Optimal Hamiltonian simulation for time-periodic systems

The implementation of time-evolution operators $U(t)$, called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution $U(t)=e^{-iHt}$, with achieving the optimal computational resource both in time $t$ and an allowable error $\varepsilon$. In contrast, those for time-dependent systems require larger cost due to the difficulty of handling time-dependency. In this paper, we establish optimal/nearly-optimal Hamiltonian simulation for generic time-dependent systems with time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped with auxiliary states labeling Fourier indices, we develop a way to certainly obtain the target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, the query complexity, which measures the cost for implementing the time-evolution, has optimal and nearly-optimal dependency respectively in time $t$ and inverse error $\varepsilon$, and becomes sufficiently close to that of qubitization. Thus, our protocol tells us that, among generic time-dependent systems, time-periodic systems provides a class accessible as efficiently as time-independent systems despite the existence of time-dependency. As we also provide applications to simulation of nonequilibrium phenomena and adiabatic state preparation, our results will shed light on nonequilibrium phenomena in condensed matter physics and quantum chemistry, and quantum tasks yielding time-dependency in quantum computation.Comment: 55 pages, 2 figures, 1 tabl

Recursive Quantum Eigenvalue/Singular-Value Transformation: Analytic Construction of Matrix Sign Function by Newton Iteration

Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable matrix functions in these techniques is difficult for large-scale quantum systems: there is no analytical result other than trivial cases as far as we know and we often suffer also from numerical instability. We propose recursive QET or QSVT (r-QET or r-QSVT), in which we can execute complicated matrix functions by recursively organizing block-encoding by low-degree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, by exploiting the recursive relation of Newton iteration, we construct the matrix sign function, which can be applied for eigenstate filtering for example, in a tractable way. We show that an analytically-obtained parameter set composed of only $8$ different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error $\varepsilon$. Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability.Comment: 10 pages, 1figur

Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials

A programmable quantum device that has a large number of qubits without fault-tolerance has emerged recently. Variational quantum eigensolver (VQE) is one of the most promising ways to utilize the computational power of such devices to solve problems in condensed matter physics and quantum chemistry. As the size of the current quantum devices is still not large for rivaling classical computers at solving practical problems, Fujii et al. proposed a method called “Deep VQE”, which can provide the ground state of a given quantum system with the smaller number of qubits by combining the VQE and the technique of coarse graining [K. Fujii, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, arXiv:2007.10917]. In this paper, we extend the original proposal of Deep VQE to obtain the excited states and apply it to quantum chemistry calculation of a periodic material, which is one of the most impactful applications of the VQE. We first propose a modified scheme to construct quantum states for coarse graining in Deep VQE to obtain the excited states. We also present a method to avoid a problem of meaningless eigenvalues in the original Deep VQE without restricting variational quantum states. Finally, we classically simulate our modified Deep VQE for quantum chemistry calculation of a periodic hydrogen chain as a typical periodic material. Our method reproduces the ground-state energy and the first-excited-state energy with the errors up to O(1)% despite the decrease in the number of qubits required for the calculation by two or four compared with the naive VQE. Our result will serve as a beacon for tackling quantum chemistry problems with classically-intractable sizes by smaller quantum devices in the near future

Lactams. XXII. Preparation of the Enantiomers of 6-Ethoxy-3-ethyl-2,3,4,5-tetrahydro-4-pyridineacetic Acid Ethyl Ester

The resolution of (±)-trans-1-benzyl-5-ethyl-2-oxo-4-piperidineacetic acid [(±)-1] was effected with (R)-(+)-α-phenylethylamine through formation of the diastereomeric salts (+)-2 and (-)-3. Conversion of (+)-1 into the (3R, 4R)-(+)-enantiomer [(+)-6] of the title compound proceeded via a route involving debenzylation of (+)-1 with Na in liquid NH_3,esterification of the resulting (+)-4 to give (+)-5,and ethylation of (+)-5 with triethyloxonium fluoroborate. A parallel sequence of reactions starting from (-)-1 produced (-)-6 through (-)-4 and (-)-5

Verification of technical elements of the advanced spacecraft based upon the CCSDS recommendation

We are going to meet the era when advanced spacecraft such as space stations are developed and operated. The current system of the satellite operations control will need to undergo many changes. We consider that the future system will require the following functions: the function for interchanging data between international agencies, processing the various kinds of space data, and distributing data as many unspecified users require. However, we have to solve the following problems in order to satisfy these requirements: the problem of standardization of space data communication protocol, establishment of multimedia data management method, and standardization of the user interface. This paper describes three techniques to solve the above mentioned problems. That is, standardization of the data communication protocol between space and ground by AOS (Advanced Orbiting System) protocol of CCSDS (Consultative Committee for Space Data Systems) Recommendation, management of multimedia data by catalog reference, standardization of user interface by SFDU(Standard Formatted Data Unit) of CCSDS Recommendation

Dependence of alkyl-substituent length for bulk heterojunction solar cells utilizing 1,4,8,11,15,18,22,25-octaalkylphthalocyanine

Tetsuro Hori, Yasuo Miyake, Tetsuya Masuda, Takeshi Hayashi, Kaoru Fukumura, Hiroyuki Yoshida, Akihiko Fujii, Masanori Ozaki, and Yo Shimizu "Dependence of alkyl-substituent length for bulk heterojunction solar cells utilizing 1,4,8,11,15,18,22,25-octaalkylphthalocyanine," Journal of Photonics for Energy 2(1), 021004 (2 March 2012). DOI: https://doi.org/10.1117/1.JPE.2.02100

Quinolizidines. XVIII. Synthesis of (-)- and (+)-ankorines through a lactim ether route

A formal chiral synthesis of the Alangium alkaloid (-)-ankorine [(-)-6] has been accomplished in the form of the synthesis of the lactam phenol (+)-14 from the (+)-trans-lactim ether (+)-5 and 2-benzyloxy-3,4-dimethoxyphenacyl bromide through the intermediates (+)-10 and 11. A parallel sequence of conversions starting from the (-)-trans-lactim ether (-)-5 and proceeding through the intermediates (-)-10,24,(-)-14,(-)-15,26,(+)-27,and (+)-28 produced the enantiomer [(+)-6] of natural ankorine. For an alternative chial synthesis of (-)-6,ethyl cincholoiponate [(+)-19] was acetylated and the resulting N-acetyl derivative (+)-20-was oxidized with RuO_4 to give the 6-piperidone (+)-21,and 2-piperidone (-)-23 in 55% and 27% yields, respectively. The (-)-cis-lactim ether (-)-16,obtained by ethylation of (+)-21 with triethyl-oxonium fluoroborate, was then converted into (-)-13,a known precursor for the synthesis of (-)-ankorine [(-)-6], in good overall yield by a "lactim ether route, " which proceeded through (+)-15 and 12