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1.
Sci Rep ; 13(1): 16140, 2023 Sep 26.
Article in English | MEDLINE | ID: mdl-37752336

ABSTRACT

Coherent Ising machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al., proposed a quantum-classical hybrid system to solve optimisation problems of [Formula: see text]-regularisation-based compressed sensing. In the hybrid system, the CIM was an open-loop system without an amplitude control feedback loop. In this case, the hybrid system is enhanced by using a closed-loop CIM to achieve chaotic behaviour around the target amplitude, which would enable escaping from local minima in the energy landscape. Both artificial and magnetic resonance image data were used for the testing of our proposed closed-loop system. Compared with the open-loop system, the results of this study demonstrate an improved degree of accuracy and a wider range of effectiveness.

2.
Pharmaceutics ; 15(8)2023 Jul 29.
Article in English | MEDLINE | ID: mdl-37631255

ABSTRACT

We evaluated the pharmaceutical properties of levofloxacin (LV) in the form of an orally disintegrating tablet (LVODT) to find a new usefulness of low frequency (LF) Raman spectroscopy. LVODT contained dispersed granules with diameters in the order of several hundred micrometers, which were composed of the active pharmaceutical ingredient (API), as confirmed by infrared (IR) microspectroscopy. On the contrary, the API and inactive pharmaceutical ingredients (non-APIs) were homogeneously distributed in LV tablet (LVT) formulations. Microscopic IR spectroscopy and thermal analyses showed that LVODT and LVT contained the API in different crystalline forms or environment around the API each other. Furthermore, powder X-ray diffraction showed that LVT contained a hemihydrate of the API, while LVODT showed a partial transition to the monohydrate form. This result was confirmed by microscopic LF Raman spectroscopy. Moreover, this method confirmed the presence of thin layers coating the outer edges of the granules that contained the API. Spectra obtained from these thin layers indicated the presence of titanium dioxide, suggesting that the layers coexisted with a polymer that masks the bitterness of API. The microscopic LF Raman spectroscopy results in this study indicated new applications of this method in pharmaceutical science.

3.
Opt Lett ; 48(15): 3853-3856, 2023 Aug 01.
Article in English | MEDLINE | ID: mdl-37527066

ABSTRACT

Soliton mode locking in high-Q microcavities provides a way to integrate frequency comb systems. Among material platforms, AlGaAs has one of the largest optical nonlinearity coefficients, and is advantageous for low-pump-threshold comb generation. However, AlGaAs also has a very large thermo-optic effect that destabilizes soliton formation, and femtosecond soliton pulse generation has only been possible at cryogenic temperatures. Here, soliton generation in AlGaAs microresonators at room temperature is reported for the first time, to the best of our knowledge. The destabilizing thermo-optic effect is shown to instead provide stability in the high-repetition-rate soliton regime (corresponding to a large, normalized second-order dispersion parameter D2/κ). Single soliton and soliton crystal generation with sub-milliwatt optical pump power are demonstrated. The generality of this approach is verified in a high-Q silica microtoroid where manual tuning into the soliton regime is demonstrated. Besides the advantages of large optical nonlinearity, these AlGaAs devices are natural candidates for integration with semiconductor pump lasers. Furthermore, the approach should generalize to any high-Q resonator material platform.

4.
Chem Pharm Bull (Tokyo) ; 71(2): 165-174, 2023.
Article in English | MEDLINE | ID: mdl-36724979

ABSTRACT

In the present study, we conducted a detailed evaluation of the effects of humidification on the quality of five types of commercial magnesium oxide (MgO) tablet formulations. When near-IR spectroscopy was performed, a peak derived from the first overtone of the stretching vibration of the hydroxyl group was observed at approximately 7200 cm-1 in a humidified MgO tablet formulation. To visually evaluate the effect of this humidification, a mapping image was created using microscopic IR spectroscopy. In the IR spectrum, a peak derived from the stretching vibration of the hydroxyl group appears at approximately 3700 cm-1, so we created a mapping image using the absorbance ratio of 3700 and 3400 cm-1 as an index. In the mapping image of humidified MgO tablet formulations, many areas had a higher absorbance ratio than the dried tablet formulations. From these results, it is qualitatively confirmed that the MgO was changed to magnesium hydroxide (Mg(OH)2) by humidification. Although these results were observed in the four types of MgO tablet formulations, only one type of tablet formulation was less affected by humidification. In addition, although most tablet formulations tended to prolong disintegration time due to humidification, there was almost no effect of humidification on the disintegration time in one type of tablet formulation, which had little change in the above evaluation. Thus, in most commercial MgO tablet formulations, humidification prolongs the disintegration time, and Mg(OH)2 significantly contributes to this factor.


