eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
1
230
10.4230/LIPIcs.TQC.2020
article
LIPIcs, Volume 158, TQC 2020, Complete Volume
Flammia, Steven T.
1
https://orcid.org/0000-0002-3975-0226
University of Sydney, Australia
LIPIcs, Volume 158, TQC 2020, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020/LIPIcs.TQC.2020.pdf
LIPIcs, Volume 158, TQC 2020, Complete Volume
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
0:i
0:x
10.4230/LIPIcs.TQC.2020.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Flammia, Steven T.
1
https://orcid.org/0000-0002-3975-0226
University of Sydney, Australia
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.0/LIPIcs.TQC.2020.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
1:1
1:16
10.4230/LIPIcs.TQC.2020.1
article
Exponential Quantum Communication Reductions from Generalizations of the Boolean Hidden Matching Problem
Doriguello, João F.
1
2
https://orcid.org/0000-0002-8265-7334
Montanaro, Ashley
1
School of Mathematics, University of Bristol, United Kingdom
Quantum Engineering Centre for Doctoral Training, University of Bristol, United Kingdom
In this work we revisit the Boolean Hidden Matching communication problem, which was the first communication problem in the one-way model to demonstrate an exponential classical-quantum communication separation. In this problem, Alice’s bits are matched into pairs according to a partition that Bob holds. These pairs are compressed using a Parity function and it is promised that the final bit-string is equal either to another bit-string Bob holds, or its complement. The problem is to decide which case is the correct one. Here we generalize the Boolean Hidden Matching problem by replacing the parity function with an arbitrary function f. Efficient communication protocols are presented depending on the sign-degree of f. If its sign-degree is less than or equal to 1, we show an efficient classical protocol. If its sign-degree is less than or equal to 2, we show an efficient quantum protocol. We then completely characterize the classical hardness of all symmetric functions f of sign-degree greater than or equal to 2, except for one family of specific cases. We also prove, via Fourier analysis, a classical lower bound for any function f whose pure high degree is greater than or equal to 2. Similarly, we prove, also via Fourier analysis, a quantum lower bound for any function f whose pure high degree is greater than or equal to 3. These results give a large family of new exponential classical-quantum communication separations.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.1/LIPIcs.TQC.2020.1.pdf
Communication Complexity
Quantum Communication Complexity
Boolean Hidden Matching Problem
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
2:1
2:22
10.4230/LIPIcs.TQC.2020.2
article
Improved Approximate Degree Bounds for k-Distinctness
Mande, Nikhil S.
1
Thaler, Justin
1
Zhu, Shuchen
1
Georgetown University, Washington DC, USA
An open problem that is widely regarded as one of the most important in quantum query complexity is to resolve the quantum query complexity of the k-distinctness function on inputs of size N. While the case of k=2 (also called Element Distinctness) is well-understood, there is a polynomial gap between the known upper and lower bounds for all constants k>2. Specifically, the best known upper bound is O (N^{(3/4)-1/(2^{k+2}-4)}) (Belovs, FOCS 2012), while the best known lower bound for k≥ 2 is Ω̃(N^{2/3} + N^{(3/4)-1/(2k)}) (Aaronson and Shi, J. ACM 2004; Bun, Kothari, and Thaler, STOC 2018).
For any constant k ≥ 4, we improve the lower bound to Ω̃(N^{(3/4)-1/(4k)}). This yields, for example, the first proof that 4-distinctness is strictly harder than Element Distinctness. Our lower bound applies more generally to approximate degree.
