eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
0
0
10.4230/LIPIcs.TQC.2019
article
LIPIcs, Volume 135, TQC'19, Complete Volume
van Dam, Wim
1
2
Mančinska, Laura
3
https://orcid.org/0000-0001-9727-4961
University of California, Santa Barbara, CA, U.S.A.
QC Ware, Palo Alto, CA, U.S.A.
University of Copenhagen, Denmark
LIPIcs, Volume 135, TQC'19, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019/LIPIcs.TQC.2019.pdf
Theory of computation, Quantum computation theory, Quantum complexity theory, Quantum communication complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
0:i
0:xiii
10.4230/LIPIcs.TQC.2019.0
article
Front Matter, Table of Contents, Preface, Conference Organization
van Dam, Wim
1
2
Mančinska, Laura
3
https://orcid.org/0000-0001-9727-4961
University of California, Santa Barbara, CA, U.S.A.
QC Ware, Palo Alto, CA, U.S.A.
University of Copenhagen, Denmark
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.0/LIPIcs.TQC.2019.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
1:1
1:23
10.4230/LIPIcs.TQC.2019.1
article
On Quantum Chosen-Ciphertext Attacks and Learning with Errors
Alagic, Gorjan
1
2
Jeffery, Stacey
3
4
Ozols, Maris
3
5
Poremba, Alexander
6
QuICS, University of Maryland, MD, USA
NIST, Gaithersburg, MD, USA
QuSoft, Amsterdam, Netherlands
CWI, Amsterdam, Netherlands
University of Amsterdam, Netherlands
Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA
Quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives.
We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key requires a linear number of decryption queries. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.1/LIPIcs.TQC.2019.1.pdf
quantum chosen-ciphertext security
quantum attacks
learning with errors
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
2:1
2:23
10.4230/LIPIcs.TQC.2019.2
article
Quantum Distinguishing Complexity, Zero-Error Algorithms, and Statistical Zero Knowledge
Ben-David, Shalev
1
Kothari, Robin
2
https://orcid.org/0000-0001-6114-943X
University of Waterloo, Waterloo, ON, Canada
Quantum Architectures and Computation (QuArC) group, Microsoft Research, Redmond, WA, USA
We define a new query measure we call quantum distinguishing complexity, denoted QD(f) for a Boolean function f. Unlike a quantum query algorithm, which must output a state close to |0> on a 0-input and a state close to |1> on a 1-input, a "quantum distinguishing algorithm" can output any state, as long as the output states for any 0-input and 1-input are distinguishable.
Using this measure, we establish a new relationship in query complexity: For all total functions f, Q_0(f)=O~(Q(f)^5), where Q_0(f) and Q(f) denote the zero-error and bounded-error quantum query complexity of f respectively, improving on the previously known sixth power relationship.
We also define a query measure based on quantum statistical zero-knowledge proofs, QSZK(f), which is at most Q(f). We show that QD(f) in fact lower bounds QSZK(f) and not just Q(f). QD(f) also upper bounds the (positive-weights) adversary bound, which yields the following relationships for all f: Q(f) >= QSZK(f) >= QD(f) = Omega(Adv(f)). This sheds some light on why the adversary bound proves suboptimal bounds for problems like Collision and Set Equality, which have low QSZK complexity.
Lastly, we show implications for lifting theorems in communication complexity. We show that a general lifting theorem for either zero-error quantum query complexity or for QSZK would imply a general lifting theorem for bounded-error quantum query complexity.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.2/LIPIcs.TQC.2019.2.pdf
Quantum query complexity
quantum algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
3:1
3:24
10.4230/LIPIcs.TQC.2019.3
article
Circuit Transformations for Quantum Architectures
Childs, Andrew M.
1
2
3
https://orcid.org/0000-0002-9903-837X
Schoute, Eddie
1
2
3
https://orcid.org/0000-0002-5613-1443
Unsal, Cem M.