Subject(s)
Magnesium Oxide , Magnesium Oxide/chemistry , Hardness , Tablets/chemistry , Solubility
5.
Yakugaku Zasshi ; 142(4): 421-430, 2022 Apr 01.
Article in Japanese | MEDLINE | ID: mdl-35082193

ABSTRACT

Clobetasol propionate ointment (CLPO) formulations have been classified as members of the "strongest" steroidal efficacy group, with eight of these formulations currently marketed in Japan. Evaluations of pharmaceutical properties of each formulation revealed three classification types: droplet dispersion type containing propylene glycol (PG) and surfactant, type with surfactant but not PG, and other types. These rheological properties were diverse, with no correlation found between viscosity and ointment type. However, when CLPO and six types of heparinoid oil-based cream (HPOC) formulation mixtures were stored at 37℃, a liquid layer was observed starting at 24 h for one CLPO formulation in which polyoxyethylene hydrogenated castor oil 40 was used as a surfactant out of the four droplet-dispersion type ointments and two low-viscosity HPOC formulations. In contrast, one other type of CLPO formulation that contained a surfactant with polysorbate 80, but not PG, exhibited a liquid layer for all of HPOC formulations. This suggests that CLPO formulations that contain a surfactant with a high hydrophilic-lipophilic balance value are likely to generate a liquid layer for mixtures containing HPOC formulation. The present results demonstrate that not only the pharmaceutical properties of the eight CLPO formulations differ from one another, but also that the stabilities of HPOC formulation mixtures are significantly different. Therefore, pharmacists need to focus on inactive as well as active pharmaceutical ingredients to select formulations that patients will want to use, in addition to successfully treating their pathological conditions.


Subject(s)
Heparinoids , Clobetasol , Excipients , Humans , Japan , Ointments
6.
Entropy (Basel) ; 23(5)2021 May 17.
Article in English | MEDLINE | ID: mdl-34067765

ABSTRACT

We analytically and numerically show that the Hillery-Zubairy's entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.

7.
iScience ; 24(4): 102260, 2021 Apr 23.
Article in English | MEDLINE | ID: mdl-33796846

ABSTRACT

Gpr52 is an orphan G-protein-coupled receptor of unknown physiological function. We found that Gpr52-deficient (Gpr52 -/- ) mice exhibit leanness associated with reduced liver weight, decreased hepatic de novo lipogenesis, and enhanced insulin sensitivity. Treatment of the hepatoma cell line HepG2 cells with c11, the synthetic GPR52 agonist, increased fatty acid biosynthesis, and GPR52 knockdown (KD) abolished the lipogenic action of c11. In addition, c11 induced the expressions of lipogenic enzymes (SCD1 and ELOVL6), whereas these inductions were attenuated by GPR52-KD. In contrast, cholesterol biosynthesis was not increased by c11, but its basal level was significantly suppressed by GPR52-KD. High-fat diet (HFD)-induced increase in hepatic expression of Pparg2 and its targets (Scd1 and Elovl6) was absent in Gpr52 -/- mice with alleviated hepatosteatosis. Our present study showed that hepatic GPR52 promotes the biosynthesis of fatty acid and cholesterol in a ligand-dependent and a constitutive manner, respectively, and Gpr52 participates in HFD-induced fatty acid synthesis in liver.

