Volume
LIPIcs, Volume 232
17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)
Publication Details
- published at: 2022-07-04
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-237-2
- DBLP: db/conf/tqc/tqc2022
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Complete Volume
LIPIcs, Volume 232, TQC 2022, Complete Volume
Abstract
LIPIcs, Volume 232, TQC 2022, Complete Volume
Cite as
17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 1-218, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@Proceedings{legall_et_al:LIPIcs.TQC.2022,
title = {{LIPIcs, Volume 232, TQC 2022, Complete Volume}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {1--218},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022},
URN = {urn:nbn:de:0030-drops-165067},
doi = {10.4230/LIPIcs.TQC.2022},
annote = {Keywords: LIPIcs, Volume 232, TQC 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{legall_et_al:LIPIcs.TQC.2022.0,
author = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {0:i--0:xii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.0},
URN = {urn:nbn:de:0030-drops-165071},
doi = {10.4230/LIPIcs.TQC.2022.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Quantum Algorithms for Learning a Hidden Graph
Abstract
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any edges. In the second ("parity queries"), the oracle returns the parity of the number of edges in a subset. In the third model, we are given copies of the graph state corresponding to the graph.
We give quantum algorithms that achieve speedups over the best possible classical algorithms in the OR and parity query models, for some families of graphs, and give quantum algorithms in the graph state model whose complexity is similar to the parity query model. For some parameter regimes, the speedups can be exponential in the parity query model. On the other hand, without any promise on the graph, no speedup is possible in the OR query model.
A main technique we use is the quantum algorithm for solving the combinatorial group testing problem, for which a query-efficient quantum algorithm was given by Belovs. Here we additionally give a time-efficient quantum algorithm for this problem, based on the algorithm of Ambainis et al. for a "gapped" version of the group testing problem.
Cite as
Ashley Montanaro and Changpeng Shao. Quantum Algorithms for Learning a Hidden Graph. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{montanaro_et_al:LIPIcs.TQC.2022.1,
author = {Montanaro, Ashley and Shao, Changpeng},
title = {{Quantum Algorithms for Learning a Hidden Graph}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {1:1--1:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.1},
URN = {urn:nbn:de:0030-drops-165081},
doi = {10.4230/LIPIcs.TQC.2022.1},
annote = {Keywords: Quantum algorithms, query complexity, graphs, combinatorial group testing}
}
Document
Quantum Algorithm for Stochastic Optimal Stopping Problems with Applications in Finance
Abstract
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on quantum access to a stochastic process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo. For this algorithm, we elucidate the intricate interplay of function approximation and quantum algorithms for Monte Carlo. Our algorithm achieves a nearly quadratic speedup in the runtime compared to the LSM algorithm under some mild assumptions. Specifically, our quantum algorithm can be applied to American option pricing and we analyze a case study for the common situation of Brownian motion and geometric Brownian motion processes.
Cite as
João F. Doriguello, Alessandro Luongo, Jinge Bao, Patrick Rebentrost, and Miklos Santha. Quantum Algorithm for Stochastic Optimal Stopping Problems with Applications in Finance. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{doriguello_et_al:LIPIcs.TQC.2022.2,
author = {Doriguello, Jo\~{a}o F. and Luongo, Alessandro and Bao, Jinge and Rebentrost, Patrick and Santha, Miklos},
title = {{Quantum Algorithm for Stochastic Optimal Stopping Problems with Applications in Finance}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {2:1--2:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.2},
URN = {urn:nbn:de:0030-drops-165091},
doi = {10.4230/LIPIcs.TQC.2022.2},
annote = {Keywords: Quantum computation complexity, optimal stopping time, stochastic processes, American options, quantum finance}
}
Document
The Parametrized Complexity of Quantum Verification
Abstract
We initiate the study of parameterized complexity of QMA problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists a classical algorithm solving the problem with a runtime scaling exponentially in the number of non-Clifford gates but only polynomially with the system size. This result follows from our main result, that for any Clifford + t T-gate quantum circuit satisfiability problem, the search space of optimal witnesses can be reduced to a stabilizer subspace isomorphic to at most t qubits (independent of the system size). Furthermore, we derive new lower bounds on the T-count of circuit satisfiability instances and the T-count of the W-state assuming the classical exponential time hypothesis (ETH). Lastly, we explore the parameterized complexity of the quantum non-identity check problem.
