by showing that an almost synchronous correlation inherits the self-testing property of the associated synchronous correlation. We also pose a new security assumption that closes the "locality" (or "causality") loophole: an unbounded adversary with even a small uncertainty about the users' choice of measurement bases cannot produce any almost synchronous correlation that approximately maximally violates a synchronous Bell inequality.
Cite as
Nishant Rodrigues and Brad Lackey. Fully Device-Independent Quantum Key Distribution Using Synchronous Correlations. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 8:1-8:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{rodrigues_et_al:LIPIcs.TQC.2023.8,
author = {Rodrigues, Nishant and Lackey, Brad},
title = {{Fully Device-Independent Quantum Key Distribution Using Synchronous Correlations}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {8:1--8:22},
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.2023.8},
URN = {urn:nbn:de:0030-drops-183185},
doi = {10.4230/LIPIcs.TQC.2023.8},
annote = {Keywords: quantum cryptography, device independence, key distribution, security proofs, randomness}
}
Document
Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection
Abstract
We define rewinding operators that invert quantum measurements. Then, we define complexity classes RwBQP, CBQP, and AdPostBQP as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that BPP^PP ⊆ RwBQP = CBQP = AdPostBQP ⊆ PSPACE. As a byproduct of this result, we show that any problem in PostBQP can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that BQP ⊉ SZK, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.
Cite as
Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, and Seiichiro Tani. Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{hiromasa_et_al:LIPIcs.TQC.2023.9,
author = {Hiromasa, Ryo and Mizutani, Akihiro and Takeuchi, Yuki and Tani, Seiichiro},
title = {{Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {9:1--9:23},
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.2023.9},
URN = {urn:nbn:de:0030-drops-183193},
doi = {10.4230/LIPIcs.TQC.2023.9},
annote = {Keywords: Quantum computing, Postselection, Lattice problems}
}
Document
Quantum Mass Production Theorems
Abstract
We prove that for any n-qubit unitary transformation U and for any r = 2^{o(n / log n)}, there exists a quantum circuit to implement U^{⊗ r} with at most O(4ⁿ) gates. This asymptotically equals the number of gates needed to implement just a single copy of a worst-case U. We also establish analogous results for quantum states and diagonal unitary transformations. Our techniques are based on the work of Uhlig [Math. Notes 1974], who proved a similar mass production theorem for Boolean functions.
Cite as
William Kretschmer. Quantum Mass Production Theorems. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 10:1-10:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{kretschmer:LIPIcs.TQC.2023.10,
author = {Kretschmer, William},
title = {{Quantum Mass Production Theorems}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {10:1--10:11},
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.2023.10},
URN = {urn:nbn:de:0030-drops-183206},
doi = {10.4230/LIPIcs.TQC.2023.10},
annote = {Keywords: mass production, quantum circuit synthesis, quantum circuit complexity}
}
Document
On the Power of Nonstandard Quantum Oracles
Abstract
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function f, and present f in different oracle models. We first give a one-query QMA protocol to test if a graph encoded in f has a small disconnected subset. We then use representation theory to show that no classical witness can help a quantum verifier efficiently decide this problem relative to an in-place oracle. Perhaps surprisingly, a simple modification to the standard oracle prevents a quantum verifier from efficiently deciding this problem, even with access to an unbounded witness.
Cite as
Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha. On the Power of Nonstandard Quantum Oracles. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bassirian_et_al:LIPIcs.TQC.2023.11,
author = {Bassirian, Roozbeh and Fefferman, Bill and Marwaha, Kunal},
title = {{On the Power of Nonstandard Quantum Oracles}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {11:1--11:25},
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.2023.11},
URN = {urn:nbn:de:0030-drops-183215},
doi = {10.4230/LIPIcs.TQC.2023.11},
annote = {Keywords: quantum complexity, QCMA, expander graphs, representation theory}
}
Document
Efficient Tomography of Non-Interacting-Fermion States
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
Quantum Policy Gradient Algorithms
Abstract
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning are possible when given quantum access to reinforcement learning environments. Yet, the applicability of quantum algorithms in this setting remains very limited, notably in environments with large state and action spaces. In this work, we design quantum algorithms to train state-of-the-art reinforcement learning policies by exploiting quantum interactions with an environment. However, these algorithms only offer full quadratic speed-ups in sample complexity over their classical analogs when the trained policies satisfy some regularity conditions. Interestingly, we find that reinforcement learning policies derived from parametrized quantum circuits are well-behaved with respect to these conditions, which showcases the benefit of a fully-quantum reinforcement learning framework.
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Sofiene Jerbi, Arjan Cornelissen, Maris Ozols, and Vedran Dunjko. Quantum Policy Gradient Algorithms. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 13:1-13:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{jerbi_et_al:LIPIcs.TQC.2023.13,
author = {Jerbi, Sofiene and Cornelissen, Arjan and Ozols, Maris and Dunjko, Vedran},
title = {{Quantum Policy Gradient Algorithms}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {13:1--13:24},
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.2023.13},
URN = {urn:nbn:de:0030-drops-183230},
doi = {10.4230/LIPIcs.TQC.2023.13},
annote = {Keywords: quantum reinforcement learning, policy gradient methods, parametrized quantum circuits}
}
Document
Local Hamiltonians with No Low-Energy Stabilizer States
Abstract
The recently-defined No Low-energy Sampleable States (NLSS) conjecture of Gharibian and Le Gall [Sevag Gharibian and François {Le Gall}, 2022] posits the existence of a family of local Hamiltonians where all states of low-enough constant energy do not have succinct representations allowing perfect sampling access. States that can be prepared using only Clifford gates (i.e. stabilizer states) are an example of sampleable states, so the NLSS conjecture implies the existence of local Hamiltonians whose low-energy space contains no stabilizer states. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [Anshu et al., 2022], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states. We hope that our techniques will eventually be helpful for constructing Hamiltonians which simultaneously satisfy NLSS and NLTS.
Cite as
Nolan J. Coble, Matthew Coudron, Jon Nelson, and Seyed Sajjad Nezhadi. Local Hamiltonians with No Low-Energy Stabilizer States. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{coble_et_al:LIPIcs.TQC.2023.14,
author = {Coble, Nolan J. and Coudron, Matthew and Nelson, Jon and Nezhadi, Seyed Sajjad},
title = {{Local Hamiltonians with No Low-Energy Stabilizer States}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {14:1--14:21},
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.2023.14},
URN = {urn:nbn:de:0030-drops-183243},
doi = {10.4230/LIPIcs.TQC.2023.14},
annote = {Keywords: Hamiltonian complexity, Stabilizer codes, Low-energy states}
}