8.
Chem Pharm Bull (Tokyo) ; 68(2): 155-160, 2020.
Article in English | MEDLINE | ID: mdl-32009083

ABSTRACT

Combination tablets containing multiple active pharmaceutical ingredients (APIs) are expected to improve patient convenience by decreasing the number of tablets to be taken; thus, numerous formulations containing multiple APIs have recently been developed. To allow for dose adjustments based on patient conditions, many tablets have a bisection line to allow equal division of tablets. However, there have been no investigations regarding content uniformity among divided combination tablets. Therefore, in this study, the content uniformity of combination tablets after division was investigated using near IR and low-frequency (LF) Raman spectroscopy imaging as well as the Japanese Pharmacopoeia (JP) content uniformity tests. As model drugs, five tablets of three combination drugs containing 3-(3,4-dihydroxyphenyl)-L-alanine (L-DOPA) and benserazide hydrochloride (BNS) as APIs for treating Parkinson's disease were bisected; the resultant 10 samples were subjected to the JP content uniformity tests. We found that acceptance values of L-DOPA and BNS were 11.0-21.9% and 13.3-17.5%, respectively, with some non-conformity to the maximum allowed acceptance value (15.0%) as per the current JP. Image analyses by near IR showed that L-DOPA, BNS, lactose, and corn starch were uniformly distributed in each tablet; moreover, LF Raman spectroscopy imaging also supported the result that L-DOPA, BNS, and lactose were evenly distributed. Therefore, drug content in the tablets was uniform; thus, careful manipulation was recommended in the tablet bisection. However, the results of bisection line specifications and hardness tests revealed that the ease of division differed depending on the tablets, which warrants attention.


Subject(s)
Antiparkinson Agents/analysis , Benserazide/analysis , Levodopa/analysis , Spectroscopy, Near-Infrared/methods , Spectrum Analysis, Raman/methods , Drug Combinations , Tablets
9.
Article in English | MEDLINE | ID: mdl-32015896

ABSTRACT

BACKGROUND: The clobetasol propionate cream formulations (CLB Cr ) belong to the "strongest" group, and are used widely. In addition, those formulations are often used as a mixture with moisturizer. Recently, we evaluated pharmaceutical properties of the CLB Cr using near infrared (NIR) spectroscopy, and characteristic NIR spectra depending on the formulation were observed. In the present study, we attempted to evaluate the more diverse pharmaceutical properties of CLB Cr , including the stability of mixture of CLB Cr and moisturizer. METHOD: Pharmaceutical properties of CLB Cr were evaluated using from rheological characteristics, microscopic observation, dye permeability observations, electrical conductivity method, thermogravimetry-differential thermal analysis (TG-DTA) and near infrared (NIR) spectroscopy. Stability of mixtures of CLB Cr and moisturizer were evaluated using from dye method and NIR spectroscopy. RESULTS: The hardness of Dermovate® (DRM), Glydil® (GDL), and Myalone® (MYA) was greater than that of CLB Cr . High concentrations of white beeswax were considered the reason for the hardness of DRM and GDL. On the other hand, the hardness of MYA may be due to the presence of macrogol 6000. After storage of the cream formulations discharged from the tube at room temperature, mass reduction and attenuation of the peak reflecting water of NIR spectroscopy occurred in a time-dependent manner, except for GDL and MYA. Only GDL was shown to be a w/o-type formulation by dye and electric conductivity measurements, which suggested that this was the reason for the lack of changes in the mass or NIR spectrum of samples after storage. In the NIR spectrum of MYA, the peak reflecting water slightly increased in a time-dependent manner, suggesting the water absorption of macrogol 6000. TG-DTA provided curves indicating the presence of water in each formulation, except for MYA, which was consistent with water quantification previously reported. Finally, when mixing the CLB Cr with a moisturizer, in any CLB Cr , the stability of the mixture with w/o-type moisturizer varies greatly depending on the each CLB Cr . CONCLUSION: Thus, even for cream formulations with the same active pharmaceutical ingredient, pharmaceutical properties and stability of mixture with moisturizer may different significantly.