Cite as
Srinivasan Arunachalam, Sergey Bravyi, Chinmay Nirkhe, and Bryan O'Gorman. The Parametrized Complexity of Quantum Verification. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{arunachalam_et_al:LIPIcs.TQC.2022.3,
author = {Arunachalam, Srinivasan and Bravyi, Sergey and Nirkhe, Chinmay and O'Gorman, Bryan},
title = {{The Parametrized Complexity of Quantum Verification}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {3:1--3:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.3},
URN = {urn:nbn:de:0030-drops-165104},
doi = {10.4230/LIPIcs.TQC.2022.3},
annote = {Keywords: parametrized complexity, quantum verification, QMA}
}
Document
Averaged Circuit Eigenvalue Sampling
Abstract
We introduce ACES, a method for scalable noise metrology of quantum circuits that stands for Averaged Circuit Eigenvalue Sampling. It simultaneously estimates the individual error rates of all the gates in collections of quantum circuits, and can even account for space and time correlations between these gates. ACES strictly generalizes randomized benchmarking (RB), interleaved RB, simultaneous RB, and several other related techniques. However, ACES provides much more information and provably works under strictly weaker assumptions than these techniques. Finally, ACES is extremely scalable: we demonstrate with numerical simulations that it simultaneously and precisely estimates all the Pauli error rates on every gate and measurement in a 100 qubit quantum device using fewer than 20 relatively shallow Clifford circuits and an experimentally feasible number of samples. By learning the detailed gate errors for large quantum devices, ACES opens new possibilities for error mitigation, bespoke quantum error correcting codes and decoders, customized compilers, and more.
Cite as
Steven T. Flammia. Averaged Circuit Eigenvalue Sampling. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 4:1-4:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{flammia:LIPIcs.TQC.2022.4,
author = {Flammia, Steven T.},
title = {{Averaged Circuit Eigenvalue Sampling}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {4:1--4:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.4},
URN = {urn:nbn:de:0030-drops-165114},
doi = {10.4230/LIPIcs.TQC.2022.4},
annote = {Keywords: Quantum noise estimation, quantum benchmarking, QCVV}
}
Document
Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions
Abstract
Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser entangled states which have more favourable decompositions, we can speed up these simulations. This is made possible by using the ZX-calculus, which allows us to easily find instances of these entangled states in the simplified diagram representing the quantum circuit to be simulated. We additionally find a new technique of partial stabiliser decompositions that allow us to trade magic states for stabiliser terms. With this technique we require only 2^{α t} stabiliser terms, where α≈ 0.396, to simulate a circuit with T-count t. This matches the α found by Qassim et al. [Qassim et al., 2021], but whereas they only get this scaling in the asymptotic limit, ours applies for a circuit of any size. Our method builds upon a recently proposed scheme for simulation combining stabiliser decompositions and optimisation strategies implemented in the software QuiZX [Kissinger and van de Wetering, 2022]. With our techniques we manage to reliably simulate 50-qubit 1400 T-count hidden shift circuits in a couple of minutes on a consumer laptop.
Cite as
Aleks Kissinger, John van de Wetering, and Renaud Vilmart. Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{kissinger_et_al:LIPIcs.TQC.2022.5,
author = {Kissinger, Aleks and van de Wetering, John and Vilmart, Renaud},
title = {{Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {5:1--5:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.5},
URN = {urn:nbn:de:0030-drops-165128},
doi = {10.4230/LIPIcs.TQC.2022.5},
annote = {Keywords: ZX-calculus, Stabiliser Rank, Quantum Simulation}
}
Document
On Converses to the Polynomial Method
Abstract
A surprising "converse to the polynomial method" of Aaronson et al. (CCC'16) shows that any bounded quadratic polynomial can be computed exactly in expectation by a 1-query algorithm up to a universal multiplicative factor related to the famous Grothendieck constant. A natural question posed there asks if bounded quartic polynomials can be approximated by 2-query quantum algorithms. Arunachalam, Palazuelos and the first author showed that there is no direct analogue of the result of Aaronson et al. in this case. We improve on this result in the following ways: First, we point out and fix a small error in the construction that has to do with a translation from cubic to quartic polynomials. Second, we give a completely explicit example based on techniques from additive combinatorics. Third, we show that the result still holds when we allow for a small additive error. For this, we apply an SDP characterization of Gribling and Laurent (QIP'19) for the completely-bounded approximate degree.
Cite as
Jop Briët and Francisco Escudero Gutiérrez. On Converses to the Polynomial Method. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{briet_et_al:LIPIcs.TQC.2022.6,
author = {Bri\"{e}t, Jop and Escudero Guti\'{e}rrez, Francisco},
title = {{On Converses to the Polynomial Method}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {6:1--6:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.6},
URN = {urn:nbn:de:0030-drops-165139},
doi = {10.4230/LIPIcs.TQC.2022.6},
annote = {Keywords: Quantum query complexity, polynomial method, completely bounded polynomials}
}
Document
The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model
Abstract
The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth p. We apply the QAOA to MaxCut on large-girth D-regular graphs. We give an iterative formula to evaluate performance for any D at any depth p. Looking at random D-regular graphs, at optimal parameters and as D goes to infinity, we find that the p = 11 QAOA beats all classical algorithms (known to the authors) that are free of unproven conjectures. While the iterative formula for these D-regular graphs is derived by looking at a single tree subgraph, we prove that it also gives the ensemble-averaged performance of the QAOA on the Sherrington-Kirkpatrick (SK) model defined on the complete graph. We also generalize our formula to Max-q-XORSAT on large-girth regular hypergraphs. Our iteration is a compact procedure, but its computational complexity grows as O(p² 4^p). This iteration is more efficient than the previous procedure for analyzing QAOA performance on the SK model, and we are able to numerically go to p = 20. Encouraged by our findings, we make the optimistic conjecture that the QAOA, as p goes to infinity, will achieve the Parisi value. We analyze the performance of the quantum algorithm, but one needs to run it on a quantum computer to produce a string with the guaranteed performance.
