eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
1
314
10.4230/LIPIcs.TQC.2023
article
LIPIcs, Volume 266, TQC 2023, Complete Volume
Fawzi, Omar
1
https://orcid.org/0000-0001-8491-0359
Walter, Michael
2
https://orcid.org/0000-0002-3073-1408
Univ Lyon, Inria, ENS Lyon, UCBL, LIP, Lyon, France
Ruhr University Bochum, Germany
LIPIcs, Volume 266, TQC 2023, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023/LIPIcs.TQC.2023.pdf
LIPIcs, Volume 266, TQC 2023, Complete Volume
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
0:i
0:xii
10.4230/LIPIcs.TQC.2023.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Fawzi, Omar
1
https://orcid.org/0000-0001-8491-0359
Walter, Michael
2
https://orcid.org/0000-0002-3073-1408
Univ Lyon, Inria, ENS Lyon, UCBL, LIP, Lyon, France
Ruhr University Bochum, Germany
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.0/LIPIcs.TQC.2023.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
1:1
1:24
10.4230/LIPIcs.TQC.2023.1
article
Approximate Degree Lower Bounds for Oracle Identification Problems
Bun, Mark
1
Voronova, Nadezhda
1
Department of Computer Science, Boston University, MA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.1/LIPIcs.TQC.2023.1.pdf
Approximate degree
quantum query complexity
communication complexity
ordered search
polynomial approximations
polynomial method
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
2:1
2:23
10.4230/LIPIcs.TQC.2023.2
article
On the Necessity of Collapsing for Post-Quantum and Quantum Commitments
Dall'Agnol, Marcel
1
https://orcid.org/0000-0002-6060-1663
Spooner, Nicholas
1
https://orcid.org/0000-0002-0085-2137
University of Warwick, Coventry, UK
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.2/LIPIcs.TQC.2023.2.pdf
Quantum cryptography
Commitment schemes
Hash functions
Quantum rewinding
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
3:1
3:24
10.4230/LIPIcs.TQC.2023.3
article
Optimal Algorithms for Learning Quantum Phase States
Arunachalam, Srinivasan
1
Bravyi, Sergey
1
Dutt, Arkopal
1
2
3
https://orcid.org/0000-0001-6942-2963
Yoder, Theodore J.
1
https://orcid.org/0000-0001-9614-2836
IBM Quantum, Thomas J Watson Research Center, Yorktown Heights, NY, USA
MIT-IBM Watson AI Lab, Cambridge, MA, USA
Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, MA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.3/LIPIcs.TQC.2023.3.pdf
Tomography
binary phase states
generalized phase states
IQP circuits
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
4:1
4:26
10.4230/LIPIcs.TQC.2023.4
article
Computational Quantum Secret Sharing
Çakan, Alper
1
https://orcid.org/0000-0003-3567-1704
Goyal, Vipul
2
1
Liu-Zhang, Chen-Da
2
Ribeiro, João
3
https://orcid.org/0000-0002-9870-0501
Carnegie Mellon University, Pittsburgh, PA, USA
NTT Research, Sunnyvale, CA, USA
NOVA LINCS and NOVA School of Science and Technology, Caparica, Portugal
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.4/LIPIcs.TQC.2023.4.pdf
Quantum secret sharing
quantum cryptography
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
5:1
5:28
10.4230/LIPIcs.TQC.2023.5
article
Quantum Algorithm for Path-Edge Sampling
Jeffery, Stacey
1
Kimmel, Shelby
2
https://orcid.org/0000-0003-0726-4167
Piedrafita, Alvaro
1
QuSoft and CWI, Amsterdam, The Netherlands
Middlebury College, VT, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.5/LIPIcs.TQC.2023.5.pdf
Algorithm design and analysis
Query complexity
Graph algorithms
Span program algorithm
Path finding
Path detection
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
6:1
6:10
10.4230/LIPIcs.TQC.2023.6
article
Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians
Hothem, Daniel
1
https://orcid.org/0000-0002-5628-9945
Parekh, Ojas
2
https://orcid.org/0000-0003-2689-9264
Thompson, Kevin
2
Quantum Algorithms and Applications Collaboratory, Sandial National Laboratories, Livermore, CA, USA
Quantum Algorithms and Applications Collaboratory, Sandial National Laboratories, Albuquerque, NM, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.6/LIPIcs.TQC.2023.6.pdf
Approximation algorithms
Extremal eigenvalues
Sparse Hamiltonians
Fermionic Hamiltonians
Qubit Hamiltonians
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
7:1
7:18