As a secondary result, we give a simple construction of an approximating polynomial of degree Õ(N^{3/4}) that applies whenever k ≤ polylog(N).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.2/LIPIcs.TQC.2020.2.pdf
Quantum Query Complexity
Approximate Degree
Dual Polynomials
k-distinctness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
3:1
3:15
10.4230/LIPIcs.TQC.2020.3
article
Building Trust for Continuous Variable Quantum States
Chabaud, Ulysse
1
https://orcid.org/0000-0003-0135-9819
Douce, Tom
2
Grosshans, Frédéric
1
3
https://orcid.org/0000-0001-8170-9668
Kashefi, Elham
1
2
Markham, Damian
1
Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom
Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405 Orsay Cedex, France
In this work we develop new methods for the characterisation of continuous variable quantum states using heterodyne measurement in both the trusted and untrusted settings. First, building on quantum state tomography with heterodyne detection, we introduce a reliable method for continuous variable quantum state certification, which directly yields the elements of the density matrix of the state considered with analytical confidence intervals. This method neither needs mathematical reconstruction of the data nor discrete binning of the sample space and uses a single Gaussian measurement setting. Second, beyond quantum state tomography and without its identical copies assumption, we promote our reliable tomography method to a general efficient protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries, i.e., making no assumptions whatsoever on the state generated by the adversary. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over the Fock basis, computed with samples from heterodyne detection of the state.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.3/LIPIcs.TQC.2020.3.pdf
Continuous variable quantum information
reliable state tomography
certification
verification
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
4:1
4:22
10.4230/LIPIcs.TQC.2020.4
article
Uncloneable Quantum Encryption via Oracles
Broadbent, Anne
1
https://orcid.org/0000-0003-1911-0093
Lord, Sébastien
1
https://orcid.org/0000-0003-0329-5628
Department of Mathematics and Statistics, University of Ottawa, Canada
Quantum information is well known to achieve cryptographic feats that are unattainable using classical information alone. Here, we add to this repertoire by introducing a new cryptographic functionality called uncloneable encryption. This functionality allows the encryption of a classical message such that two collaborating but isolated adversaries are prevented from simultaneously recovering the message, even when the encryption key is revealed. Clearly, such functionality is unattainable using classical information alone.
We formally define uncloneable encryption, and show how to achieve it using Wiesner’s conjugate coding, combined with a quantum-secure pseudorandom function (qPRF). Modelling the qPRF as an oracle, we show security by adapting techniques from the quantum one-way-to-hiding lemma, as well as using bounds from quantum monogamy-of-entanglement games.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.4/LIPIcs.TQC.2020.4.pdf
Quantum Cryptography
Symmetric Key
Monogamy-of-Entanglement
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
5:1
5:20
10.4230/LIPIcs.TQC.2020.5
article
Quasirandom Quantum Channels
Bannink, Tom
1
2
Briët, Jop
1
2
Labib, Farrokh
1
2
Maassen, Hans
2
3
CWI, 1098 XG Amsterdam, Netherlands
QuSoft, Science Park 123, 1098 XG Amsterdam, Netherlands
Korteweg-de Vries Institute for Mathematics, Radboud University, Nijmegen, Netherlands
Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of sparse vertex transitive graphs using the famous Grothendieck inequality.
Here we generalize these results to the non-commutative, or "quantum", case, where a transition matrix becomes a quantum channel. In particular, we show that for irreducibly covariant quantum channels, expansion is equivalent to a natural analog of uniformity for graphs, generalizing the result of Conlon and Zhao. Moreover, we show that in these results, the non-commutative and commutative (resp.) Grothendieck inequalities yield the best-possible constants.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.5/LIPIcs.TQC.2020.5.pdf
Quantum channels
quantum expanders
quasirandomness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
6:1
6:25
10.4230/LIPIcs.TQC.2020.6
article
Towards Quantum One-Time Memories from Stateless Hardware
Broadbent, Anne
1
Gharibian, Sevag
2
3
Zhou, Hong-Sheng
3
Department of Mathematics and Statistics, University of Ottawa, Canada
Department of Computer Science, Paderborn University, Germany
Department of Computer Science, Virginia Commonwealth University, Richmond, VA, USA
A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver, against a linear number of adaptive queries to the token, in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also show our scheme is "tight" according to two scenarios.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.6/LIPIcs.TQC.2020.6.pdf
quantum cryptography
one-time memories
semi-definite programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
7:1
7:15
10.4230/LIPIcs.TQC.2020.7
article
Beyond Product State Approximations for a Quantum Analogue of Max Cut
Anshu, Anurag
1
2
3
https://orcid.org/0000-0002-3859-9309