Cite as
Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, and Leo Zhou. The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{basso_et_al:LIPIcs.TQC.2022.7,
author = {Basso, Joao and Farhi, Edward and Marwaha, Kunal and Villalonga, Benjamin and Zhou, Leo},
title = {{The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {7:1--7:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.7},
URN = {urn:nbn:de:0030-drops-165144},
doi = {10.4230/LIPIcs.TQC.2022.7},
annote = {Keywords: Quantum algorithm, Max-Cut, spin glass, approximation algorithm}
}
Document
A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation
Abstract
Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice’s and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near perfect) security is impossible, even for quantum protocols. We generalize this no-go result by exhibiting a constant lower bound on the cheating probabilities for any quantum protocol for secure function evaluation, and present many applications from oblivious transfer to the millionaire’s problem. Constant lower bounds are of practical interest since they imply the impossibility to arbitrarily amplify the security of quantum protocols by any means.
Cite as
Sarah A. Osborn and Jamie Sikora. A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{osborn_et_al:LIPIcs.TQC.2022.8,
author = {Osborn, Sarah A. and Sikora, Jamie},
title = {{A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {8:1--8:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.8},
URN = {urn:nbn:de:0030-drops-165151},
doi = {10.4230/LIPIcs.TQC.2022.8},
annote = {Keywords: Quantum cryptography, security analysis, secure function evaluation}
}
Document
Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension
Abstract
We present a classical algorithm that, for any D-dimensional geometrically-local, quantum circuit C of polylogarithmic-depth, and any bit string x ∈ {0,1}ⁿ, can compute the quantity |<x|C|0^{⊗ n}>|² to within any inverse-polynomial additive error in quasi-polynomial time, for any fixed dimension D. This is an extension of the result [Nolan J. Coble and Matthew Coudron, 2021], which originally proved this result for D = 3. To see why this is interesting, note that, while the D = 1 case of this result follows from a standard use of Matrix Product States, known for decades, the D = 2 case required novel and interesting techniques introduced in [Sergy Bravyi et al., 2020]. Extending to the case D = 3 was even more laborious, and required further new techniques introduced in [Nolan J. Coble and Matthew Coudron, 2021]. Our work here shows that, while handling each new dimension has historically required a new insight, and fixed algorithmic primitive, based on known techniques for D ≤ 3, we can now handle any fixed dimension D > 3.
Our algorithm uses the Divide-and-Conquer framework of [Nolan J. Coble and Matthew Coudron, 2021] to approximate the desired quantity via several instantiations of the same problem type, each involving D-dimensional circuits on about half the number of qubits as the original. This division step is then applied recursively, until the width of the recursively decomposed circuits in the D^{th} dimension is so small that they can effectively be regarded as (D-1)-dimensional problems by absorbing the small width in the D^{th} dimension into the qudit structure at the cost of a moderate increase in runtime. The main technical challenge lies in ensuring that the more involved portions of the recursive circuit decomposition and error analysis from [Nolan J. Coble and Matthew Coudron, 2021] still hold in higher dimensions, which requires small modifications to the analysis in some places. Our work also includes some simplifications, corrections and clarifications of the use of block-encodings within the original classical algorithm in [Nolan J. Coble and Matthew Coudron, 2021].
Cite as
Suchetan Dontha, Shi Jie Samuel Tan, Stephen Smith, Sangheon Choi, and Matthew Coudron. Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{dontha_et_al:LIPIcs.TQC.2022.9,
author = {Dontha, Suchetan and Tan, Shi Jie Samuel and Smith, Stephen and Choi, Sangheon and Coudron, Matthew},
title = {{Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {9:1--9:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.9},
URN = {urn:nbn:de:0030-drops-165163},
doi = {10.4230/LIPIcs.TQC.2022.9},
annote = {Keywords: Low-Depth Quantum Circuits, Matrix Product States, Block-Encoding}
}
Document
Memory Compression with Quantum Random-Access Gates
Abstract
In the classical RAM, we have the following useful property. If we have an algorithm that uses M memory cells throughout its execution, and in addition is sparse, in the sense that, at any point in time, only m out of M cells will be non-zero, then we may "compress" it into another algorithm which uses only m log M memory and runs in almost the same time. We may do so by simulating the memory using either a hash table, or a self-balancing tree.
