日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

/pdf/digitized-adiabatic-quantum-computing-with-a-superconducting-2nhmfcnqj4.pdf

Digitized adiabatic quantum computing with a superconducting circuit, part I: Theory

A machine equivalent to Turing machine, that is more intuitive in its working is defined. Three derivation rules are added to Elementary Arithmetic of Godel and his incompleteness theorems are proved without using any metalanguage. Two axioms are added to Zermelo-Fraenkel theory to derive the Continuum Hypothesis and to split the unit interval into infinitesimals.

Foundations of Computer Science

Ising machines are hardware solvers that aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because any problem in the complexity class NP can be formulated as an Ising problem with only polynomial overhead, and thus a scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications. We survey the status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors and digital hardware accelerators; dynamical systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses. Minimizing the energy of the Ising model is a prototypical combinatorial optimization problem, ubiquitous in our increasingly automated world. This Review surveys Ising machines — special-purpose hardware solvers for this problem — and examines the various operating principles and compares their performance. 

/pdf/ising-machines-as-hardware-solvers-of-combinatorial-2ul6a5j8.pdf

Ising machines as hardware solvers of combinatorial optimization problems

The papers in this volume were presented at the Thirty-Sixth Annual ACM Symposium on Theory of Computing (STOC 2004), held in Chicago, Illinois, June 13-15, 2004. The Symposium was sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT).In response to a Call For Papers, posted at a University of Chicago website, 271 submissions were received by the submission deadline of November 5, 4:59pm EST. All were submitted electronically on the Microsoft Conference Management Toolkit (CMT) website.The Program Committee began its deliberations electronically on December 10, and continued in that medium until its meeting in New Orleans, Louisiana, on January 9 and 10. Electronic discussion of unresolved issues continued for some weeks after the meeting.The CMT website was used for paper submission and initial posting of reviews and comments; most of the discussion was conducted and coordinated on a University of Chicago website using software produced by Daniel Tefankovic and tailored to the needs of the PC.The Program Committee selected 71 papers for presentation; one was later withdrawn.The submissions were not refereed, and many of these papers represented reports of continuing research. It is expected that most of them will appear in a more polished and complete form in scientific journals.The papers encompass a wide variety of areas of theoretical computer science, ranging from classical problems in algorithms and complexity theory (including lower bounds, graph algorithms, network flows, cryptography, random structures, inapproximabilty/PCPs), to heavily represented emerging areas and models such as quantum computing and algorithmic game theory. A number of additional areas of traditional or more recent interest to the SIGACT community are represented by one or two papers each; these include: distributed computing, computational geometry/topology, mathematical algorithms, metric spaces/embeddings, data mining, analysis of data streams, property testing.In addition to the contributed talks, the program included three invited plenary talks, represented by brief abstracts in this volume: Quantum Algorithms a Decade After Shor, by Andris Ambainis (see page 111); Network Games, by Eva Tardos (see page 341); and Depth Through Breadth, or Why Should We Attend Talks In Other Areas?, by Avi Wigderson (see page 579).The Program Committee would like to thank all authors who submitted papers for consideration. The PC also wishes to thank the large number of members of the community who assisted the PC in assessing the merits of the submissions (see "Reviewers," page xii).The PC is grateful to Microsoft Research and to the CMT Web Support staff for providing the web-site and assisting with its use.

Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for continued exploration and interest in the QA framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms that have been introduced in the literature. These continuous-time Hamiltonian computation algorithms rely on control protocols that are more advanced than those in traditional ground-state QA, while still being considerably simpler than those used in gate-model implementations. The inclusion of coherent diabatic transitions to excited states results in a generalization called diabatic quantum annealing (DQA), which we argue for as the most promising route to quantum enhancement within this framework. Other promising variants of traditional QA include reverse annealing and continuous-time quantum walks, as well as analog analogues of parameterized quantum circuit ansatzes for machine learning. Most of these algorithms have no known (or likely to be discovered) efficient classical simulations, and in many cases have promising (but limited) early signs for the possibility of quantum speedups, making them worthy of further investigation with quantum hardware in the intermediate-scale regime. We argue that all of these protocols can be explored in a state-of-the-art manner by embracing the full range of novel out-of-equilibrium quantum dynamics generated by time-dependent effective transverse-field Ising Hamiltonians that can be natively implemented by, e.g., inductively-coupled flux qubits, both existing and projected at application scale.

Prospects for Quantum Enhancement with Diabatic Quantum Annealing

Optimization, sampling and machine learning are topics of broad interest that have inspired significant developments and new approaches in quantum computing. One such approach is quantum annealing (QA). In this Review, we assess the prospects for algorithms within the general framework of QA to achieve a quantum speedup relative to classical state-of-the-art methods. We argue for continued exploration in the QA framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms. These continuous-time Hamiltonian computation algorithms rely on control protocols that are more advanced than those in traditional ground-state QA, while still being considerably simpler than those used in gate-model implementations. The inclusion of coherent diabatic transitions to excited states results in a generalization we refer to collectively as diabatic quantum annealing, which we believe is the most promising route to quantum enhancement within this framework. Other promising variants of traditional QA include reverse annealing, continuous-time quantum walks and analogues of parameterized quantum circuit ansatzes for machine learning. Most of these algorithms have no known efficient classical simulations, making them worthy of further investigation with quantum hardware in the intermediate-scale regime. Quantum annealing is a widely used heuristic algorithm for optimization and sampling, implemented in commercial processors. This Review provides a critical assessment of the field and points to new opportunities for a quantum advantage via recently developed alternative quantum annealing protocols.

E. J. Crosson

Papers

Prospects for Quantum Enhancement with Diabatic Quantum Annealing

Prospects for quantum enhancement with diabatic quantum annealing