10.
Biol Pharm Bull ; 42(12): 2102-2108, 2019.
Article in English | MEDLINE | ID: mdl-31787725

ABSTRACT

The poultice formulation is a patch containing a large amount of water. It is known that the water contained in the adhesive polymer layer (ADPL) of poultice affects the cooling sensation and skin permeability of the active pharmaceutical ingredient (API). In this study, we evaluated the relationship between the water content in a ketoprofen poultice formulation and the amount of time the poultice was left out at room temperature after removal from the airtight container, as well as the influence of the decreasing water content on the skin permeability of the API. After removing the poultice from the container for 1 h, the mass of the ADPL decreased by approximately 40%. When the near-infrared (NIR) spectrum of the ADPL of poultice was measured, the peaks reflecting the hydroxyl group were attenuated depending on the time left out at room temperature. It is suggested that the changes in the mass and NIR spectrum of the ADPL are caused by the change in the water content. Moreover, when the permeability of API was evaluated on hairless mouse skin, the cumulative skin permeation amount and flux decreased, while the lag time was prolonged as the time left out increased. These results suggest that the skin permeability of the API is impaired by water evaporation and that maintaining the water in the ADPL in poultice is very important from not only the viewpoint of cooling sensation, tackiness and moisturizing but also the skin permeability of the API.


Subject(s)
Anti-Inflammatory Agents, Non-Steroidal/administration & dosage , Anti-Inflammatory Agents, Non-Steroidal/chemistry , Ketoprofen/administration & dosage , Ketoprofen/chemistry , Skin/metabolism , Transdermal Patch , Water/analysis , Animals , Drug Stability , Drug Storage , In Vitro Techniques , Mice, Hairless , Permeability , Skin Absorption , Temperature
11.
Chem Pharm Bull (Tokyo) ; 67(9): 929-934, 2019.
Article in English | MEDLINE | ID: mdl-31474731

ABSTRACT

We investigated the water contents in commercial semi-solid preparations used for pressure ulcer (PU) treatment using near-IR spectroscopy (NIRS) and compared the results with those measured using the Karl Fischer (KF) method. The aim of this study was to determine a standard method and select the appropriate topical preparation with the optimal moisture for PU treatment. The water absorption properties of bases and formulations were evaluated with a time-dependent factor using Transwell as the model membrane. KF and NIRS were applicable as measurement methods of the water content in semi-solid formulations. NIRS was shown to be a useful, simple, nondestructive tool that is more advantageous than the KF method. The water absorption characteristics tested using Transwell revealed that the rate of and capacity for water absorption are determined not only by the absorption ability of the polymer base but also by other factors, such as the osmotic pressure exerted by additives. KF and NIR measurements can be used to choose external skin preparations to control the amount of water in PU treatment.


Subject(s)
Drug Compounding/methods , Water/chemistry , Administration, Topical , Glycerol/chemistry , Humans , Ointments/chemistry , Ointments/therapeutic use , Polyethylene Glycols/chemistry , Pressure Ulcer/drug therapy , Spectroscopy, Near-Infrared
12.
Appl Spectrosc ; 73(10): 1183-1192, 2019 Oct.
Article in English | MEDLINE | ID: mdl-31271295

ABSTRACT

We demonstrated the difference in the distribution state of pharmaceutical ingredients between tacrolimus (TCR) original ointment and six kinds of generic medicines. Two-dimensional imaging and depth analysis using attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy and confocal Raman microscopy were used, in addition to the evaluation of pharmaceutical properties, including spreading properties, rheological properties, and amount of solvent. The solvents, such as propylene carbonate and triacetin, in TCR ointments formed liquid droplets and dispersed in hydrocarbon oils. Waxes, white beeswax and beeswax, formed other domains. Confocal Raman microscopy could detect liquid droplet size without coalescence of that on germanium or glass surfaces. The combination of ATR FT-IR and confocal Raman imaging would be a powerful tool to reveal the size and shape of liquid droplets of pharmaceutical ingredients in semisolid formulations.


Subject(s)
Ointments/analysis , Spectroscopy, Fourier Transform Infrared/methods , Tacrolimus/analysis , Drug Compounding/methods , Microscopy, Confocal/methods , Rheology , Spectrum Analysis, Raman/methods
13.
Sci Adv ; 5(5): eaau0823, 2019 May.
Article in English | MEDLINE | ID: mdl-31139743

ABSTRACT

Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.

