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Towards simulating 2D effects in lattice gauge theories on a quantum computer

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arXiv 2020年

作者： Paulson, Danny Dellantonio, Luca Haase, Jan F. Celi, Alessio Kan, Angus Jena, Andrew Kokail, Christian van Bijnen, Rick Jansen, Karl Zoller, Peter Muschik, Christine A. Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics & Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Departament de Física Universitat Autònoma de Barcelona BellaterraE-08193 Spain Center of Quantum Physics University of Innsbruck InnsbruckA-6020 Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences InnsbruckA-6020 Austria Department of Combinatorics & Optimization University of Waterloo WaterlooONN2L 3G1 Canada NIC DESY Zeuthen Platanenallee 6 Zeuthen15738 Germany Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada

quantum computing is in its greatest upswing, with so-called Noisy-Intermediate-Scale-quantum devices heralding the computational power to be expected in the near future. While the field is progressing towards quantum advantage, quantum computers already have the potential to tackle classically intractable problems. Here, we consider gauge theories describing fundamental particle interactions. On the way to their full-fledged quantum simulations, the challenge of limited resources on near-term quantum devices has to be overcome. We propose an experimental quantum simulation scheme to study ground state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. Our protocols can be adapted to larger lattices and offer the perspective to connect the lattice simulation to low energy observable quantities, e.g. the hadron spectrum, in the continuum theory. By including both dynamical matter and a non-minimal gauge field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware. More specifically, we present two Variational quantum Eigensolver (VQE) based protocols for the study of magnetic field effects, and for taking an important first step towards computing the running coupling of QED. For both instances, we include variational quantum circuits for qubit-based hardware. We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions. While this feasibility analysis is done for trapped ions, our approach can be directly adapted to other platforms. The techniques presented here, combined with advancements in quantum hardware, pave the way for reaching beyond the capabilities of classical simulations. Copyright © 2020, The Authors. All rights reserved.

关键词： quantum chemistry

Practical quantum appointment scheduling

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arXiv 2018年

作者： Touchette, Dave Lovitz, Benjamin Lütkenhaus, Norbert Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo Perimeter Institute for Theoretical Physics Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo

We propose a protocol based on coherent states and linear optics operations for solving the appointmentscheduling problem. Our main protocol leaks strictly less information about each party's input than the optimal classical protocol, even when considering experimental errors. Along with the ability to generate constant-amplitude coherent states over two modes, this protocol requires the ability to transfer these modes back-and-forth between the two parties multiple times with low coupling loss. The implementation requirements are thus still challenging. Along the way, we develop new tools to study quantum information cost of interactive protocols in the finite regime. Copyright © 2018, The Authors. All rights reserved.

关键词： Scheduling

quantum advantage with noisy shallow circuits in 3D

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arXiv 2019年

作者： Bravyi, Sergey Gosset, David Konig, Robert Tomamichel, Marco IBM T. J. Watson Research Center Yorktown Heights United States Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo Waterloo Canada Institute for Advanced Study and Zentrum Mathematik Technical University of Munich Munich Germany Centre for Quantum Software and Information and School of Software University of Technology Sydney Sydney Australia

Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any classical constant depth circuit composed of bounded fan-in gates. Here we provide two extensions of this result. Firstly, we show that a separation in computational power persists even when the constant-depth quantum circuit is restricted to geometrically local gates in one dimension. The corresponding quantum algorithm is the simplest we know of which achieves a quantum advantage of this type. It may also be more practical for future implementations. Our second, main result, is that a separation persists even if the shallow quantum circuit is corrupted by noise. We construct a relation problem which can be solved with near certainty using a noisy constant-depth quantum circuit composed of geometrically local gates in three dimensions, provided the noise rate is below a certain constant threshold value. On the other hand, the problem cannot be solved with high probability by a noise-free classical circuit of constant depth. A key component of the proof is a quantum error-correcting code which admits constant-depth logical Clifiord gates and single-shot logical state preparation. We show that the surface code meets these criteria. To this end, we provide a protocol for single-shot logical state preparation in the surface code which may be of independent interest. Copyright © 2019, The Authors. All rights reserved.

关键词： quantum theory

Eventually entanglement breaking maps

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arXiv 2018年

作者： Rahaman, Mizanur Jaques, Sam Paulsen, Vern I. Department of Pure Mathematics University of Waterloo Institute for Quantum Computing University of Waterloo Department of Combinatorics and Optimization University of Waterloo

We analyze linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor product space. If a linear map becomes entanglement breaking after finitely many iterations, we say the map has a finite index of separability. In particular we show that every unital PPT-channel has a finite index of separability and that the class of unital channels that have finite index of separability is a dense subset of the unital channels. We construct concrete examples of maps which are not PPT but have finite index of separability. We prove that there is a large class of unital channels that are asymptotically entanglement breaking. This analysis is motivated by the PPT-squared conjecture made by M. Christandl that says every PPT channel, when composed with itself, becomes entanglement breaking. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