We show an analogous result for quantum algorithms equipped with quantum random-access gates. If we have a quantum algorithm that runs in time T and uses M qubits, such that the state of the memory, at any time step, is supported on computational-basis vectors of Hamming weight at most m, then it can be simulated by another algorithm which uses only O(m log M) memory, and runs in time Õ(T).
We show how this theorem can be used, in a black-box way, to simplify the presentation in several papers. Broadly speaking, when there exists a need for a space-efficient history-independent quantum data-structure, it is often possible to construct a space-inefficient, yet sparse, quantum data structure, and then appeal to our main theorem. This results in simpler and shorter arguments.
Cite as
Harry Buhrman, Bruno Loff, Subhasree Patro, and Florian Speelman. Memory Compression with Quantum Random-Access Gates. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{buhrman_et_al:LIPIcs.TQC.2022.10,
author = {Buhrman, Harry and Loff, Bruno and Patro, Subhasree and Speelman, Florian},
title = {{Memory Compression with Quantum Random-Access Gates}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {10:1--10:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.10},
URN = {urn:nbn:de:0030-drops-165177},
doi = {10.4230/LIPIcs.TQC.2022.10},
annote = {Keywords: complexity theory, data structures, algorithms, quantum walk}
}
Document
Quantum Speedups for Treewidth
Abstract
In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses O(2.616ⁿ) time and polynomial space. We show three quantum algorithms with the following complexity, using QRAM in both exponential space algorithms:
- O(1.618ⁿ) time and polynomial space;
- O(1.554ⁿ) time and O(1.452ⁿ) space;
- O(1.538ⁿ) time and space. In contrast, the fastest known classical algorithm for treewidth uses O(1.755ⁿ) time and space. The first two speed-ups are obtained in a fairly straightforward way. The first version uses additionally only Grover’s search and provides a quadratic speedup. The second speedup is more time-efficient and uses both Grover’s search and the quantum exponential dynamic programming by Ambainis et al. (SODA '19). The third version uses the specific properties of the classical algorithm and treewidth, with a modified version of the quantum dynamic programming on the hypercube. As a small side result, we give a new classical time-space tradeoff for computing treewidth in O^*(2ⁿ) time and O^*(√{2ⁿ}) space.
Cite as
Vladislavs Kļevickis, Krišjānis Prūsis, and Jevgēnijs Vihrovs. Quantum Speedups for Treewidth. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{klevickis_et_al:LIPIcs.TQC.2022.11,
author = {K\c{l}evickis, Vladislavs and Pr\={u}sis, Kri\v{s}j\={a}nis and Vihrovs, Jevg\={e}nijs},
title = {{Quantum Speedups for Treewidth}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {11:1--11:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.11},
URN = {urn:nbn:de:0030-drops-165186},
doi = {10.4230/LIPIcs.TQC.2022.11},
annote = {Keywords: Quantum computation, Treewidth, Exact algorithms, Dynamic programming}
}
Document
Qutrit Metaplectic Gates Are a Subset of Clifford+T
Abstract
A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes Clifford+T approximately universal, is injectable by a magic state, and supports magic state distillation. However, it was claimed that a better gate set for qutrits might be Clifford+R, where R = diag(1,1,-1) is the metaplectic gate, as certain protocols and gates could more easily be implemented using the R gate than the T gate. In this paper we show that the qutrit Clifford+R unitaries form a strict subset of the Clifford+T unitaries when we have at least two qutrits. We do this by finding a direct decomposition of R ⊗ 𝕀 as a Clifford+T circuit and proving that the T gate cannot be exactly synthesized in Clifford+R. This shows that in fact the T gate is more expressive than the R gate. Moreover, we additionally show that it is impossible to find a single-qutrit Clifford+T decomposition of the R gate, making our result tight.
Cite as
Andrew N. Glaudell, Neil J. Ross, John van de Wetering, and Lia Yeh. Qutrit Metaplectic Gates Are a Subset of Clifford+T. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
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@InProceedings{glaudell_et_al:LIPIcs.TQC.2022.12,
author = {Glaudell, Andrew N. and Ross, Neil J. and van de Wetering, John and Yeh, Lia},
title = {{Qutrit Metaplectic Gates Are a Subset of Clifford+T}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {12:1--12:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.12},
URN = {urn:nbn:de:0030-drops-165195},
doi = {10.4230/LIPIcs.TQC.2022.12},
annote = {Keywords: Quantum computation, qutrits, gate synthesis, metaplectic gate, Clifford+T}
}