14.
Phys Rev Lett ; 122(4): 040607, 2019 Feb 01.
Article in English | MEDLINE | ID: mdl-30768355

ABSTRACT

The relaxation of binary spins to analog values has been the subject of much debate in the field of statistical physics, neural networks, and more recently quantum computing, notably because the benefits of using an analog state for finding lower energy spin configurations are usually offset by the negative impact of the improper mapping of the energy function that results from the relaxation. We show that it is possible to destabilize trapping sets of analog states that correspond to local minima of the binary spin Hamiltonian by extending the phase space to include error signals that correct amplitude inhomogeneity of the analog spin states and controlling the divergence of their velocity. Performance of the proposed analog spin system in finding lower energy states is competitive against state-of-the-art heuristics.

15.
Yakugaku Zasshi ; 139(2): 299-308, 2019.
Article in Japanese | MEDLINE | ID: mdl-30713242

ABSTRACT

To clarify the volume of water required to paste pediatric powders, we herein established a standard for the powder paste state by measuring yield values when water was added to powders. The powders used in the present study were selected from 8 types including original and generic drugs. Tipepidine hibenzate is prescribed in the pediatric field in combination with ambroxol hydrochloride and l-carbocysteine. The volumes of water needed to achieve the paste state of ambroxol hydrochloride between the original and generic drugs were similar. However, the volumes of water needed for l-carbocysteine markedly differed between the original and generic drugs due to differences in their additives. The spreadability of the mixture when water was added to the powders was evaluated using a spread meter. Among the powders tested in the present study, the yield value to achieve a paste state with the addition of water was approximately 1000 dyne/cm2. The optimum volume of water estimated from this yield value using the linear proportional relationship for the amount of powder may be applied to the mixture of each pediatric power for dosage/body weight.


Subject(s)
Drug Compounding/methods , Drug Compounding/standards , Drugs, Generic , Ointments , Powders , Water , Adjuvants, Pharmaceutic , Ambroxol , Carbocysteine , Ointments/standards , Piperidines , Powders/standards
16.
Biol Pharm Bull ; 41(9): 1348-1354, 2018.
Article in English | MEDLINE | ID: mdl-30175772

ABSTRACT

The molecular states of ketoprofen and the interaction between ketoprofen and other pharmaceutical excipients in the matrix layer were examined to determine their effect on the pharmaceutical properties of original and generic ketoprofen dermal patches (generic patches A and B). Molecular states of ketoprofen were evaluated using polarized light microscopy, Raman spectroscopy and powder X-ray diffraction. For the original ketoprofen patch, crystalline components were not observed in the matrix layer. However, crystalline ketoprofen was observed in the two generic ketoprofen patches. Moreover, the ketoprofen exhibited hydrogen bonding with the pharmaceutical excipients or patch materials in the generic products. Skin permeation of ketoprofen from the patches was evaluated using hairless mouse skin. Twelve hours after application, the original patch demonstrated the highest level of cumulative skin permeation of ketoprofen. This was followed by generic patch B while generic patch A showed the lowest level of permeation. Fluxes were calculated from the skin permeation profiles. The original patch was approx. 2.4-times faster compared with generic patch A and approximately 1.9-times faster compared with generic patch B. This investigation suggested that pharmaceutical properties such as skin permeability for these types of products are affected by the precipitation of crystalline ketoprofen in the matrix layer and the interaction of ketoprofen with the pharmaceutical excipients or patch materials.


Subject(s)
Anti-Inflammatory Agents, Non-Steroidal/administration & dosage , Ketoprofen/administration & dosage , Transdermal Patch , Animals , Anti-Inflammatory Agents, Non-Steroidal/chemistry , Anti-Inflammatory Agents, Non-Steroidal/pharmacokinetics , Drug Liberation , Ketoprofen/chemistry , Ketoprofen/pharmacokinetics , Male , Mice, Hairless , Skin/metabolism , Skin Absorption
17.
Eur J Pharm Sci ; 124: 199-207, 2018 Nov 01.
Article in English | MEDLINE | ID: mdl-30171983