4
https://orcid.org/0000-0002-7426-9702
Joint Center for Quantum Information and Computer Science, University of Maryland, USA
Institute for Advanced Computer Studies, University of Maryland, USA
Department for Computer Science, University of Maryland, USA
Department of Mathematics, University of Maryland, USA
Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the ROUTING VIA MATCHINGS framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize ROUTING VIA MATCHINGS to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the TOKEN SWAPPING framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.3/LIPIcs.TQC.2019.3.pdf
quantum circuit
quantum architectures
circuit mapping
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
4:1
4:17
10.4230/LIPIcs.TQC.2019.4
article
The RGB No-Signalling Game
Coiteux-Roy, Xavier
1
Crépeau, Claude
2
Facoltà di scienze informatiche, Università della Svizzera italiana, Lugano, Switzerland
School of Computer Science, McGill University, Montréal, Québec, Canada
Introducing the simplest of all No-Signalling Games: the RGB Game where two verifiers interrogate two provers, Alice and Bob, far enough from each other that communication between them is too slow to be possible. Each prover may be independently queried one of three possible colours: Red, Green or Blue. Let a be the colour announced to Alice and b be announced to Bob. To win the game they must reply colours x (resp. y) such that a != x != y != b.
This work focuses on this new game mainly as a pedagogical tool for its simplicity but also because it triggered us to introduce a new set of definitions for reductions among multi-party probability distributions and related non-locality classes. We show that a particular winning strategy for the RGB Game is equivalent to the PR-Box of Popescu-Rohrlich and thus No-Signalling. Moreover, we use this example to define No-Signalling in a new useful way, as the intersection of two natural classes of multi-party probability distributions called one-way signalling. We exhibit a quantum strategy able to beat the classical local maximum winning probability of 8/9 shifting it up to 11/12. Optimality of this quantum strategy is demonstrated using the standard tool of semidefinite programming.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.4/LIPIcs.TQC.2019.4.pdf
No-Signalling
Quantum Entanglement
Non-Locality
Bell inequality
Semidefinite Programming
Non-locality Hierarchy
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
5:1
5:32
10.4230/LIPIcs.TQC.2019.5
article
On the Qubit Routing Problem
Cowtan, Alexander
1
Dilkes, Silas
1
Duncan, Ross
1
2
https://orcid.org/0000-0001-6758-1573
Krajenbrink, Alexandre
1
3
Simmons, Will
1
Sivarajah, Seyon
1
Cambridge Quantum Computing Ltd, 9a Bridge Street, Cambridge, CB2 1UB, United Kingdom
University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XH, United Kingdom
Laboratoire de Physique de l'École Normale Supérieure, PSL University, CNRS, Sorbonne Universités, 24 rue Lhomond, 75231 Paris Cedex 05, France
We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing’s t|ket> compiler. We present empirical results showing the effectiveness of this method in terms of reducing two-qubit gate depth and two-qubit gate count, compared to other implementations.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.5/LIPIcs.TQC.2019.5.pdf
Quantum Computing
Qubit routing
Compilation
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
6:1
6:14
10.4230/LIPIcs.TQC.2019.6
article
Applications of the Quantum Algorithm for st-Connectivity
DeLorenzo, Kai
1
Kimmel, Shelby
1
Witter, R. Teal
1
Middlebury College, Computer Science Department, Middlebury, VT, USA
We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity. Furthermore, we show that our algorithm for cycle detection has improved performance under the promise of large circuit rank or a small number of edges. We also provide algorithms for detecting even-length cycles and for estimating the circuit rank of a graph. All of our algorithms have logarithmic space complexity.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.6/LIPIcs.TQC.2019.6.pdf
graphs
algorithms
query complexity
quantum algorithms
span programs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
7:1
7:19
10.4230/LIPIcs.TQC.2019.7
article
Bayesian ACRONYM Tuning
Gamble, John
1
Granade, Christopher
1
Wiebe, Nathan
1
Quantum Architectures and Computing Group, Microsoft Research, Redmond WA, USA
We provide an algorithm that uses Bayesian randomized benchmarking in concert with a local optimizer, such as SPSA, to find a set of controls that optimizes that average gate fidelity. We call this method Bayesian ACRONYM tuning as a reference to the analogous ACRONYM tuning algorithm. Bayesian ACRONYM distinguishes itself in its ability to retain prior information from experiments that use nearby control parameters; whereas traditional ACRONYM tuning does not use such information and can require many more measurements as a result. We prove that such information reuse is possible under the relatively weak assumption that the true model parameters are Lipschitz-continuous functions of the control parameters. We also perform numerical experiments that demonstrate that over-rotation errors in single qubit gates can be automatically tuned from 88% to 99.95% average gate fidelity using less than 1kB of data and fewer than 20 steps of the optimizer.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.7/LIPIcs.TQC.2019.7.pdf