Factoring semi-primes with (quantum) SAT-solvers

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arXiv 2019年

作者： Mosca, Michele Verschoor, Sebastian R. Institute for Quantum Computing University of Waterloo Canada Department of Combinatorics & Optimization University of Waterloo Canada David R. Cheriton School of Computer Science University of Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada Canadian Institute for Advanced Research Toronto Canada evolutionQ Inc. Waterloo Canada

The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms for classical computers run in sub-exponential time. Since integer factorization is in NP, one can reduce this problem to any NP-hard problem, such as Boolean Satisfiability (SAT). While reducing factoring to SAT has proved to be useful for studying SAT solvers, attempting to factor large integers via such a reduction has not been found to be successful. Shor’s quantum factoring algorithm factors any integer in polynomial time. Large-scale fault-tolerant quantum computers capable of implementing Shor’s algorithm are not yet available, so relevant benchmarking experiments for factoring via Shor’s algorithm are not yet possible. In recent years, however, several authors have attempted factorizations with the help of quantum processors via reductions to NP-hard problems. While this approach may shed some light on some algorithmic approaches for quantum solutions to NP-hard problems, in this paper we study and question the practical effectiveness of this approach for factoring large numbers. We find no evidence that this is a viable path toward factoring large numbers, even for scalable fault-tolerant quantum computers, as well as for various quantum annealing or other special purpose quantum hardware. Copyright © 2019, The Authors. All rights reserved.

关键词： Computational complexity

Neural ensemble decoding for topological quantum error-correcting codes

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Physical Review A 2020年第3期101卷 032338-032338页

作者： Milap Sheth Sara Zafar Jafarzadeh Vlad Gheorghiu Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada N2L 3G1 David R. Cheriton School of Computer Science University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Computer Science and Operations Research Université de Montreal Montreal Quebec Canada H3T 1J4 softwareQ Inc. Kitchener Ontario Canada N2M 0A9

Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We classify each error syndrome to the decoder which is more likely to decode it correctly using machine learning techniques. We apply our framework to an ensemble of minimum-weight perfect matching (MWPM) and hard-decision re-normalization-group decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudothreshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability.

关键词： Machine learning quantum computation quantum memories Surface code quantum computing Topological quantum computing

On speeding up factoring with quantum SAT solvers

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arXiv 2019年

作者： Mosca, Michele Basso, João Marcos Vensi Verschoor, Sebastian R. Institute for Quantum Computing University of Waterloo Canada Department of Physics and Astronomy Tufts University United States Department of Combinatorics & Optimization University of Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada evolutionQ Inc. Waterloo Canada David R. Cheriton School of Computer Science University of Waterloo Canada

There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is competitive with the best known classical method, the Number Field Sieve. Many of the techniques tried involved directly encoding multiplication to SAT or an equivalent NP-hard problem and looking for satisfying assignments of the variables representing the prime factors. The main challenge in these cases is that, to compete with the Number Field Sieve, the quantum SAT solver would need to be superpolynomially faster than classical SAT solvers. In this paper the use of SAT solvers is restricted to a smaller task related to factoring: finding smooth numbers, which is an essential step of the Number Field Sieve. We present a SAT circuit that can be given to quantum SAT solvers such as annealers in order to perform this step of factoring. If quantum SAT solvers achieve any speedup over classical brute-force search, then our factoring algorithm is faster than the classical NFS. Copyright © 2019, The Authors. All rights reserved.

关键词： Model checking

Neural ensemble decoding for topological quantum error-correcting codes

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arXiv 2019年

作者： Sheth, Milap Jafarzadeh, Sara Zafar Gheorghiu, Vlad Institute for Quantum Computing University of Waterloo WaterlooON Canada Department of Combinatorics and Optimization University of Waterloo WaterlooON Canada David R. Cheriton School of Computer Science University of Waterloo WaterlooON Canada Department of Computer Science and Operations Research Université de Montreal MontrealQC Canada softwareQ Inc. KitchenerON Canada

Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We use machine learning techniques to assign a given error syndrome to the decoder which is likely to decode it correctly. We apply our framework to an ensemble of Minimum-Weight Perfect Matching (MWPM) and Hard-Decision Re-normalization Group (HDRG) decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudo-threshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability. Copyright © 2019, The Authors. All rights reserved.

关键词： Decoding

A compressed classical description of quantum states

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arXiv 2018年

作者： Gosset, David Smolin, John Ibm T.J. Watson Research Center United States Department of Combinatorics and Optimization 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 ψ consists of its inner products with O(√2n) stabilizer states. A quantum state initially specified by its 2nentries in the computational basis can be compressed to this form in time O(2npoly(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. Copyright © 2018, The Authors. All rights reserved.

关键词： Computational efficiency