ABSTRACT

Betamethasone butyrate propionate ointment (BBPO) is mainly used for adult patients in dermatology and is often prescribed as a mixture containing a base or moisturizing cream for various reasons. However, in the case of a moisturizing cream, since this formulation is composed of various ingredients, a physical change is expected to occur by mixing it with an ointment. Therefore, in the present study, the physical stability of a mixture of four BBPO formulations and heparinoid oily cream (HPOC) was examined. Layer separation was observed in all mixtures following centrifugation. The near-infrared (NIR) measurement showed a peak at 5200 cm-1 on the lower layer side, which strongly suggests the presence of water. The peak at 5200 cm-1 in the middle layer was hardly observed in the mixtures of two BBPO generic formulations and HPOC, thus suggesting that the separation was more advanced in those mixtures than in the others. These two mixtures separated into a semisolid layer (upper side) and a liquid layer (lower side) after 3 h of storage at 37 °C. The NIR measurement of each layer revealed that most of the semisolid layer was oil while the liquid layer was water. Furthermore, backscattered light measurements were conducted to monitor the behavior of the mixture's layer separation. An evaluation using model formulations revealed that the layer separation of the mixtures was due to the propylene glycol (PG) and surfactant content of the two generic BBPO formulations. Thus, these findings suggest that excipients need to be considered in selecting formulations for mixtures of skin preparations.


Subject(s)
Betamethasone/analogs & derivatives , Excipients/chemistry , Heparinoids/chemistry , Lipids/chemistry , Skin Cream/chemistry , Betamethasone/chemistry , Drug Stability , Ointments , Propylene Glycol/chemistry
18.
Chem Pharm Bull (Tokyo) ; 65(5): 487-491, 2017.
Article in English | MEDLINE | ID: mdl-28458370

ABSTRACT

A moisturizing cream mixed with a steroid ointment is frequently prescribed to patients suffering from atopic dermatitis. However, there is a concern that the mixing operation causes destabilization. The present study was performed to investigate the stability of such preparations closely using magnetic resonance imaging (MRI). As sample preparations, five commercial moisturizing creams that are popular in Japan were mixed with an ointment base, a white petrolatum, at a volume ratio of 1 : 1. The mixed preparations were stored at 60°C to accelerate the destabilization processes. Subsequently, the phase separations induced by the storage test were monitored using MRI. Using advanced MR technologies including spin-spin relaxation time (T2) mapping and MR spectroscopy, we successfully characterized the phase-separation behavior of the test samples. For most samples, phase separations developed by the bleeding of liquid oil components. From a sample consisting of an oil-in-water-type cream, Urepearl Cream 10%, a distinct phase-separation mode was observed, which was initiated by the aqueous component separating from the bottom part of the sample. The resultant phase separation was the most distinct among the test samples. To investigate the phase separation quantitatively and objectively, we conducted a histogram analysis on the acquired T2 maps. The water-in-oil type creams were found to be much more stable after mixing with ointment base than those of oil-in-water type creams. This finding strongly supported the validity of the mixing operation traditionally conducted in pharmacies.


Subject(s)
Magnetic Resonance Imaging , Ointment Bases/analysis , Skin Cream/analysis , Drug Stability , Humans
19.
Phys Rev E ; 95(2-1): 022118, 2017 Feb.
Article in English | MEDLINE | ID: mdl-28297856

ABSTRACT

The dynamics of driven-dissipative systems is shown to be well-fitted for achieving efficient combinatorial optimization. The proposed method can be applied to solve any combinatorial optimization problem that is equivalent to minimizing an Ising Hamiltonian. Moreover, the dynamics considered can be implemented using various physical systems as it is based on generic dynamics-the normal form of the supercritical pitchfork bifurcation. The computational principle of the proposed method relies on an hybrid analog-digital representation of the binary Ising spins by considering the gradient descent of a Lyapunov function that is the sum of an analog Ising Hamiltonian and archetypal single or double-well potentials. By gradually changing the shape of the latter potentials from a single to double well shape, it can be shown that the first nonzero steady states to become stable are associated with global minima of the Ising Hamiltonian, under the approximation that all analog spins have the same amplitude. In the more general case, the heterogeneity in amplitude between analog spins induces the stabilization of local minima, which reduces the quality of solutions to combinatorial optimization problems. However, we show that the heterogeneity in amplitude can be reduced by setting the parameters of the driving signal near a regime, called the dynamic phase transition, where the analog spins' DC components map more accurately the global minima of the Ising Hamiltonian which, in turn, increases the quality of solutions found. Last, we discuss the possibility of a physical implementation of the proposed method using networks of degenerate optical parametric oscillators.

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