Quantum Computing
Randomized Benchmarking
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
8:1
8:9
10.4230/LIPIcs.TQC.2019.8
article
A Compressed Classical Description of Quantum States
Gosset, David
1
2
Smolin, John
1
IBM T. J. Watson Research Center, Yorktown Heights, USA
Department of Combinatorics and Optimization and Institute for Quantum Computing, University of Waterloo, Canada
We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an n-qubit state psi consists of its inner products with O(sqrt{2^n}) stabilizer states. A quantum state initially specified by its 2^n entries in the computational basis can be compressed to this form in time O(2^n poly(n)), and, subsequently, the compressed description can be used to additively approximate the expectation value of an arbitrary observable. Our compression scheme directly gives a new protocol for the vector in subspace problem with randomized one-way communication complexity that matches (up to polylogarithmic factors) the optimal upper bound, due to Raz. We obtain an exponential improvement over Raz’s protocol in terms of computational efficiency.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.8/LIPIcs.TQC.2019.8.pdf
Quantum computation
Quantum communication complexity
Classical simulation
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
9:1
9:22
10.4230/LIPIcs.TQC.2019.9
article
Approximate Unitary n^{2/3}-Designs Give Rise to Quantum Channels with Super Additive Classical Holevo Capacity
Nema, Aditya
1
Sen, Pranab
1
School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India
In a breakthrough, Hastings [2009] showed that there exist quantum channels whose classical Holevo capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings' proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate n^{2/3}-design gives rise to a quantum channel with superadditive classical Holevo capacity, where n is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We do so by showing that the minimum output von Neumann entropy of a quantum channel arising from an approximate unitary n^{2/3}-design is subadditive, which by Shor’s work [2002] implies superadditivity of classical Holevo capacity of quantum channels.
We follow the geometric functional analytic approach of Aubrun, Szarek and Werner [Aubrun et al., 2010] in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate t-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low’s technique [2009] for proving concentration of measure for an approximate t-design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work.
Haar random unitaries require at least Omega(n^2) random bits in order to describe them with good precision. In contrast, there exist exact n^{2/3}-designs using only O(n^{2/3} log n) random bits [Kuperberg, 2006]. Thus, our work can be viewed as a partial derandomisation of Hastings' result, and a step towards the quest of finding an explicit quantum channel with superadditive classical Holevo capacity.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.9/LIPIcs.TQC.2019.9.pdf
classical Holevo capacity
super additivity
Haar measure
approximate unitary t-design
polyomial approximation
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-05-31
135
10:1
10:19
10.4230/LIPIcs.TQC.2019.10
article
Parameterization of Tensor Network Contraction
O'Gorman, Bryan
1
2
https://orcid.org/0000-0001-5164-8083
Berkeley Quantum Information & Computation Center, University of California, Berkeley, CA, USA
Quantum Artificial Intelligence Laboratory, NASA Ames, Moffett Field, CA, USA
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and hyperedges. The fundamental objects of our framework are rooted and unrooted contraction trees, which represent classes of contraction orders. Properties of a contraction tree correspond directly and precisely to the time and space costs of tensor network contraction. The properties of rooted contraction trees give the costs of parallelized contraction algorithms. We show how contraction trees relate to existing tree-like objects in the graph theory literature, bringing to bear a wide range of graph algorithms and tools to tensor network contraction. Independent of tensor networks, we show that the edge congestion of a graph is almost equal to the branchwidth of its line graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol135-tqc2019/LIPIcs.TQC.2019.10/LIPIcs.TQC.2019.10.pdf
tensor networks
parameterized complexity
tree embedding
congestion