Gosset, David
1
2
https://orcid.org/0000-0003-3975-2253
Morenz, Karen
1
2
4
https://orcid.org/0000-0001-9652-1879
Institute for Quantum Computing, University of Waterloo, Canada
Department of Combinatorics and Optimization, University of Waterloo, Canada
Perimeter Institute for Theoretical Physics, Waterloo, Canada
Department of Chemistry, University of Toronto, Canada
We consider a computational problem where the goal is to approximate the maximum eigenvalue of a two-local Hamiltonian that describes Heisenberg interactions between qubits located at the vertices of a graph. Previous work has shed light on this problem’s approximability by product states. For any instance of this problem the maximum energy attained by a product state is lower bounded by the Max Cut of the graph and upper bounded by the standard Goemans-Williamson semidefinite programming relaxation of it. Gharibian and Parekh described an efficient classical approximation algorithm for this problem which outputs a product state with energy at least 0.498 times the maximum eigenvalue in the worst case, and observe that there exist instances where the best product state has energy 1/2 of optimal. We investigate approximation algorithms with performance exceeding this limitation which are based on optimizing over tensor products of few-qubit states and shallow quantum circuits. We provide an efficient classical algorithm which achieves an approximation ratio of at least 0.53 in the worst case. We also show that for any instance defined by a 3 or 4-regular graph, there is an efficiently computable shallow quantum circuit that prepares a state with energy larger than the best product state (larger even than its semidefinite programming relaxation).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.7/LIPIcs.TQC.2020.7.pdf
Approximation algorithms
Quantum many-body systems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
8:1
8:14
10.4230/LIPIcs.TQC.2020.8
article
Simpler Proofs of Quantumness
Brakerski, Zvika
1
Koppula, Venkata
1
Vazirani, Umesh
2
Vidick, Thomas
3
Weizmann Institute of Science, Rehovot, Israel
University of California, Berkeley, CA, USA
California Institute of Technology, Pasadena, CA, USA
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the first step towards constructing a useful quantum computer.
There are currently three approaches for exhibiting proofs of quantumness: (i) Inverting a classically-hard one-way function (e.g. using Shor’s algorithm). This seems technologically out of reach. (ii) Sampling from a classically-hard-to-sample distribution (e.g. BosonSampling). This may be within reach of near-term experiments, but for all such tasks known verification requires exponential time. (iii) Interactive protocols based on cryptographic assumptions. The use of a trapdoor scheme allows for efficient verification, and implementation seems to require much less resources than (i), yet still more than (ii).
In this work we propose a significant simplification to approach (iii) by employing the random oracle heuristic. (We note that we do not apply the Fiat-Shamir paradigm.)
We give a two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function. In contrast to earlier proposals we do not need an adaptive hard-core bit property. This allows the use of smaller security parameters and more diverse computational assumptions (such as Ring Learning with Errors), significantly reducing the quantum computational effort required for a successful demonstration.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.8/LIPIcs.TQC.2020.8.pdf
Proof of Quantumness
Random Oracle
Learning with Errors
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
9:1
9:10
10.4230/LIPIcs.TQC.2020.9
article
Quantum Algorithms for Computational Geometry Problems
Ambainis, Andris
1
https://orcid.org/0000-0002-8716-001X
Larka, Nikita
1
Faculty of Computing, University of Latvia, Raina bulvaris 19, Riga, LV-1586, Latvia
We study quantum algorithms for problems in computational geometry, such as Point-On-3-Lines problem. In this problem, we are given a set of lines and we are asked to find a point that lies on at least 3 of these lines. Point-On-3-Lines and many other computational geometry problems are known to be 3Sum-Hard. That is, solving them classically requires time Ω(n^{2-o(1)}), unless there is faster algorithm for the well known 3Sum problem (in which we are given a set S of n integers and have to determine if there are a, b, c ∈ S such that a + b + c = 0). Quantumly, 3Sum can be solved in time O(n log n) using Grover’s quantum search algorithm. This leads to a question: can we solve Point-On-3-Lines and other 3Sum-Hard problems in O(n^c) time quantumly, for c<2? We answer this question affirmatively, by constructing a quantum algorithm that solves Point-On-3-Lines in time O(n^{1 + o(1)}). The algorithm combines recursive use of amplitude amplification with geometrical ideas. We show that the same ideas give O(n^{1 + o(1)}) time algorithm for many 3Sum-Hard geometrical problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.9/LIPIcs.TQC.2020.9.pdf
Quantum algorithms
quantum search
computational geometry
3Sum problem
amplitude amplification
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
10:1
10:17
10.4230/LIPIcs.TQC.2020.10
article
Quantum Coupon Collector
Arunachalam, Srinivasan
1
Belovs, Aleksandrs
2
Childs, Andrew M.