10.4230/LIPIcs.TQC.2023.7
article
Improved Algorithm and Lower Bound for Variable Time Quantum Search
Ambainis, Andris
1
https://orcid.org/0000-0002-8716-001X
Kokainis, Martins
1
https://orcid.org/0000-0003-3381-7271
Vihrovs, Jevgēnijs
1
https://orcid.org/0000-0002-3143-2610
Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Riga, Latvia
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.7/LIPIcs.TQC.2023.7.pdf
quantum search
amplitude amplification
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
8:1
8:22
10.4230/LIPIcs.TQC.2023.8
article
Fully Device-Independent Quantum Key Distribution Using Synchronous Correlations
Rodrigues, Nishant
1
2
https://orcid.org/0000-0001-8882-4677
Lackey, Brad
3
https://orcid.org/0000-0002-3823-8757
Department of Computer Science, University of Maryland, College Park, MD, USA
Joint Center for Quantum Information and Computer Science, College Park, MD, USA
Microsoft Quantum, Redmond, WA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.8/LIPIcs.TQC.2023.8.pdf
quantum cryptography
device independence
key distribution
security proofs
randomness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
9:1
9:23
10.4230/LIPIcs.TQC.2023.9
article
Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection
Hiromasa, Ryo
1
Mizutani, Akihiro
1
Takeuchi, Yuki
2
Tani, Seiichiro
2
3
Information Technology R&D Center, Mitsubishi Electric Corporation, Kamakura, Japan
NTT Communication Science Laboratories, NTT Corporation, Atsugi, Japan
International Research Frontiers Initiative (IRFI), Tokyo Institute of Technology, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.9/LIPIcs.TQC.2023.9.pdf
Quantum computing
Postselection
Lattice problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
10:1
10:11
10.4230/LIPIcs.TQC.2023.10
article
Quantum Mass Production Theorems
Kretschmer, William
1
https://orcid.org/0000-0002-7784-9817
University of Texas at Austin, TX, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.10/LIPIcs.TQC.2023.10.pdf
mass production
quantum circuit synthesis
quantum circuit complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
11:1
11:25
10.4230/LIPIcs.TQC.2023.11
article
On the Power of Nonstandard Quantum Oracles
Bassirian, Roozbeh
1
Fefferman, Bill
1
Marwaha, Kunal
1
https://orcid.org/0000-0001-9084-6971
University of Chicago, IL, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.11/LIPIcs.TQC.2023.11.pdf
quantum complexity
QCMA
expander graphs
representation theory
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
12:1
12:18
10.4230/LIPIcs.TQC.2023.12
article
Efficient Tomography of Non-Interacting-Fermion States
Aaronson, Scott
1
Grewal, Sabee
1
https://orcid.org/0000-0002-8241-560X
The University of Texas at Austin, TX, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.12/LIPIcs.TQC.2023.12.pdf
free-fermions
Gaussian fermions
non-interacting fermions
quantum state tomography
efficient tomography
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
13:1
13:24
10.4230/LIPIcs.TQC.2023.13
article
Quantum Policy Gradient Algorithms
Jerbi, Sofiene
1
https://orcid.org/0000-0001-8171-5742
Cornelissen, Arjan
2
https://orcid.org/0000-0002-9160-5261
Ozols, Maris
2
https://orcid.org/0000-0002-3238-8594
Dunjko, Vedran
3
https://orcid.org/0000-0002-2632-7955
Institute for Theoretical Physics, Universität Innsbruck, Austria
QuSoft and University of Amsterdam, The Netherlands
applied Quantum algorithms (aQa), Leiden University, The Netherlands
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.13/LIPIcs.TQC.2023.13.pdf
quantum reinforcement learning
policy gradient methods
parametrized quantum circuits
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-07-18
266
14:1
14:21
10.4230/LIPIcs.TQC.2023.14
article
Local Hamiltonians with No Low-Energy Stabilizer States
Coble, Nolan J.
1
Coudron, Matthew
1
2
Nelson, Jon
1
Nezhadi, Seyed Sajjad
1
Joint Center for Quantum Information and Computer Science (QuICS), Department of Computer Science, University of Maryland, College Park, MD, USA
National Institute of Standards and Technology, Gaithersburg, MD, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol266-tqc2023/LIPIcs.TQC.2023.14/LIPIcs.TQC.2023.14.pdf
Hamiltonian complexity
Stabilizer codes
Low-energy states