3
4
Kothari, Robin
5
6
Rosmanis, Ansis
7
de Wolf, Ronald
8
9
10
IBM Research, Yorktown Heights, NY, USA
Faculty of Computing, University of Latvia, Riga, Latvia
Department of Computer Science, Institute for Advanced Computer Studies, University of Maryland, College Park, MD, USA
Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA
Microsoft Quantum, Redmond, WA, USA
Microsoft Research, Redmond, WA, USA
Graduate School of Mathematics, Nagoya University, Japan
QuSoft, Amsterdam, The Netherlands
CWI, Amsterdam, The Netherlands
University of Amsterdam, The Netherlands
We study how efficiently a k-element set S⊆[n] can be learned from a uniform superposition |S> of its elements. One can think of |S>=∑_{i∈S}|i>/√|S| as the quantum version of a uniformly random sample over S, as in the classical analysis of the "coupon collector problem." We show that if k is close to n, then we can learn S using asymptotically fewer quantum samples than random samples. In particular, if there are n-k=O(1) missing elements then O(k) copies of |S> suffice, in contrast to the Θ(k log k) random samples needed by a classical coupon collector. On the other hand, if n-k=Ω(k), then Ω(k log k) quantum samples are necessary.
More generally, we give tight bounds on the number of quantum samples needed for every k and n, and we give efficient quantum learning algorithms. We also give tight bounds in the model where we can additionally reflect through |S>. Finally, we relate coupon collection to a known example separating proper and improper PAC learning that turns out to show no separation in the quantum case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.10/LIPIcs.TQC.2020.10.pdf
Quantum algorithms
Adversary method
Coupon collector
Quantum learning theory
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
11:1
11:23
10.4230/LIPIcs.TQC.2020.11
article
Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities
de Beaudrap, Niel
1
https://orcid.org/0000-0001-9549-5146
Bian, Xiaoning
2
Wang, Quanlong
1
3
Department of Computer Science, University of Oxford, United Kingdom
Department of Mathematics & Statistics, Dalhousie University, Halifax, Canada
Cambridge Quantum Computing Ltd., Cambridge, United Kingdom
In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to say a circuit of CNOT, Hadamard, and π/2-phase rotations, together with T operations (π/4-phase rotations). For many error correcting codes, fault-tolerant realisations of Clifford operations are significantly less resource-intensive than those of T gates, which motivates finding ways to realise the same transformation involving T-count (the number of T gates involved) which is as low as possible. Investigations into this problem [Matthew Amy et al., 2013; Gosset et al., 2014; Matthew Amy et al., 2014; Matthew Amy et al., 2018; Earl T. Campbell and Mark Howard, 2017; Matthew Amy and Michele Mosca, 2019] has led to observations that this problem is closely related to NP-hard tensor decomposition problems [Luke E. Heyfron and Earl T. Campbell, 2018] and is tantamount to the difficult problem of decoding exponentially long Reed-Muller codes [Matthew Amy and Michele Mosca, 2019]. This problem then presents itself as one for which must be content in practise with approximate optimisation, in which one develops an array of tactics to be deployed through some pragmatic strategy. In this vein, we describe techniques to reduce the T-count, based on the effective application of "spider nest identities": easily recognised products of parity-phase operations which are equivalent to the identity operation. We demonstrate the effectiveness of such techniques by obtaining improvements in the T-counts of a number of circuits, in run-times which are typically less than the time required to make a fresh cup of coffee.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.11/LIPIcs.TQC.2020.11.pdf
T-count
Parity-phase operations
Phase gadgets
Clifford hierarchy
ZX calculus
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
158
12:1
12:15
10.4230/LIPIcs.TQC.2020.12
article
A Device-Independent Protocol for XOR Oblivious Transfer
Kundu, Srijita
1
Sikora, Jamie
2
Tan, Ernest Y.-Z.
3
https://orcid.org/0000-0003-4872-158X
Centre for Quantum Technologies, National University of Singapore, Singapore
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
Institute for Theoretical Physics, ETH Zürich, Switzerland
Oblivious transfer is a cryptographic primitive where Alice has two bits and Bob wishes to learn some function of them. Ideally, Alice should not learn Bob’s desired function choice and Bob should not learn any more than logically implied by the function value. While decent quantum protocols for this task are known, many quickly become insecure if an adversary were to control the quantum devices used in the implementation of the protocol. Here we present how some existing protocols fail in this device-independent framework, and give a fully-device independent quantum protocol for XOR oblivious transfer which is provably more secure than any classical protocol.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol158-tqc2020/LIPIcs.TQC.2020.12/LIPIcs.TQC.2020.12.pdf
Quantum cryptography
device independence
oblivious transfer
semidefinite programming
security analysis